Material generalized reaction modeling method based on multi-cycle optimization

Abstract

The invention discloses a material generalized reaction modeling method based on multi-cycle optimization, which performs optimization analysis on thermal reaction characteristics of a material by establishing an inner cycle and an outer cycle, and quickly establishes a generalized reaction model of the material. The internal circulation is realized through a semi-theoretical empirical formula and an intelligent optimization algorithm, and reaction parameter optimization is realized; and performing error analysis based on goodness-of-fit in outer circulation, and optimizing and adjusting a reaction path. And internal and external circulation is automatically realized through algorithm programming, so that the modeling precision and the calculation efficiency can be effectively improved, and model support is provided for material reaction characteristic research and material reaction simulation.

Description

Technical Field

[0001] The present invention relates to a generalized reaction modeling method for materials based on multi-cycle optimization, belonging to the technical field of materials science and chemical reaction analysis. Background Art

[0002] PMMA materials are widely used in the structural design of aircraft and spacecraft. However, research shows that they are extremely prone to decomposition under heating conditions, releasing a large amount of combustible gases, which can then trigger combustion or even fire accidents, causing serious damage. Therefore, in-depth understanding and mastery of the thermal reaction characteristics of this material, establishing a high-precision generalized reaction model, and realizing the prediction of its thermal stability and reaction have become the key technical requirements for the safety and fire prevention design of aircraft and spacecraft.

[0003] In order to accurately predict the reaction characteristics of materials under various conditions, some studies analyze the Arrhenius formula based on factors such as temperature and reaction rate, fit the simplified theoretical model or single experimental data, and then propose semi-empirical and semi-theoretical formulas, mainly including the FWO method, Kissinger method, CR method, etc. Although these methods have a fast calculation speed, due to only using the parameters of individual characteristic points of the reaction and not considering the influence of the actual reaction order / the number of reaction paths n, the error is relatively large.

[0004] To further improve the model accuracy, some scholars have proposed to introduce intelligent algorithms (such as genetic algorithms, particle swarm optimization) or machine learning (such as deep neural networks) on the basis of traditional methods to adjust and optimize the reaction parameters. These methods have improved the model accuracy to a certain extent, but they are highly dependent on the setting of the initial value, are prone to falling into local optima, and still may have relatively large errors due to not fully considering the chain changes and the influence of reaction paths in the real reaction process, and cannot reflect the characteristics of the real pyrolysis behavior.

[0005] In summary, there is an urgent need to develop a new generalized reaction modeling method for materials that can improve the model accuracy and modeling efficiency and provide a model basis for fire safety analysis. Summary of the Invention

[0006] In view of the above problems, the application discloses a generalized reaction modeling method for materials based on multi-cycle optimization, which establishes two sets of internal and external cycles to respectively conduct optimization analysis of the reaction model parameters. The internal cycle realizes rapid optimization of the reaction parameters through semi-theoretical empirical formulas and intelligent optimization algorithms, and the external cycle automatically establishes the optimal reaction path, which can effectively improve the accuracy and calculation efficiency of the generalized reaction modeling.

[0007] To solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A generalized reaction modeling method for materials based on multi-cycle optimization includes the following steps:

[0009] Step 1: Obtain the TG curve and DTG curve of the material through a thermogravimetric reaction analysis experiment;

[0010] Step 2: Determine the initial number of reaction paths N based on the peak points of the DTG curve, and estimate the activation energy E, pre-exponential factor A, and number of reaction paths n as initial thermogravimetric reaction parameters through a model-free fitting method and / or a model fitting method;

[0011] Step 3: Inner loop optimization - Use one or more of the particle swarm optimization algorithm, genetic algorithm, and trust region reflection algorithm to perform cyclic iterative optimization on the thermogravimetric reaction parameters described in Step 2, select the parameter group with the best fitting effect and substitute it into the finite reaction rate model to establish a reaction model under the initial reaction path;

[0012] Step 4: Outer loop optimization - Determine whether the goodness of fit between the optimized DTG curve and the experimental DTG curve meets the requirements. If not, adjust the number of reaction paths through residual analysis, and use the current optimal parameters as the initial values of the inner loop, and repeat Steps 3-4 until the fitting requirements are met;

[0013] Step 5: Output the final reaction model.

[0014] Preferably, in Step 1, a synchronous thermal analyzer is used to monitor the data of the pyrolysis experiment of the target material, and the temperature and mass percentage change data of the target material during the pyrolysis reaction are obtained by thermogravimetric analysis and converted into a thermogravimetric curve TG and a thermogravimetric differential curve DTG.

[0015] Preferably, the thermogravimetric curve TG characterizes the change of the weight of the target material with temperature during the pyrolysis reaction, and is expressed as:

[0016]

[0017] In the formula, m p is the real-time mass percentage of PMMA;

[0018] The thermogravimetric differential curve DTG characterizes the change of the dimensionless weight change rate with temperature or time, and is expressed as:

[0019] shown as:

[0020]

[0021] In the formula, T is the real-time temperature of the material.

[0022] Preferably, in Step 2, when there are multiple peak points in the DTG curve, computer programming is used to smooth the DTG curve to obtain the temperature and corresponding reaction rate of each peak point, and the initial number of reaction paths N is the number of peak points.

[0023] Preferably, in step 2, the model-free fitting method includes the FWO method and the Kissinger method.

[0024] In the FWO method, the thermokinetic equation is expressed as:

[0025]

[0026] In the formula, is the heating rate, E is the apparent activation energy of the reaction, A is the pre-exponential factor, is the integral of the conversion function, T is the absolute temperature of the sample, and R is the universal gas constant. For different materials, by comparing the errors of the activation energy E and the pre-exponential factor A calculated under different f(α) models, the mechanism function that best fits the experimental data is selected; during linear fitting, with 1 / T max as the abscissa and lgβ as the ordinate to plot a graph, where T max is the peak temperature, and the slope of the fitted straight line corresponds to to obtain the activation energy E, and the y-axis intercept corresponds to to obtain the pre-exponential factor A;

[0027] In the Kissinger method, the thermokinetic equation is expressed as:

[0028]

[0029] During linear fitting, with 1 / T max as the abscissa, as the ordinate to plot a graph, and the slope of the fitted straight line corresponds to to obtain the activation energy E, and the y-axis intercept corresponds to to obtain the pre-exponential factor A;

[0030] The model fitting method includes the CR method, and the thermokinetic equation is expressed as:

[0031]

[0032] During linear fitting, with 1 / T as the abscissa, as the ordinate to plot a graph, and the slope of the fitted straight line corresponds to to obtain the activation energy E, and the y-axis intercept corresponds to to obtain the pre-exponential factor A;

[0033] When calculating E and A using multiple methods, compare the fitting effects under different methods and select the optimal model as the initial parameter.

[0034] Preferably, the finite reaction rate model is calculated based on the Arrhenius formula, specifically:

[0035]

[0036] Among them, is the reaction conversion rate, t is the reaction time, m0 is the mass of the sample at the initial moment, m is the real-time mass of the sample, and m ∞ is the final residual mass of the sample, k(T) is the temperature relationship of the rate constant, and f(α) is the reaction mechanism function.

[0037] Preferably, in step 3, the particle swarm algorithm realizes global search by simulating swarm intelligence. Each particle represents a parameter combination (E, A), and the optimal solution is searched by iteratively updating the particle position and velocity;

[0038] The genetic algorithm realizes parameter space exploration by simulating biological evolution. Real number coding is used to take E and A as individual genes, and the population is iteratively optimized through selection, crossover, and mutation operations;

[0039] The trust region reflection algorithm realizes efficient and fine optimization through local linearization. Taking (E, A) as the initial value, a trust region radius is constructed, and the second-order approximation model is solved within the region to update the parameters;

[0040] When multiple intelligent algorithms are used for cyclic optimization, the optimization results of different intelligent algorithms are compared, and the optimal model parameters with the goodness of fit closest to 1 are selected to establish a model under the initial reaction path. The model reaction characteristic curve is established through numerical calculation and compared with the experimental DTG curve.

[0041] Preferably, in steps 2 and 4, the goodness of fit is used to evaluate the fitting effect under different methods: Substitute the E and A obtained by each method into the DTG calculation formula, draw the DTG curve, compare it with the experimental DTG curve obtained in step 1, and evaluate the fitting and optimization effects by calculating the goodness of fit.

[0042] Preferably, the thermal reaction DTG curve is drawn from the parameters E, A, and experimental data, and its specific formula is:

[0043]

[0044] In the formula, DTG optimized is the optimized thermogravimetric differential curve, β is the heating rate, R is the universal gas constant, and T is the absolute temperature of the sample.

[0045] Preferably, the coefficient of determination r 2 is used as a statistic for measuring the goodness of fit. The closer r 2 is to 1, the higher the goodness of fit. The calculation formula of the coefficient of determination r 2 is:

[0046]

[0047] Wherein, DTG is the experimental thermogravimetric differential curve, and DTG optimized is the optimized thermogravimetric differential curve, is the average value of the experimental DTG curve. The method with the goodness of fit closest to 1 corresponding to E and A is used as the basis for the next optimization.

[0048] Preferably, in step 4, the method for adjusting the number of reaction paths N through residual analysis is as follows: Calculate the residual sequence between the experimental DTG curve and the optimized simulated DTG curve, and its formula is:

[0049] ΔDTG = |DTG - DTG optimized |

[0050] Locate the temperature range where ΔDTG is greater than the set threshold through the sliding window method. If there is no corresponding peak point in this range, the number of reactions needs to be increased; if the temperature ranges of adjacent reaction stages overlap and the residual ΔDTG distributions are similar, they are combined into a single reaction stage to reduce the number of reactions.

[0051] Beneficial effects

[0052] The present invention proposes a generalized reaction modeling method for materials based on double loops. The inner loop combines theoretical formulas and intelligent algorithms, greatly improving the efficiency and calculation accuracy of reaction parameter optimization; the outer loop realizes the automatic optimization of reaction paths, improves the model accuracy and reliability, and further improves the modeling efficiency.

[0053] The interaction between the inner and outer loops is not a one-way transmission, but forms a closed loop through parameter initialization, residual feedback, and convergence conditions. The path adjustment of the outer loop will change the optimization dimension of the inner loop, and the optimization result of the inner loop will affect the path selection of the outer loop through residual analysis. The optimization of the inner and outer loops can be dynamically coupled through programming to achieve the adaptive optimization improvement of reaction paths and reaction parameters, and an optimal reaction model that conforms to the complex real reaction mechanism of materials can be obtained, which is more superior than the simple series mode of "parameter optimization + path adjustment". Description of the drawings

[0054] Figure 1 is a flowchart of a generalized reaction modeling method for materials based on multi-loop optimization designed by the present invention;

[0055] Figure 2 is the thermogravimetric curve of the PMMA material pyrolysis experiment;

[0056] Figure 3 is the thermogravimetric differential curve of the PMMA material pyrolysis experiment;

[0057] Figure 4 is a comparison diagram of the DTG curve estimated by the FWO algorithm and the experimental DTG curve;

[0058] Figure 5 The comparison graph of the DTG curve estimated by the Kissinger algorithm and the experimental DTG curve;

[0059] Figure 6 The comparison graph of the DTG curve optimized by the particle swarm optimization algorithm and the experimental DTG curve;

[0060] Figure 7 The comparison graph of the DTG curve optimized by the genetic algorithm and the experimental DTG curve;

[0061] Figure 8 The comparison graph of the DTG curve optimized by the trust region reflection algorithm and the experimental DTG curve. Specific implementation manners

[0062] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the available embodiment libraries of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0063] The present invention discloses a method for modeling the general reaction of materials based on multi-cycle optimization. The basic process of this method is as Figure 1 shown. The present invention establishes a high-precision general reaction model of materials through two sets of internal and external cycles. Among them, the internal cycle: estimate the reaction parameters and use them as inputs, and cycle through multiple optimization algorithms to optimize the reaction parameters, and establish the reaction model and parameters under the initial reaction path; the external cycle: optimize the reaction path based on the goodness of fit and the model deviation to obtain a more accurate general reaction model reflecting the material reaction process.

[0064] In this embodiment, taking the pyrolysis reaction of PMMA material as an example, combined with Figures 2 - 8 , the implementation steps of the present invention are specifically described.

[0065] Step 1, obtain the parameter changes such as the mass and heat of the material during the heating process through a thermal reaction analysis experiment, and draw the corresponding experimental curves, including the TG curve and the DTG curve.

[0066] In this embodiment, a synchronous thermal analyzer is used to monitor the data of the pyrolysis experiment of the PMMA material. The synchronous thermal analyzer combines thermogravimetric analysis and differential scanning calorimetry into one.

[0067] From the thermogravimetric analysis, the data of the temperature and mass percentage change of PMMA during the pyrolysis reaction are obtained, and they are converted into a thermogravimetric curve (TG) and a thermogravimetric differential curve (DTG).

[0068] (1) The thermogravimetric curve TG is as Figure 2As shown, it characterizes the change of the weight of PMMA material with temperature during the pyrolysis reaction. The vertical coordinate is the dimensionless weight percentage, representing the ratio of the weight of PMMA material at the current temperature to the initial weight. The calculation formula of TG is (assuming the initial mass is 100%):

[0069]

[0070] In the formula, m p is the real-time mass percentage of PMMA.

[0071] (2) The differential thermogravimetry curve DTG is as Figure 3 shown, that is, the first derivative of the TG curve, which characterizes the change of the dimensionless weight change rate with temperature. Its peak point represents the temperature at which the weight change rate of each weight loss stage is the fastest. The calculation formula of DTG is:[[]]END]]

[0072]

[0073] In the formula, T is the real-time temperature of PMMA.

[0074] Step 2: Obtain reaction characteristic data from the DTG curve based on image analysis technology and estimate the key parameters in the thermal reaction rate model.

[0075] There may be multiple peak points in the DTG curve obtained in Step 1. Use computer programming to smooth the DTG curve, and obtain the reaction characteristic data of the DTG curve through image analysis technology, that is, the temperature of each peak point, the corresponding reaction rate and the number of peak points. The initial reaction number N is the same as the number of peak points. And based on this, use the model-free fitting method and the model fitting method to estimate the key parameters activation energy E, pre-exponential factor A, and reaction order n in the thermal reaction model, compare the fitting effects under different methods, and select the parameters with the best effect.

[0076] In this embodiment, using programming, obtain the thermal reaction parameters of the peak points from the TG curve. The initial peak number N can be taken as 1. The specific thermal reaction parameters of the peak points are shown in Table 1.

[0077] Table 1 Peak data of PMMA differential thermogravimetry curve

[0078] Heating rate (K / min) Temperature (K) Weight change rate (% / min) 10 648.568 1.993 20 657.237 2.010

[0079] In this embodiment, the initial general reaction model is expressed as:

[0080]

[0081] During the pyrolysis process of PMMA, the main chain breaks, decomposes, and the residue carbonizes, which can be divided into multiple-step reactions, corresponding to the above three reaction models. In the actual analysis process, according to the temperature range and reaction rate of adjacent reaction paths, the outer loop algorithm can consider merging them into a single path to simplify the calculation, or perform dynamic correction, adjust the reaction path and re-analyze.

[0082] The pyrolysis reaction rate is calculated according to the finite reaction rate model based on the Arrhenius formula, specifically as follows:

[0083]

[0084] Among them,

[0085] In the formula, m0 is the mass of the sample at the initial moment, m is the real-time mass of the sample, m ∞ is the final residual mass of the sample, T is the absolute temperature of the sample, k(T) is the temperature relationship of the rate constant, f(α) is the reaction mechanism function, E is the apparent activation energy of the reaction, A is the pre-exponential factor, R is the universal gas constant, taking 8.3145 J / mol·K. In this embodiment, f(α) takes (1 - α) n .

[0086] To establish the above thermal reaction model, in this embodiment,

[0087] Step 2.1, use the FWO method, Kissinger method, and CR method to estimate the activation energy E and the pre-exponential factor A respectively.

[0088] (1) In the FWO method, the thermokinetic equation can be expressed as:

[0089]

[0090] In the formula, is the heating rate, is the integral of the conversion rate function. When performing linear fitting, select 1 / T max as the abscissa and lgβ as the ordinate to plot the graph, T max is the peak temperature. Take the peak points corresponding to β = 10 K / min and 20 K / min for fitting. The equation of the fitted line is y = kx + b, is the slope of the line, is the y-axis intercept. The E estimated by the FWO method = 150.84 kJ / mol, A = 9.57×10 9 s -1 .

[0091] (2) In the Kissinger method, the thermokinetic equation can be expressed as:

[0092]

[0093] When performing linear fitting, select 1 / T max as the abscissa, and use T max as the peak temperature to plot a graph. Take the peak points corresponding to β = 10 K / min and 20 K / min for fitting. The fitting straight line is as shown in Figure 5 . The equation of the fitting straight line is y = kx + b, where k is the slope of the straight line, and b 9 is the y-axis intercept. The E value estimated by the Kissinger method is 147.82 kJ / mol, and A = 7.68×10 -1 .

[0094] (3) In the CR method, the thermokinetic equation can be expressed as:

[0095]

[0096] In this embodiment, G(α) takes When performing linear fitting, select 1 / T as the abscissa, and use it as the ordinate to plot a graph. Use the least squares method for linear fitting. The equation of the fitting straight line is y = kx + b, where k is the slope of the straight line, and b

[0097] Step 2.2: Compare the fitting effects under different methods and select the optimal model as the initial parameter.

[0098] Substitute the parameters E and A into the formula to plot the DTG curve. The specific formula is:

[0099]

[0100] Substitute the parameters estimated by the FWO method and the Kissinger method into the DTG calculation formula respectively. The comparison graphs of the obtained curves with the experimental DTG curve are as shown in Figure 4 、 Figure 5 .

[0101] Use the goodness of fit to evaluate the fitting effects of these two methods. The statistic for measuring the goodness of fit is the coefficient of determination r 2 , which can directly reflect the closeness between the model predicted values and the actual observed values. The closer r 2 is to 1, the higher the goodness of fit, and the better the fitting effect of the model on the data. The calculation formula for the coefficient of determination r 2 is:

[0102]

[0103] It can be calculated that the goodness of fit corresponding to the Kissinger method is 0.89012, which is closer to 1. Therefore, the parameters E and A estimated by this method are used as the basis for the next step of optimization.

[0104] Step 3, inner loop optimization - Based on the estimated parameters E and A, various intelligent algorithms such as the particle swarm optimization algorithm, genetic algorithm, and trust region reflection algorithm are used to cyclically optimize the thermal reaction parameters. The corresponding ideal DTG curves are plotted using the experimental data and the parameters optimized by different intelligent algorithms, and compared with the experimental DTG curve. The optimization algorithm with the smallest error is selected by the goodness of fit to establish a model under the initial reaction path.

[0105] Specifically,

[0106] In Step 3.1, in this embodiment, the particle swarm optimization algorithm, genetic algorithm, and trust region reflection algorithm are used to optimize the parameters:

[0107] (1) The particle swarm optimization algorithm (PSO) simulates the solution of the optimization problem as particles in the search space. Each particle has position and velocity attributes, and searches for the optimal solution by iteratively updating the position. During the iteration process, the particle adjusts its velocity and position based on its own historical best position and the global best position found by the entire population, so that the entire particle swarm evolves in the direction of the optimal solution. The standard form is:

[0108] v i = ω × v i + c1 × rand × (pbest i - x i ) + c2 × rand() × (gbest i - x i )

[0109] In the formula, v i is the velocity of the particle, x i is the position of the particle, c1 and c2 are learning factors, usually c1 = c2 = 2, rand is a random number between (0, 1), pbest i is the historical best position, and gbest is the global best position.

[0110] In this embodiment, the particle swarm size is set to 100, the maximum number of iterations is set to 200, the value range of the reaction order n is limited to n ∈ [0, 3]. In the initial population, n is randomly generated within the interval. The optimized parameter E = 207.48 kJ / mol, A = 4.03 × 10 14 s -1, n takes 1.23. Substituting it into the DTG calculation formula, the comparison graph of the obtained curve and the experimental DTG curve is as Figure 6 shown.

[0111] (2) The genetic algorithm (GA) is a stochastic search algorithm that simulates natural selection and genetic mechanisms. It represents the solution of a problem as a chromosome (individual), and through genetic operations such as selection, crossover, and mutation, it simulates the evolutionary process of a population, enabling the individuals in the population to continuously adapt to the environment, thereby gradually searching for the optimal solution. One iteration of the genetic algorithm can be expressed as:

[0112] Selection: In the formula, p i is the probability that the i-th individual is selected, f(x i ) is the fitness of the i-th individual, and N is the total number of individuals in the population.

[0113] Crossover: x new =(x i1 , x i2 , …, x ik , x j(k+1) , …x jn ), in the formula, x i and x j are any two individuals, x new is the offspring of the individuals, and k is the crossover point.

[0114] Mutation: x′ nk =x nk +δ, in the formula, x nk is the gene, x′ nk is the mutated gene, and δ is a random small change.

[0115] In this embodiment, the population size is set to 100, the maximum number of iterations is set to 200, the crossover fraction is newly set to 0.8, the number of elites is newly set to 2, and the maximum stagnation generation is set to 50 to avoid unnecessary calculations. The reaction order n is algorithmically crossed using a random weight α, and Gaussian perturbation is applied to n to ensure extensive exploration of the n space in the initial stage and gradual convergence in the later stage. The optimized parameters are E = 151.48 kJ / mol, A = 1.1×10 10 s -1 , n takes 1.22. Substituting it into the DTG calculation formula, the comparison graph of the obtained curve and the experimental DTG curve is as Figure 7 shown.

[0116] (3) The trust region reflection algorithm is used to fit a nonlinear model, defining the optimization problem as a nonlinear least squares problem to minimize the error between the fitting result and the actual data, usually expressed as:

[0117]

[0118] In the formula, y i is the observed data, x i is the independent variable, f(x i , β) is the non-linear function to be fitted, β is the parameter vector to be estimated, and m is the number of data points.

[0119] In this embodiment, the number of iterations is set to 1000, the initial value of the reaction order n is set to 1, and n ∈ [0, 3] is defined. By iteratively updating and adjusting n, combined with the adaptive reduction of the trust region radius, it finally converges. The optimized parameter E = 150.68 kJ / mol, A = 9.57×10 9 s -1 , and n takes 0.91. Substituting it into the DTG calculation formula, the comparison graph of the obtained curve and the experimental DTG curve is as Figure 8 shown.

[0120] Step 3.2, evaluate the optimization effects of the three optimization methods using the goodness of fit. The calculated coefficient of determination r 2 is shown in Table 4 below.

[0121] Table 4 Goodness of fit of calculation results of different optimization algorithms

[0122] <![CDATA[r 2 > Before intelligent optimization 0.8901 Particle swarm optimization 0.9987 Genetic algorithm 0.9894 Trust region reflection algorithm 0.9889

[0123] It can be obtained from the comparison in Table 4 that the coefficient of determination of the particle swarm optimization algorithm is closest to 1, that is, the DTG curve drawn by the optimized parameters is closest to the experimental curve, and the optimization effect is the best.

[0124] The model under the initial reaction path is expressed as:

[0125]

[0126] Step 4, determine whether the model under the initial reaction path meets the goodness of fit requirements. If not,

[0127] return to Step 2, and optimize and adjust the reaction path based on the analysis of the difference between the current model and the experimental results. Repeat Steps 2 - 3 until the requirements are met.

[0128] Calculate the residual sequence between the experimental DTG curve and the optimized simulation DTG curve, and its formula is:

[0129] ΔDTG = |DTG - DTG optimized |

[0130] Locate the temperature range where ΔDTG > 3% by the sliding window method (window width ΔT = 10K). If there is no corresponding peak point in this range, the number of reactions needs to be increased; if the temperature ranges of adjacent reaction stages overlap (ΔT < 20K) and the residual distributions are similar (ΔDTG difference < 2%), they are combined into a single reaction stage to reduce the number of reactions. The present invention first creates a dynamic update mechanism for the number of paths triggered by the residual threshold, and realizes a closed-loop feedback of residual analysis → path merging / splitting → parameter re-optimization through an outer loop.

[0131] Step 5: Obtain the optimal reaction path and thermal reaction parameters, and output the final model of the generalized reaction of the material and the DTG curve of the reaction.

[0132] In this embodiment, after two kinds of inner and outer loops, the parameters that meet the accuracy requirements are E = 206.23 kJ / mol, A = 4.05×10 14 s -1 , thus establishing a generalized reaction model for the pyrolysis process of PMMA material.

[0133] In this embodiment, the final generalized reaction model can be expressed as:

[0134]

[0135] In the implementation process of the present invention, the dynamic optimization of the reaction path realizes the precise inversion of parameters through the cooperation mechanism of inner and outer loops. Specifically, first determine the initial number of reactions based on the number of peak points of the thermogravimetric analysis (TGA) curve. For example, in the pyrolysis process of PMMA in this embodiment, three characteristic stages of main chain breakage, decomposition, and residue carbonization correspond to setting 3 groups of kinetic parameter calculation tasks. Subsequently, the activation energy (E) and pre-exponential factor (A) of each path are locally optimized through the inner loop. Based on the goodness of fit (r 2 ) judge whether the model under the initial reaction path meets the goodness-of-fit requirements. When the requirements are not met, trigger the outer loop adjustment mechanism: when the temperature ranges of adjacent paths overlap and the residuals converge, merge them into a single path to simplify the calculation; if the parameter inversion is unqualified, dynamically correct the reaction path and re-trigger the inner loop calculation until the goodness of fit (r 2 ) meets the requirements. In this example, the inner loop obtains the optimized reaction parameters corresponding to the model through the optimal combination of the Kissinger algorithm and the particle swarm algorithm, and the outer loop further improves the efficiency and accuracy of the model by merging and optimizing multi-step reactions.

[0136] As described above, it is only a part of the embodiments of the present invention. Although some terms are used in the present invention, the possibility of using other terms is not excluded. These terms are used only for the convenience of describing and explaining the essence of the present invention, and interpreting them as any additional limitation is contrary to the spirit of the present invention. The above description only uses examples to further illustrate the content of the present invention for easier understanding, but it does not mean that the embodiments of the present invention are limited to this. Any technical extension or re-creation based on the present invention is protected by the present invention.

Claims

1. A generalized reaction modeling method for materials based on multi-cycle optimization, characterized in that It includes the following steps: Step 1: Obtain the TG curve and DTG curve of the material through a thermal reaction analysis experiment; Step 2: Determine the initial number of reaction paths N based on the peak points of the DTG curve, and estimate the activation energy E, pre-exponential factor A, and reaction order n as the initial thermal reaction parameters through a model-free fitting method and / or a model fitting method; Step 3: Inner loop optimization - Use one or more of the particle swarm algorithm, genetic algorithm, and trust-region reflection algorithm to perform cyclic iterative optimization on the thermal reaction parameters described in Step 2, select the parameter group with the best fitting effect and substitute it into the finite reaction rate model to establish a reaction model under the initial reaction path; Step 4: Outer loop optimization - Determine whether the goodness of fit between the optimized DTG curve and the experimental DTG curve meets the requirements. If not, adjust the number of reaction paths through residual analysis, and use the current optimal parameters as the initial values of the inner loop. Repeat Steps 3-4 until the fitting requirements are met; Step 5: Output the final reaction model.

2. The generalized reaction modeling method of materials based on multi-cycle optimization according to claim 1, characterized in that In Step 1, a synchronous thermal analyzer is used to monitor the data of the pyrolysis experiment of the target material. The temperature and mass percentage change data of the target material during the pyrolysis reaction are obtained through thermogravimetric analysis and converted into a thermogravimetric curve TG and a thermogravimetric differential curve DTG; The thermogravimetric curve TG characterizes the change in weight of the target material with temperature during the pyrolysis reaction and is expressed as: where m p is the real-time mass percentage of PMMA; The thermogravimetric differential curve DTG characterizes the change in the rate of dimensionless weight change with temperature or time and is expressed as: In the formula, T is the real-time temperature of the material.

3. The generalized reaction modeling method for materials based on multi-cycle optimization according to claim 1, wherein In Step 2, when there are multiple peak points in the DTG curve, computer programming is used to smooth the DTG curve to obtain the temperature and corresponding reaction rate of each peak point. The initial reaction path N is the number of peak points.

4. The generalized reaction modeling method for materials based on multi-cycle optimization according to claim 1, characterized in that, In Step 2, the model-free fitting method includes the FWO method and the Kissinger method. In the FWO method, the thermokinetic equation is expressed as: In the formula, is the heating rate, E is the apparent activation energy of the reaction, A is the pre-exponential factor, is the integral of the conversion function, T is the absolute temperature of the sample, and R is the universal gas constant. For different materials, by comparing the errors of the activation energy E and the pre-exponential factor A calculated under different f(α) models, the mechanism function that best fits the experimental data is selected; during linear fitting, with 1 / T max as the abscissa and lgβ as the ordinate to plot a graph, where T max is the peak temperature, the slope of the fitted straight line corresponds to to obtain the activation energy E, and the y-axis intercept corresponds to to obtain the pre-exponential factor A; In the Kissinger method, the thermokinetic equation is expressed as: During linear fitting, with 1 / T max as the abscissa, a graph is plotted with the slope of the fitted straight line corresponding to the activation energy E obtained, and the y-axis intercept corresponding to the pre-exponential factor A obtained; The model fitting method includes the CR method, and the thermokinetic equation is expressed as: When performing linear fitting, with 1 / T as the abscissa, plot a graph with as the ordinate. The slope of the fitted straight line corresponds to obtain the activation energy E, and the y-axis intercept corresponds to obtain the pre-exponential factor A; When calculating E and y using multiple methods, compare the fitting effects under different methods and select the optimal model as the initial parameters.

5. The material generalized reaction modeling method based on multi-cycle optimization according to claim 4, characterized in that The finite reaction rate model is calculated based on the Arrhenius formula, specifically: Among them, is the reaction conversion rate, t is the reaction time, m0 is the mass of the sample at the initial moment, m is the real-time mass of the sample, m ∞ is the final residual mass of the sample, k(T) is the temperature relationship of the rate constant, and f(α) is the reaction mechanism function.

6. The generalized reaction modeling method for materials based on multi-cycle optimization according to claim 1, wherein In Step 3, the particle swarm algorithm realizes global search by simulating swarm intelligence. Each particle represents a parameter combination (E, A), and the optimal solution is searched by iteratively updating the particle position and velocity; the genetic algorithm realizes parameter space exploration by simulating biological evolution, uses real number coding to take E and A as individual genes, and iteratively optimizes the population through selection, crossover, and mutation operations; The trust-region reflection algorithm realizes efficient and fine optimization through local linearization. Taking (E, A) as the initial value, a trust-region radius is constructed, and the second-order approximation model is solved within the region to update the parameters; When using multiple intelligent algorithms for cyclic optimization, compare the optimization results of different intelligent algorithms, select the optimal model parameters with the goodness of fit closest to 1 to establish a model under the initial reaction path, and establish a model reaction characteristic curve through numerical calculation and compare it with the experimental DTG curve.

7. The generalized reaction modeling method of materials based on multi-cycle optimization according to claim 1, wherein In Steps 2 and 4, the goodness of fit is used to evaluate the fitting effect under different methods: substitute E and A obtained by each method into the DTG calculation formula, plot the DTG curve, compare it with the experimental DTG curve obtained in Step 1, and evaluate the fitting and optimization effects by calculating the goodness of fit.

8. The generalized reaction modeling method of materials based on multi-cycle optimization according to claim 7, characterized in that Draw the thermal reaction DTG curve from the parameters E, A and experimental data, and its specific formula is: where DTG optimized is the optimized thermogravimetric differential curve, β is the heating rate, R is the universal gas constant, and T is the absolute temperature of the sample.

9. The material general reaction modeling method based on multi-cycle optimization according to claim 8, characterized in that, Taking the coefficient of determination r 2 as a statistic for measuring the goodness of fit, r 2 the closer it is to 1, the higher the goodness of fit. The coefficient of determination r 2 is calculated by the formula: where DTG is the experimental thermogravimetric differential curve, and DTG optimized is the optimized thermogravimetric differential curve, is the average value of the experimental DTG curve. The method with the goodness of fit closest to 1 corresponds to E and A as the basis for the next optimization.

10. The method for general reaction modeling of materials based on multi-cycle optimization according to any one of claims 1-9, characterized in that In Step 4, the method of adjusting the number of reaction paths N through residual analysis is: calculate the residual sequence between the experimental DTG curve and the optimized simulation DTG curve, and its formula is: ΔDTG = |DTG - DTG optimized | Locate the temperature range where ΔDTG is greater than the set threshold by the sliding window method. If there is no corresponding peak point in this range, the number of reactions needs to be increased; if the temperature ranges of adjacent reaction stages overlap and the residual ΔDTG distributions are similar, they are merged into a single reaction stage to reduce the number of reactions.

Images