Optimization method for lead steffensate synthesis based on response surface methodology and artificial neural network

Abstract

The application discloses a lead styphnate compound process optimization method based on a response surface method and an artificial neural network, belongs to the field of primers and pyrotechnics, and solves the problem that in the existing lead styphnate production line, compound process parameters are adjusted depending on artificial experience, leading to great product purity fluctuation, wide particle size distribution, poor flowability and insufficient batch consistency. The method comprises the following steps: determining key compound process parameters influencing the performance of lead styphnate based on collected lead styphnate compound process related data; and establishing a mathematical model for describing the relationship between the key compound process parameters, the interaction thereof and the performance index of lead styphnate. The method forms a stable and reliable performance influence rule by optimizing the lead styphnate compound process parameters, improves production efficiency, and solves the problem that the performance control mainly relies on artificial experience setting in the past.

Description

Technical Field

[0001] This invention relates to the field of energetic material chemical synthesis technology, specifically to the field of process optimization of detonators and pyrotechnic agents, and to a method for optimizing lead stemonate synthesis process based on response surface methodology and artificial neural networks. Background Technology

[0002] Lead styphnate (LS), as a high-performance single-element detonator, occupies an irreplaceable core position in semiconductor bridge (SCB) pyrotechnics and various weapon systems. Its quality stability directly determines the detonation reliability of pyrotechnics and the combat effectiveness of weapon systems. Existing research has confirmed that, based on the crystallization behavior characteristics of lead styphnate in different media, the crystal particle size can be precisely controlled by adjusting the chemical processing conditions, providing important theoretical support and technical foundation for optimizing its physicochemical properties.

[0003] In the actual industrial preparation process, lead stemonate still faces prominent problems such as large fluctuations in product purity, wide particle size distribution and poor particle flowability. These problems not only lead to uneven charge density and reduced detonation consistency in pyrotechnics, but may also cause safety hazards such as misfires and premature detonation, seriously threatening the safety of weapon systems and tactical reliability.

[0004] Therefore, identifying and balancing key parameters within a complex process parameter space has become one of the core methods for improving the physicochemical properties of lead stemonate. Numerous process parameters are involved in the chemical compounding process, and a comprehensive study of all parameters would consume a significant amount of manpower, material resources, and financial resources. Therefore, how to identify the key factors that significantly affect the target performance and analyze their influence patterns based on sample data is a pressing technical problem that needs to be solved in lead stemonate production. Summary of the Invention

[0005] The purpose of this invention is to circumvent existing experience-based production models and provide an optimized chemical process for lead stemonate, along with optimization methods and evaluation and testing methods for this process, to achieve standardized production of lead stemonate and improve product quality stability and ignition performance.

[0006] Technical solution At least one embodiment of the present invention provides a method for optimizing lead stemonate compounding processes based on response surface methodology and artificial neural networks, the method comprising the following steps: Based on the collected data on the lead stemonate compounding process, the key compounding process parameters affecting the performance of lead stemonate were determined. A mathematical model is established to describe the relationship between key chemical process parameters and their interactions and the performance index of lead stemonate. Based on the mathematical model, the predicted performance index of lead stemonate under different combinations of key chemical process parameters is calculated. From this, the performance index of lead stemonate that meets the preset requirements and the corresponding combination of key chemical process parameters are predicted, which serves as the preliminary optimization result dataset. Based on the preliminary optimization result dataset, an artificial neural network model was constructed to predict the lead stemonate performance index corresponding to different combinations of key chemical process parameters, and the optimal combination of key chemical process parameters and its corresponding lead stemonate performance index were selected.

[0007] In embodiments of the present invention, key chemical process parameters affecting the performance of lead stemonate are determined based on collected data related to the lead stemonate compounding process, including: Dimensionless processing was performed on different chemical process parameters; The Hassan method was used to normalize the scores of each indicator to obtain the overall normalized value (OD value). Based on the dimensionless processing results, the key chemical process parameters affecting the OD value of lead stemonate were screened using the single-factor experimental method. The optimal range of the key chemical process parameters was obtained, and the influence of the key chemical process parameters and their interactions on the OD value of lead stearate was analyzed in conjunction with Box-Behnken design.

[0008] Based on the mathematical model, the predicted OD values ​​of lead stearate performance index under different combinations of key chemical process parameters were calculated. The influence of different combinations of key chemical process parameters on the OD value of lead stemonate was analyzed by using 3D surface plots and contour plots. The lead stemonate that meets the preset requirements and its corresponding combination of key chemical process parameters were identified as preliminary optimization results.

[0009] In embodiments of the present invention, a mathematical model is established using regression analysis to describe the influence of key chemical process parameters and their interactions on the OD value of lead stemonate, including: A multiple quadratic regression equation model was established to describe the influence of key chemical process parameters and their interactions on the OD value of lead stemonate. The regression coefficients of the multivariate quadratic polynomial regression equation model are determined using the Quadratic Process Order. The established model was evaluated as a whole through analysis of variance, and the influence weights and patterns of the individual and interactive effects of each key chemical process parameter on the performance indicators of lead stemonate were further analyzed.

[0010] In embodiments of the present invention, the established model is evaluated as a whole through analysis of variance, and the influence weights and patterns of the individual and interactive effects of each key chemical process parameter on the performance indicators of lead stemonate are further analyzed, including: The performance metrics of the mathematical model are obtained through analysis of variance. The F-score of the model is calculated to evaluate the overall performance of the model; The p-value of the model was calculated to evaluate the effects of single-factor and multi-factor lead stearate performance; Calculate the coefficient of determination R of the model 2 Adjusted coefficient of determination and predictive determination coefficient To evaluate the predictive power of the model, and to analyze and optimize the conditions for lead stemonate performance.

[0011] In an embodiment of the present invention, the artificial neural network is an ANN model optimized to verify the reliability of the response surface model.

[0012] In an embodiment of the present invention, constructing an artificial neural network model includes: The number of hidden layer nodes is determined by hit-testing to optimize the error performance during network training and testing.

[0013] By adopting a 3-layer network architecture, including an input layer, an output layer, and a hidden layer with 2 nodes, the Levenberg-Marquardt algorithm is used for data training and testing. Through MSE and R 2 Analyze the performance of the model; The model can be intuitively analyzed through the fitting effect graph; The performance of the model can be intuitively analyzed using the mean square error distribution plot; The ANN model was trained using the BBD result key parameter dataset, and the RSM model and ANN model were validated using laboratory-level experiments.

[0014] Beneficial effects Compared with the prior art, the beneficial effects of the present invention are as follows: 1) This invention proposes an optimization method for the lead stemonate compounding process (especially a method combining response surface methodology (RSM) and artificial neural networks (ANN) to improve the production efficiency and product performance of lead stemonate. Through single-factor experiments, the influence of multiple process parameters (such as feed time, compounding temperature, and pH of sodium trinitroresorcinol solution) on the performance indicators of lead stemonate is analyzed, and a response surface model is constructed to help optimize the parameter combination. Furthermore, an artificial neural network (ANN) prediction model is used to improve the physicochemical properties of lead stemonate and reduce quality defects such as purity and flowability.

[0015] 2) This method, by combining machine learning algorithms with traditional process optimization, can not only improve the physicochemical properties of lead stemonate but also effectively reduce the defect rate in production. Through precise modeling and analysis of the interactions of multiple process parameters, key parameters in the production process can be optimized to ensure the quality and stability of lead stemonate. Attached Figure Description

[0016] Figure 1 This is a flowchart of the optimization method for lead stemonate compounding process based on response surface methodology and artificial neural networks used in embodiments of the present invention.

[0017] Figure 2 This is a schematic diagram of a three-layer feedforward neural network structure based on feed time, reaction temperature and pH of sodium trinitroresorcinol solution used in an embodiment of the present invention (3 nodes in the input layer, several nodes in the hidden layer, and 1 node in the output layer for predicting OD value).

[0018] Figure 3 This is a graph showing the effect of OD value changing with feeding time in an embodiment of the present invention.

[0019] Figure 4 This is a graph showing the effect of OD value on reaction temperature in an embodiment of the present invention.

[0020] Figure 5 The graph shows the effect of OD value on pH value of sodium trinitroresorcinol solution used in the embodiments of the present invention.

[0021] Figure 6 This is a schematic diagram of the prediction results analysis of the RSM model used in the embodiments of the present invention, and a comparison diagram of the model prediction values ​​and experimental values.

[0022] Figure 7 This is a schematic diagram of the prediction results analysis of the RSM model used in the embodiments of the present invention, and a residual analysis diagram of the estimated model.

[0023] Figure 8 This is a schematic diagram of the prediction results analysis of the RSM model used in the embodiments of the present invention, including an internal residual analysis diagram.

[0024] Figure 9 The following are the RSM multi-parameter 3D response surfaces and contour plots used in the embodiments of the present invention, wherein (a), (c) and (e) are three-dimensional surface plots of feed time-reaction temperature, feed time-pH value of sodium trinitroresorcinol solution, and reaction temperature-pH value of sodium trinitroresorcinol solution, respectively; (b), (d) and (f) are their corresponding contour plots.

[0025] Figure 10 This is a schematic diagram showing the optimal combination of chemical process parameters and corresponding OD values ​​in an embodiment of the present invention.

[0026] Figure 11 This is a graph showing the change in mean squared error (MSE) with the number of iterations during the training process of the neural network used in this embodiment of the invention.

[0027] Figure 12 Here is a scatter plot showing the fitted values ​​of the neural network output and target values ​​used in this embodiment of the invention: (a) Training set (R²=0.93310); (b) Validation set (R²=0.93310). 2 =0.99956); (c) Test set (R 2 =0.99325); (d) All data (R 2 =0.96103), the dashed line is the ideal fitting line of y=T.

[0028] Figure 13 This is a graph comparing the predicted OD value with the actual experimental value using the neural network model employed in this embodiment of the invention.

[0029] Figure 14 Radar graphs showing the physicochemical properties and OD values ​​of lead stearate produced using different processes in the comparative example of this invention.

[0030] Figure 15 This is a radar comparison chart showing the physicochemical properties and OD values ​​of lead stearate with different particle sizes used in the comparative example of this invention.

[0031] Figure 16 The following are comparative diagrams of the energy-carrying bridge before and after ignition, used as a comparative example in this invention: (a) Semiconductor bridge dipped in lead styrene; (b) Schematic diagram of SCB transducer structure; (c) Semiconductor bridge before ignition; (d) Semiconductor bridge after ignition.

[0032] Figure 17 This diagram illustrates the effect of different LS-loaded drugs on the ignition sensitivity of the semiconductor bridge pulse voltage in the comparative example of this invention.

[0033] Figure 18 This diagram illustrates the effect of different LS-loaded propellants on the constant current ignition sensitivity of the semiconductor bridge in the comparative example of this invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of the present invention to facilitate a better understanding of the invention. However, the technical solutions claimed in the present invention can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0035] Machine learning algorithms such as artificial neural networks can be used to effectively model the nonlinear coupling relationships between chemical parameters, thereby improving target performance. In view of this, this invention proposes a collaborative optimization strategy based on response surface methodology (RSM) and optimized artificial neural networks (ANN). This is an integrated strategy combining parameter selection, collaborative optimization, and intelligent modeling to improve the final performance of lead stemonate.

[0036] To address the technical problems mentioned in the background section, this invention employs a combination of response surface methodology (RSM) and artificial neural networks (ANNs) with experimental verification to study the influence of chemical process parameters on the performance of lead stemonate. To this end, a single-factor experimental method is used to determine the weights of each process parameter. The optimal ranges for key chemical process parameters are then obtained. Next, a Box-Behnken design (BBD) experimental model is used to study the influence trend of the interaction of key process parameters on the performance of lead stemonate. Finally, an artificial neural network (ANN)-based model is used to predict the performance of lead stemonate corresponding to different combinations of process parameters. The effectiveness of the RSM and ANN predictions is verified through laboratory-level experiments, and comparative analysis is conducted to select the optimal model and corresponding parameter combinations.

[0037] The implementation details of the above method are described in detail below through examples. The following content is only for the convenience of understanding the implementation details and is not necessary for implementing this solution.

[0038] Example 1 This embodiment provides a method for optimizing the lead stemonate compounding process, particularly a method based on response surface methodology (RSM) and artificial neural networks (ANN). This method uses RSM and ANN for comparative screening and analysis to find the optimal combination of compounding process parameters. It achieves bidirectional verification based on laboratory-level experimental research and model prediction, aiming to improve the overall physicochemical properties (purity, flowability, and particle size uniformity) of lead stemonate. It should be noted that although this embodiment uses a semiconductor bridge insensitive pyrotechnic product as an example, the technical solution of the present invention is not limited to this. The technical solution of the present invention is applicable to the optimization of lead stemonate preparation methods under any application requirements, including mixed products such as needle-punching or firing agents, electro-pyrotechnic products with thicker bridge wires, igniting agents of insensitive bridge-wire electro-pyrotechnic products and initial charge of flame detonators, semiconductor bridge insensitive pyrotechnic products, and electro-pyrotechnic products with thinner bridge wires and higher sensitivity. The physicochemical properties of lead stemonate are predicted and analyzed, including purity, angle of repose, and bulk density. The chemical process parameters include feeding time, reaction temperature, holding time, pH of sodium trinitroresorcinol solution, and pH of the base solution, etc., which are not limited.

[0039] To achieve the above objectives, the specific execution process of the technical solution adopted in this embodiment is as follows. Figure 1 As shown, this embodiment employs an optimization method for the semiconductor bridged drug lead stearate compounding process based on response surface methodology, artificial neural networks, and laboratory-level experimental verification and comparison. The main steps include: Step 1: Collect chemical process parameter data from multiple sources, including industrial production, published literature, and experimental records; Step 2: Use single-factor experimental methods to investigate the key parameters affecting the performance of lead stemonate; Step 3: A mathematical model was established using Box-Behnken design (BBD) based on response surface methodology to analyze the influence of the combination of chemical process parameters on the OD value of the overall performance of lead stemonate. Step 4: Analyze the BBD optimization results dataset, and based on the dataset, construct an artificial neural network model (ANN) to predict the overall performance OD value of lead stemonate corresponding to the combination of key process parameters; Step 5: Verify the prediction results of RSM and ANN models through laboratory-level experiments, and further optimize process parameters.

[0040] The following provides a detailed explanation of each step.

[0041] Step 1: Collect data from multiple sources, including historical production data, published literature, and experimental records.

[0042] In step 1, industrial production data typically includes records of various process parameters during production (such as temperature, feeding time, and holding time for each combination), as well as corresponding physicochemical property data (such as purity and flowability). This data is mainly obtained through the production workshop's data management system and quality inspection reports. Published literature on lead stemonate production explores the effects of different process parameters on physicochemical properties, particularly the effects of combination temperature, feeding time, and pH of sodium trinitroresorcinol solution. This data is primarily obtained through academic papers, technical reports, patents, and industry research. Experimental records come from experimental studies on lead stemonate combination 1, including experimental data under different process conditions (such as the combination temperature and duration of the experiment). This data is mainly obtained through laboratories or collaborative research teams, especially those with detailed records and data analysis. Finally, all data is collected, organized, and refined.

[0043] Data splitting: The data is divided into training set and test set. The training set is used for model training and parameter optimization, while the test set is used to evaluate the model's performance on unseen data. Typically, the data is split according to a certain ratio (e.g., 70% training set, 15% test set, 15% validation set) to further verify the model's generalization ability and improve the model's stability.

[0044] Step 2: Use single-factor experimental methods to investigate the key parameters affecting the overall performance of lead stemonate.

[0045] In step 2, based on the collected data, since different process parameters (feed time, reaction temperature, holding time, pH of sodium trinitroresorcinol solution, pH of bottom solution) have different dimensions, pretreatment is used to make the different process parameters dimensionless, and the key process parameters that can significantly affect the overall performance of lead stemonate (such as purity and particle size uniformity) are screened out.

[0046] The optimal range of key parameters was further confirmed based on the results of the single-factor experiments.

[0047] Further, in step 2, the lead content of the sample is determined by complexometric titration according to the method in "GJB737.12-2020 Test Methods for Pyrotechnic Agents: Determination of Lead Content in Initiating Explosives"; the ammonium acetate insoluble content of the sample is determined by gravimetric method according to the method in "WJ 617-2020 Standard for Lead Stefanate: Part 4.5.8: Content of Ammonium Acetate Insolubles"; the flowability of the sample is determined according to the method in "GJB5891.4-2006 Test Methods for Pyrotechnic Agents Part 4: Determination of Spread Type of Initiating Explosives by Angle of Repose"; and the bulk density of the sample is determined by graduated cylinder method according to the method in "GJB5891.2-2006 Test Methods for Pyrotechnic Agents Part 2: Determination of Bulk Density".

[0048] The particle size distribution of lead styrene was determined using a laser particle size analyzer, and the particle size distribution span was calculated. ): In the formula , , This represents the cumulative particle size distribution percentile parameter in laser particle size analysis. This indicates that 10% of the particles in the sample have a diameter smaller than this value, reflecting the distribution of fine particles; This indicates that 50% of the particles in the sample have a diameter smaller than this value, and it is the core indicator representing the average particle size. This indicates that 90% of the particles in the sample are smaller than this value, reflecting the distribution of coarse particles; calculations based on these three factors are performed. This is used to measure the breadth of the particle size distribution. The smaller the particle size, the more uniform the particle size distribution.

[0049] The relative standard deviation (RSD) of a single measurement is ≤5% to ensure data reliability.

[0050] Furthermore, the Hassan method was used to evaluate the physicochemical properties of lead stearate (purity: lead content, ammonium acetate insoluble content; flowability: angle of repose, bulk density) and... The values ​​are comprehensively scored to obtain the overall desirability (OD) score. To avoid the geometric mean OD value being zero in multiple places, a correction value δ (0.0002 is used to avoid the OD value being zero) is uniformly added to the numerator and denominator of each OD value calculation. The formula is as follows: For indicators where smaller values ​​are better: ; For indicators where a larger value is better: ; In the formula, y The numerical value of the indicator; i For the experiment number; This represents the original measurement value of a certain indicator in the i-th experiment / sample; y max The maximum value in the indicator. y min It is the minimum value in the indicator; This represents the normalized value of an indicator where smaller values ​​are better; the closer the value is to 1, the better the indicator performs. This represents the normalized value of an indicator where a larger value indicates better performance; the closer the value is to 1, the better the indicator performs.

[0051] In the formula, n For the number of indicators; d It is the normalized value.

[0052] Step 3: A mathematical model is established using Box-Behnken design (BBD) based on response surface methodology to analyze the influence of the combined interaction of chemical process parameters

[0104] on the overall performance OD value of lead stemonate. Specifically, Step 3 can be further subdivided into the following steps: Step 3.1: The Box-Behnken design (BBD) of the response surface methodology is used to generate the experimental matrix, handling combinations located at the midpoint of the experimental space edge. This avoids factor combinations under extreme conditions, and is symmetrical, rotatable, and efficient. This method is used to investigate the interaction effects of key chemical process parameters on the performance of lead stemonate. In step 3.1, a Box-Behnken design (BBD) generates a randomized experimental sequence, and the overall performance OD value is used as the response variable for analysis. Three key parameters need to be determined, with three levels (+1, 0, -1). A partial factorial design is used to identify the main effects and interactions between the factors. Axial point experiments are designed, with two extreme values ​​for each factor, to detect nonlinear effects. Intermediate value experiments are conducted among the factors to evaluate experimental error and ensure the reliability of the model.

[0053] Step 3.2: After data preprocessing, a multiple quadratic regression mathematical model is established, and ANOVA analysis and coefficient analysis are used to test the significance of the model; Furthermore, in step 3.2, the relationship between chemical process parameters and lead stemonate performance is described using response surface methodology. A mathematical model is established by using analysis of variance to build a polynomial regression equation (in this embodiment, a multiple quadratic regression equation). The general form of the response surface methodology model is as follows: in, This represents the response variable (OD value). ~i represents the model coefficients ( As the benchmark, i For linear terms, For square terms, i i (for interactive items) , , This indicates experimental factors (such as feed time, reaction temperature, and pH of sodium trinitroresorcinol solution). 2 Represents the squared terms of the factors. 1 2 indicates the interaction between factors. Analysis of variance is used to evaluate model performance, and the relationship between factors and response values ​​is reflected through response surfaces and contour plots. Ultimately, this achieves optimization and effective prediction of the chemical combination process.

[0054] In step 3.3, an analysis of variance (ANOVA) is performed to determine the significance of each parameter and the performance of the model; Furthermore, in step 3.3, the coefficients of each parameter and interaction term are obtained through regression analysis, and the predicted results of the comprehensive performance OD value of lead stemonate under different parameter combinations are calculated.

[0055] The model was tested for significance using ANOVA, and several metrics were used to evaluate the model's goodness of fit: R 2 As the coefficient of determination, the closer to 1 the better, if R 2 A value >0.9 indicates that the model can explain more than 90% of the parameter variation; The p-value is used to test whether the regression coefficient is significant. If p < 0.05, it indicates that the parameter has a significant impact on the result. For example, the p-value for combination temperature is 0.001, indicating that it has a great influence on the strength. Furthermore, in step 3.3, it is checked whether the residuals conform to a normal distribution. The distribution of normal residual probabilities is used to explain the difference between the model's predicted values ​​and the actual values, making the model's significance more reliable. 1) Use a variance distribution line plot; 2) Fit the model to the effect graph.

[0056] Step 3.4: Visually analyze the impact of key parameter combinations on the performance of lead stemonate using 3D surface plots and contour plots, and find the optimal parameter combination.

[0057] Furthermore, in step 3.4, after analyzing the significance of the fitted regression model, multiple response surface plots (3D surface plots or contour plots in this embodiment) are plotted to visually demonstrate the influence of different combinations of chemical process parameters on the performance parameters of the response variable, lead stearate (which can be multiple performance parameters, i.e., multiple objectives). For example, the interaction between feed time and reaction temperature, the interaction between feed time and pH of the sodium trinitroresorcinol solution, and the interaction between reaction temperature and pH of the sodium trinitroresorcinol solution on the OD value are used to find the optimal combination of process parameters for lead stearate performance.

[0058] Step 4: Analyze the BBD optimization results dataset, and construct an artificial neural network model (ANN) based on the dataset to predict the physicochemical properties of lead stemonate corresponding to the combination of key process parameters.

[0059] 1) The number of hidden layer nodes is determined by hit-testing to optimize the error performance during network training and testing. During model construction, the joint minimum of training and testing errors is used as a measure of network topology performance optimization, while the time step parameter is set to a minimum threshold to effectively prevent overfitting. 2) A three-layer network architecture is adopted, including an input layer, an output layer, and a hidden layer with two nodes; 3) Use the Levenberg-Marquardt algorithm for data training and testing.

[0060] Based on the establishment and improvement of the database, an artificial neural network model was established to optimize the production process of lead stemonate. The model uses data of different combinations of process parameters (such as feed time, reaction temperature and pH value of sodium trinitroresorcinol solution) and corresponding performance indicators of lead stemonate as input to the ANN, and uses these data as training data for the artificial neural network. Through MSE and R 2 To further evaluate the model's performance; The optimal prediction of the effect of different combinations of chemical process parameters on the OD value of lead stemonate performance index was determined, and the production process of lead stemonate was optimized. Step 5: Validate the RSM and ANN models through industrial-grade experiments.

[0061] Furthermore, the specific process of step 5 is as follows: 1) Comparison of ANN and RSM results 2) Analysis of laboratory-level experimental results For model prediction validation, it is necessary to train the model based on these optimized parameter combinations and then validate the model using experimental data, so as to more accurately optimize the lead stemonate production process.

[0062] It should be noted that if there is a discrepancy between the experimental test results and the predicted results, the test results will be used as the basis for correcting the entire design system. Through several rounds of prediction-experiment-feedback-prediction-experiment-feedback..., it is ensured that the selected optimal combination of process parameters can achieve the expected results in actual production, and further improve the quality and production efficiency of lead stemonate.

[0063] In summary, a novel method based on artificial neural networks and response surface methodology was adopted to optimize the chemical reaction process of lead stemonate loaded onto semiconductor bridges. This method establishes a high-precision model of the chemical reaction process parameters and performance, thereby improving the performance of semiconductor bridge products.

[0064] Example 2 The following detailed explanation uses specific examples, accompanied by data tables and graphs, but the specific examples are not limited to this: In this embodiment, a semiconductor bridged pharmaceutical lead stearate compounding process optimization method based on response surface methodology + machine learning + experimental verification analysis is presented. Five main compounding process parameters (feed time, reaction temperature, compounding time, cooling rate, and pH value of sodium trinitroresorcinol solution) were selected, and three key parameters were screened to study their impact on the overall performance OD value. The method includes the following steps: Step 1: Collect chemical process parameter data from multiple sources, including industrial production, published literature, and experimental records.

[0065] In the optimization of lead stemonate (LST) compounding processes, data collection and analysis are crucial. First, industrial production data provides the most direct foundation, including records of various process parameters used in production, such as feed rate and compounding temperature, as well as performance indicators of LST under these parameters, such as angle of repose and bulk density. Second, published literature offers valuable references. Many studies have explored the impact of different process parameters (e.g., compounding temperature, feed rate) on LST quality, providing theoretical support on how to adjust these parameters and identifying which factors are most important for optimizing LST performance. Finally, experimental records are an indispensable data source in the optimization process. These records include data from LST production experiments conducted under different process conditions, recording the feed rate, compounding temperature parameters used in each experiment, and the performance of LST under these conditions. These actual data provide real production feedback, verify the accuracy of the prediction model, and provide a strong basis for adjusting process parameters, helping to successfully establish a chemical process database. In this embodiment, after preliminary screening, five main chemical process parameters (A: feed time, B: reaction temperature, C: chemical reaction time, D: cooling rate, and E: pH value of sodium trinitroresorcinol solution) were selected to study the influence of chemical process parameters on the comprehensive performance OD value and collect data.

[0066] Step 2: Use single-factor experiments to investigate the key parameters affecting the performance of lead stemonate, see... Figure 3 , Figure 4 , Figure 5 .

[0067] Step 3: A Box-Behnken design (BBD) based on response surface methodology was used to establish a mathematical model to analyze the influence of the combined interactions of chemical process parameters on the overall performance (OD) value of lead stemonate. Based on three key chemical process parameters selected using a single-factor experimental method, response surface modeling was performed to establish a multiple second-order regression equation for the three process parameters: feed time, reaction temperature, and pH value of the sodium trinitroresorcinol solution. This equation was then used to predict the performance indicators of lead stemonate. The second-order regression equation can capture the linear relationship between process parameters and their possible quadratic effects, thus providing a reliable mathematical model for predicting the overall performance (OD) value of lead stemonate.

[0068] Table 1. Results of the influence of process parameters on OD value Table 2 Box-Behnken Design Factors and Levels To ensure the effectiveness of the model, analysis of variance (ANOVA) was used to check its adequacy, assess its fit to the data, and evaluate the significance of each process parameter. ANOVA was used to determine which process parameters significantly impacted lead stemonate quality, which interaction effects required close attention, and the model's explanatory and predictive power.

[0069] Based on response surface methodology and analysis of variance, the chemical process parameters were optimized to find the optimal combination of process parameters. In the experiment, actual production was carried out according to the optimized parameter combination, and the comprehensive performance OD value of lead stemonate was compared to verify the accuracy of the model prediction and the optimization effect.

[0070] Table 3 Box-Behnken Design Results Furthermore, in step 3.1, the Box-Behnken design (BBD) for generating the experimental matrix is ​​specifically implemented as follows: In this embodiment, the effects of the interaction of three parameters—feed time, reaction temperature, and pH of the sodium trinitroresorcinol solution—on the overall performance OD value were investigated using experimental design. Feed time ranged from 6 min to 10 min, reaction temperature from 65℃ to 75℃, and the pH of the sodium trinitroresorcinol solution from 4.25 to 4.75. Table 2 shows the design scheme and results of 17 randomized experiments involving the three factors, including 12 experimental points with different factor combinations and 5 center points used to assess experimental error. This unequal random distribution effectively represents the factor space by eliminating unnecessary experimental points, thus ensuring the rationality of the design. The strategy of varying the number of experiments in the design maintained statistical accuracy, captured the curvature of the response, and reduced experimental costs.

[0071] Furthermore, in step 3.2, the specific implementation of establishing the multiple quadratic regression equation is as follows: See formula (1). The Box-Behnken design (BBD) establishes a mathematical model and quickly and effectively identifies the optimal combination of process parameters corresponding to the expected results through the interaction of different variables.

[0072] Y(OD) = 0.6885 - 0.0081 X1+0.0105 X2-0.0813 X3 +0.0781 X1X2-0.0014 X1X3-0.0044 X2X3-0.1128 X1 2 -0.2277 X2 2 -0.1376 X3 2 (1) Where Y represents the OD value, X1 represents the feed time, X2 represents the reaction temperature, and X3 represents the pH value of the sodium trinitroresorcinol solution. X1X2, X1X3, and X2X3 represent the interaction of chemical process parameters, X1 2 X2 2 and X3 2 These represent the secondary effects of each factor. The plus and minus signs indicate the synergistic and antagonistic effects of the parameters on the response, respectively.

[0073] Furthermore, based on steps 3.1 and 3.2, step 3.3 yields the specific process of the analysis of variance: The analysis of variance for BBD is shown in Table 3. The F-value is used to assess the significance of each factor and the model as a whole on the response variable, while the p-value reflects the significance level. Generally, a p-value less than 0.05 indicates statistical significance. As can be seen from the table, the F-value of this model is 559.69, and the p-value is much less than 0.0001, indicating that the model fits the experimental data well in the equation and has strong overall significance. The coefficient of determination (R²) of the model... 2 The coefficient of determination (COP) is 0.9986, indicating that 98.05% of the experimental data fluctuations can be explained by the written model given by the equation, demonstrating high fitting accuracy. The adjusted COP is... The coefficient of determination (CCD) is 0.9968, indicating that the model maintains high stability in explaining the variation in OD values. The value is 0.9903, and and The difference between the values ​​is less than 2%, further indicating that the model has good predictive ability and can be used to analyze and optimize the processing conditions for OD values.

[0074] Table 4. Results of ANOVA for the Regression Model of OD Values Furthermore, in step 3.3, such as Figure 6 , 7 As shown in Figure 8, a visual analysis of the fitting plot demonstrates the reliability of the established model. (See Figure 8) Figure 6 Comparison of predicted and actual values Figure 7 Residual analysis of the estimation model and Figure 8 Internal residual analysis).

[0075] Furthermore, in step 3.4, 3D surface plots and contour plots are used to visually analyze the impact of different parameter combinations on the overall performance OD value: By fitting a regression model and analyzing its significance, multiple response surface plots (3D surface plots or contour plots in this example) are generated to visually demonstrate the impact of different combinations of chemical process parameters on the overall performance OD value of the response variable. For example, the effects of feed time – reaction temperature, feed time – pH value of sodium trinitroresorcinol solution, and reaction temperature – pH value of sodium trinitroresorcinol solution on the overall performance OD value of lead stearate, etc. (the feed solution is sodium trinitroresorcinol solution). The response surface plots are used to find the optimal combination of process parameters that optimizes the performance of lead stearate.

[0076] like Figure 9 As shown, the RSM multi-parameter 3D response surface and contour plots are as follows: (a), (c) and (e) are the three-dimensional surface plots of feed time-reaction temperature, feed time-pH value of sodium trinitroresorcinol solution, and reaction temperature-pH value of sodium trinitroresorcinol solution, respectively; (b), (d) and (f) are their corresponding contour plots.

[0077] like Figure 10 As shown, the optimal chemical process parameters predicted by RSM analysis are: feeding time of 8.05 min, reaction temperature of 69.96℃, and pH of sodium trinitroresorcinol solution of 4.45. After laboratory-level experimental verification, the corresponding OD value was found to be 0.6990.

[0078] Step 4: Based on the BBD optimization results dataset, construct an artificial neural network model (ANN) to predict the lead stemonate OD value corresponding to the combination of key process parameters; Based on the BBD dataset and with appropriate data expansion, a neural network was used to optimize the chemical process of lead stemonate. In this process, different combinations of process parameters (such as reaction temperature, feed time, and pH of the sodium trinitroresorcinol solution) and corresponding comprehensive performance indicators of lead stemonate (such as OD value) were used as input and output data. By establishing an artificial neural network model, this data was used to train the model, helping it learn the complex nonlinear relationship between process parameters and lead stemonate performance, thereby enabling performance prediction for different future combinations of process parameters.

[0079] Furthermore, the error performance during the testing phase was examined. During model construction, the joint minimum of the training error and the testing error was used as a measure of network topology performance optimization. Simultaneously, the time step parameter was set to a minimum threshold to effectively prevent overfitting. The experiment employed a three-layer network architecture, including an input layer, an output layer, and a hidden layer with two nodes. The Levenberg-Marquardt algorithm was used for data training and testing. Seventeen sets of experimental data were randomly divided into a 70% training set, a 15% validation set, and a 15% test set, with a learning rate of 0.001 and a maximum of 9 iterations for model validation.

[0080] The Levenberg-Marquardt algorithm used for network training yielded the best validation results for the dependent variable OD value. Figure 11 The mean-squared error (MSE) of the OD values ​​decreased rapidly at the beginning, reaching its optimal validation effect in stage 3 when the OD values ​​showed the MSE (MSE was 8.6162 × 10⁻⁶). -4 R 2 =0.9610 reflects the reliability of the model. The closer this value is to 1, the better the model. The regression coefficient (r) used for training, testing, validation, and the overall model should all be ≥0.9. Figure 12 This indicates that the model has good predictive ability for OD values. The established ANN model was used to predict 17 sets of response surface data, and the predicted values ​​were compared with the measured values. Figure 13As shown in the figure, the optimal value predicted by ANN is similar to the optimal value obtained from the experiment, proving that the response surface model and the ANN model are equally stable and reliable, and the optimal process is similar.

[0081] It should be noted that the dataset used to construct the ANN model in this study originated from 17 experimental points designed by Box-Behnken, which is a relatively small sample size for traditional ANN applications. However, judging from the model validation results ( Figure 13 The R-values ​​for the training, validation, and test sets are all greater than 0.9, and the model's predictions are in high agreement with the measured values. Figure 12 This indicates that within the parameter space pre-optimized by response surface methodology within the constraints of this study, the constructed ANN model effectively captures the nonlinear relationship between each factor and the overall score, without exhibiting significant overfitting. This suggests that combining ANN as an advanced validation tool with classic experimental design methods such as RSM has significant application value and reference value, even in research on the optimization of traditional Chinese medicine processes with limited sample sizes.

[0082] Furthermore, in step 5, the specific process of verifying the prediction results of the RSM and ANN models through laboratory-level experiments and further optimizing the process parameters is as follows: Artificial neural networks (ANNs) are then used for further optimization, prediction, and selection. This process begins with training the model based on optimized parameter combinations, followed by model validation using experimental data. The artificial neural network can accurately predict the quality and performance of lead stemonate under different combinations of process parameters, thus enabling more precise optimization of the lead stemonate production process.

[0083] If the experimental test results deviate from the predicted results, the entire design system will be corrected based on the test results. This process of prediction-experiment-feedback-prediction-experiment-feedback continues until the selected optimal combination of process parameters achieves the expected results in actual production, further improving the quality and production efficiency of lead stemonate.

[0084] Furthermore, in step 5.1, the specific process of comparing the results of ANN and RSM is as follows: Both RSM and ANN have shown strong application potential in modeling process variables for process optimization. However, the statistical error of the model can affect its generalization ability, and thus its prediction accuracy. This study evaluates the performance of the two models, mainly using MSE, RMSE, MAE, and RSM. 2As shown in Table 4, the ANN model exhibits lower error and higher fitting accuracy compared to RSM. The comparison between actual and predicted values ​​is shown in the following figure. The figure clearly shows that both models demonstrate good fitting performance, but ANN is more accurate. ANN effectively handles complex nonlinear relationships between process parameters, indicating that compared to the quadratic multiple regression equation of RSM, the neural network model has stronger expressive power, wider applicability, and higher fitting accuracy. However, the optimization capability of ANN relies on sufficient data samples, which is one of the limitations of neural network models. Therefore, combining RSM with auxiliary analysis can be used to initially screen key parameters and quickly verify the impact of parameter combinations on the overall performance OD value. Combining this with ANN for accurate prediction helps to significantly improve the efficiency of process parameter optimization.

[0085] Table 5. Comparison of prediction performance between RSM and ANN models Furthermore, in step 5.2, the specific process of analyzing laboratory-level experimental results is as follows: To verify the prediction accuracy of the two constructed models, this study adjusted the chemical process parameters and designed and implemented a laboratory-scale verification experiment. The specific methods are as follows: 20 g of styrene raw material was used in production, and three batches of lead styrene were randomly selected from this batch of finished products as test samples (batch numbers labeled (a)-(c)). These three batches of samples were then subjected to rigorous physicochemical property testing. The results are shown in Table 12, and the corresponding OD values ​​are summarized in Table 5. The test results show that the OD values ​​of all samples are between 0.68 and 0.72, and the average OD value of the three batches is 0.7015, which is basically consistent with the predicted value (0.7010) of the established ANN model. In particular, the measured OD values ​​of samples (a) and (c) are almost identical to the predicted values, fully verifying the reliability of the constructed ANN optimization model.

[0086] Table 6. Physicochemical properties and OD values Table 7. Comparison of Model Predictions and Experiments Comparative Example 1 This comparative example provides the overall performance OD value test results for different lead stemonates.

[0087] The comparison results of the physicochemical properties and OD values ​​of lead stemonate samples #1 to #4 are as follows: Figure 14As shown in the figure. Sample #1 was prepared using an optimized process based on the OD value model, while samples #2 to #4 were prepared using conventional processes. The particle size D50 of the four samples was similar, at 62.4 μm, 59.1 μm, 60.5 μm, and 63.0 μm respectively. The particle size D50 of lead stearate samples #5 and #6 were 10.0 μm and 110.0 μm, respectively. The comparison results of their physicochemical properties, particle size distribution (Span), and OD values ​​are shown in the figure. Figure 15 As shown.

[0088] Two six-dimensional radar images, using OD value, lead content, ammonium acetate insoluble content, angle of repose, bulk density, and particle size distribution span as characterization indicators, systematically present the comprehensive physicochemical properties of the lead stearate sample. Figure 14 The analysis focused on the impact of the processing technology on the performance of lead stemonate samples. Samples #1 to #4 had similar particle sizes. Sample #1, prepared using an OD value model-optimized process, exhibited a synergistic and balanced performance across all indicators. Its lead content was relatively high, while the ammonium acetate insoluble content and particle size distribution span remained low. The angle of repose and bulk density were within the reasonable range for industrial applications. Samples #2 to #4, prepared using conventional processes, exhibited significant deficiencies in individual indicators. Sample #2 had a high angle of repose and poor particle flowability; Sample #3 had a wider particle size distribution span and insufficient particle uniformity; and Sample #4 had low lead content but high ammonium acetate insoluble content, resulting in lower product purity.

[0089] Depend on Figure 15 It can be seen that particle size has a significant impact on sample performance. Samples #1, #5, and #6 have similar purity but significant differences in particle size. Sample #5, with a particle size of 10.0 μm, has the advantages of both high purity and good flowability (high packing density and low angle of repose), while sample #6, with a particle size of 110.0 μm, has a wide particle size distribution and poor flowability, thus weakening the overall performance OD value of lead stearate.

[0090] Comparative Example 2 This comparative example provides ignition characteristics results for semiconductor bridges coated with different lead styrene.

[0091] To test the ignition sensitivity of the active bridge, SCB was dipped in lead stearate, with 4% nitrocellulose as the binder (solvent: ethyl acetate) in a 1:1 mass ratio. Each dipped amount was approximately 10 mg. After drying in a water bath oven without power for about 12 hours, ignition sensitivity experiments were conducted to test the pulsed and constant-current ignition sensitivity of the active bridge. To investigate the effect of optimized lead stearate preparation on the ignition performance of the semiconductor bridge, an ignition experimental setup was constructed. Figure 16The results show the state of the core components used in the experiment: (a) is a physical image of the energetic bridge, (b) is a schematic diagram of the SCB structure, and (c) and (d) respectively show the morphological characteristics of the energetic bridge before and after ignition, clearly demonstrating the adhesion state of lead stemonate to the semiconductor bridge, as well as the structural changes of the SCB after ignition.

[0092] Furthermore, to ensure consistency in charge amount and charge density, each energetic bridge was prepared by pipetting a lead stearate-nitrocellulose mixture and uniformly dripping it onto the functional layer. Energetic bridge experiments I-VI correspond to lead stearate samples #1-#6 mentioned above, respectively.

[0093] Furthermore, the results of the safety current test were as follows: The semiconductor bridges dipped with lead stearate No. 1 to No. 6 were subjected to a safety current test. Ten samples were tested in each group. A constant current of 1A and a power of 1W were applied for 5 minutes. None of the samples sparked, which meets the requirements of GJB5309.10-2004.

[0094] Furthermore, using the D-optimization method, the sensitivity of a 1 Ω semiconductor bridge dipped in lead styrene at room temperature (25℃) was tested for constant current ignition and pulse voltage ignition. The experimental comparison results are as follows: Figure 17 , 18 As shown. The pulse ignition sensitivity experiment used a storage discharge device with a discharge capacitor of 47 μF. The instrument resolution was 0.1 V, the lower stimulus limit was 0 V, the upper stimulus limit was 15 V, and the standard deviation estimate σ was... guess The value was 0.2. The constant current ignition sensitivity experiment used a constant current ignition tester with a resolution of 1 mA. The lower limit of stimulation was 0 mA, and the upper limit of stimulation was 4000 mA. The estimated standard deviation σ was... guess It is 20.

[0095] Furthermore, the ignition sensitivity test results show that: Experiment V has a 50% ignition voltage of 7.05 V, the lowest among all propellant loads, corresponding to the highest sensitivity; Experiment IV has a 50% ignition voltage of 10.39 V, the highest among all propellant loads, corresponding to the lowest ignition sensitivity; meanwhile, Experiment III exhibits the largest dispersion in voltage ignition response, with a standard deviation of 0.50, while Experiment V has a standard deviation of only 0.30. The current ignition test results show that Experiments I and V have 50% ignition currents of 2580.33 mA and 2572.06 mA, respectively, which are at a relatively low level, corresponding to higher sensitivity; Experiment IV has a 50% ignition current of 2889.20 mA, the highest among all propellant loads, corresponding to the lowest sensitivity; Experiment II exhibits a more pronounced dispersion in current ignition response, with a standard deviation of 8.44, while Experiment IV has a standard deviation of 6.32.

[0096] The differences in ignition sensitivity of the aforementioned energetic bridges are due to the fact that the purity of lead styrene determines the stability of its thermal decomposition reaction, its flowability relates to the uniformity of its charge in the bridge region, and its particle size distribution enhances the synchronicity of the particle reaction. These three factors work synergistically to determine the ignition sensitivity of the semiconductor bridge. Verification results of the ignition sensitivity of energetic bridges I, V, and VI with different particle sizes (D50) show that particle size has a significant impact on the ignition sensitivity of SCBs. As D50 increases, the semiconductor bridge coated with lead styrene requires a higher 50% ignition voltage and 50% ignition current. However, the difference in 50% ignition voltage and 50% ignition current between semiconductor bridge I and semiconductor bridge V (which is only 10.0 μm) is less than 1 V and 20 mA, respectively. Therefore, it can be considered that semiconductor bridges coated with lead styrene using an OD value model-optimized process have good ignition sensitivity.

Claims

1. A method for optimizing lead stemonate compounding process based on response surface methodology and artificial neural networks, characterized in that, Includes the following steps: S1. Collect data on the lead stemonate compounding process to determine the key compounding process parameters that affect the performance of lead stemonate. S2. Establish a mathematical model to describe the relationship between key chemical process parameters and their interactions and the performance index of lead stemonate, and calculate the prediction results of lead stemonate performance index under different combinations of key chemical process parameters based on the mathematical model. From this, predict the lead stemonate performance index that meets the preset requirements and the corresponding key chemical process parameter combinations, as a preliminary optimization result dataset. S3. Based on the preliminary optimization result dataset, construct an artificial neural network model to predict the lead stemonate performance index corresponding to different combinations of key chemical process parameters, and select the optimal combination of key chemical process parameters and the corresponding lead stemonate performance index.

2. The method for optimizing lead stemonate compounding process based on response surface methodology and artificial neural networks according to claim 1, characterized in that, Step S1 includes: The Hassan method was introduced to normalize the scores of each performance index, and the total score normalized value, i.e., the OD value, was obtained. Key chemical process parameters affecting the OD value of lead stemonate were screened using a single-factor experimental method. The optimal range of the key chemical process parameters was obtained, and the influence of the key chemical process parameters and their interactions on the OD value of lead stearate was analyzed in conjunction with Box-Behnken design.

3. The method for optimizing lead stemonate compounding process based on response surface methodology and artificial neural networks according to claim 2, characterized in that, The key chemical process parameters affecting the OD value of lead stemonate were screened through single-factor experimental analysis, including: intuitively analyzing the ranking of the influencing factors on the OD value of lead stemonate based on the experimental results graph; and determining the key chemical process parameters.

4. The method for optimizing lead stemonate compounding process based on response surface methodology and artificial neural networks according to claim 3, characterized in that, Step S2 includes: The Box-Behnken design based on response surface methodology was used to generate an experimental matrix, which was then used to investigate the interaction between key chemical process parameters and the OD value of lead stemonate. A mathematical model was established using regression analysis to describe the influence of key chemical process parameters and their interactions on the OD value of lead stemonate performance, and the key chemical process parameters of the mathematical model were evaluated using analysis of variance. Based on the mathematical model, the predicted OD values ​​of lead stearate performance index under different combinations of key chemical process parameters were calculated. The influence of different combinations of key chemical process parameters on the OD value of lead stemonate was analyzed by using 3D surface plots and contour plots. The lead stemonate that meets the preset requirements and its corresponding combination of key chemical process parameters were identified as preliminary optimization results.

5. The method for optimizing lead stemonate compounding process based on response surface methodology and artificial neural networks according to claim 4, characterized in that, A mathematical model was established using regression analysis to describe the influence of key chemical process parameters and their interactions on the OD value of lead stemonate, including: A multiple quadratic regression equation model was established to describe the influence of key chemical process parameters and their interactions on the OD value of lead stemonate. The regression coefficients of the multivariate quadratic polynomial regression equation model were determined using the Quadratic fitting method. The established model was evaluated as a whole through analysis of variance, and the influence weights and patterns of each key chemical process parameter individually and in interaction on the performance indicators of lead stemonate were further analyzed.

6. The method for optimizing lead stemonate compounding process based on response surface methodology and artificial neural networks according to claim 5, characterized in that, Analysis of variance was used to evaluate the established model as a whole, and the influence weights and patterns of the individual and interactive effects of each key chemical process parameter on the OD value of lead stemonate were further analyzed, including: The performance metrics of the mathematical model are obtained through analysis of variance. The F-value of the model is calculated to evaluate the overall performance of the model; The p-value of the model was calculated to evaluate the effects of single-factor and multi-factor lead stearate performance; the coefficient of determination R of the model was calculated. 2 Adjusted coefficient of determination and predictive determination coefficient To evaluate the predictive power of the model, and to analyze and optimize the conditions for lead stemonate performance.

7. The method for optimizing lead stemonate compounding process based on response surface methodology and artificial neural networks according to claim 6, characterized in that, Constructing artificial neural network models includes: The number of hidden layer nodes is determined by hit test method in order to optimize the error performance of the network during training and testing phases; By employing a 3-layer feedforward neural network with 3 nodes in the input layer corresponding to 3 key process parameters, the number of hidden layer nodes was determined by hit-testing, and the Levenberg-Marquardt algorithm was used for data training and testing. Through MSE and R 2 Analyze the performance of the model; The model can be intuitively analyzed through the fitting effect graph; The performance of the model can be intuitively analyzed using the mean square error distribution plot; The ANN model was trained using the BBD result key parameter dataset, and the RSM model and ANN model were validated using laboratory-level experiments.

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