Method for predicting storage life of composite material based on variable transformation and genetic algorithm

Abstract

The invention discloses a composite material storage life prediction method based on variable transformation and a genetic algorithm, and relates to the technical field of composite material performance evaluation and life prediction, and the method comprises the steps: obtaining performance degradation data at different temperatures through an accelerated aging test, and building a semi-empirical performance degradation model; specific variable transformation is introduced, a nonlinear optimization problem is converted into a linear regression problem, partial model parameters are rapidly solved by adopting a least square method, and meanwhile, key nonlinear parameters are globally optimized by using a genetic algorithm, so that the defect that a traditional method is easy to fall into local optimum is overcome. And establishing a temperature-service life relationship by combining with an archenius model, and realizing storage life prediction at normal temperature. The method also integrates sensitivity analysis and uncertainty quantification functions, and provides reliability evaluation for a prediction result. The method fully considers the influence of the environment temperature, meets the requirement of efficient prediction, and improves the precision and stability of life prediction.

Description

Technical Field

[0001] This invention relates to the field of composite material performance evaluation and life prediction technology, and particularly to a method for predicting the storage life of composite materials based on variable transformation and genetic algorithms. This method is applicable to accurately predicting the lifespan of composite materials during their research, development, storage, and use, especially for predicting the lifespan of composite materials affected by temperature factors. Background Technology

[0002] Composite materials are widely used in aerospace, automotive manufacturing, construction, and other fields. However, due to their performance degradation over long-term use, especially under high temperature and high humidity conditions, predicting the storage life of composite materials is particularly important. Traditional life prediction methods mainly rely on accelerated aging tests and empirical formulas. These methods often cannot accurately predict the storage life of materials under complex environments and are easily affected by nonlinear factors, resulting in unstable prediction results and low computational efficiency.

[0003] In existing technologies, although there are schemes for lifetime prediction using semi-empirical performance degradation models, most of them have the following shortcomings: First, traditional methods rely heavily on linearization assumptions and cannot handle complex nonlinear degradation processes; second, they fail to fully consider the impact of ambient temperature on material properties; and third, they have low computational efficiency and are difficult to adapt to the high-efficiency prediction needs in large-scale production.

[0004] Therefore, there is an urgent need for a new method that combines the advantages of variable transformation and genetic algorithms to improve prediction accuracy, optimize computational efficiency, and comprehensively assess the lifespan of composite materials under different environmental conditions. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] The purpose of this invention is to address the shortcomings of existing technologies, such as reliance on linearization assumptions, inability to handle complex nonlinear degradation processes, failure to fully consider the influence of ambient temperature on material properties, low computational efficiency, and difficulty in meeting the high-efficiency prediction requirements of large-scale production. The invention proposes a composite material storage life prediction method based on variable transformation and genetic algorithms.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the storage life of composite materials based on variable transformation and genetic algorithms, comprising the following steps:

[0009] S1. The composite material samples were treated under different temperature conditions, and the performance degradation data related to the composite material properties were collected in real time.

[0010] S2. Construct a semi-empirical performance degradation model for composite material performance degradation based on performance degradation data;

[0011] S3. Introduce a specific variable transformation method to transform the semi-empirical performance degradation model into a linear regression model;

[0012] S4. Solve the linear regression model using the least squares method to obtain the parameters η and β in the linear regression model;

[0013] S5. Based on the genetic algorithm, global optimization is performed on the nonlinear parameters λ and α to be determined to obtain the optimized nonlinear parameters λ and α. Based on the optimized nonlinear parameters, the error between the model output and the experimental data is minimized.

[0014] S6. Based on the performance degradation model optimized by the linear parameters η and β and the optimized nonlinear parameters λ and α, and the preset failure criteria, calculate the material failure time under each temperature condition.

[0015] S7. Based on the material failure time under the aforementioned temperature conditions, perform linear regression using the least squares method to fit the Arrhenius model parameters, establish the Arrhenius model, and establish the temperature-lifetime relationship based on the Arrhenius model.

[0016] S8. Predict the storage life of composite materials at room temperature based on the temperature-life relationship.

[0017] Furthermore, the process of treating the composite material samples under different temperature conditions and collecting performance degradation data related to the composite material properties in real time includes:

[0018] Standard samples of the composite material are prepared and initial performance is tested to obtain a sample group with initial performance parameters. Based on a preset temperature profile, the sample group is subjected to temperature grouping and accelerated aging treatment to obtain aged sample groups under different temperature conditions.

[0019] At preset aging time points, the performance parameters of the aging sample group are tested to obtain time-series performance test data; the time-series performance test data is aligned based on temperature group to obtain performance degradation data arranged in temperature sequence.

[0020] Furthermore, the construction of a semi-empirical performance degradation model for composite material performance degradation based on performance degradation data includes: analyzing the performance evolution law of the performance degradation data to obtain the material performance evolution characteristics of the performance degradation data; identifying the competition mechanism based on the material performance evolution characteristics to obtain a competition mechanism model framework in which the enhancing effect and the deterioration effect of the material performance evolution characteristics are parallel.

[0021] A semi-empirical performance degradation model of the competition mechanism model framework is obtained by constructing a mathematical expression for the competition mechanism model framework; the parameters of the semi-empirical performance degradation model are initialized based on the statistical characteristics of the performance degradation data to obtain a semi-empirical performance degradation model with a physically meaningful initial value range.

[0022] Based on the time variable transformation relationship, the semi-empirical performance degradation model is restructured to obtain a linear combination form of the semi-empirical performance degradation model; a linear regression model is identified from the linear combination form to obtain the linear regression model of the semi-empirical performance degradation model.

[0023] Furthermore, the introduction of a specific variable transformation method to transform the semi-empirical performance degradation model into a linear regression model includes: defining a function transformation for the time variable in the semi-empirical performance degradation model to obtain the time variable transformation relationship of the semi-empirical performance degradation model;

[0024] The transformation formula is:

[0025] and

[0026] in, and For the nonlinear parameters to be determined, This refers to the aging time.

[0027] Based on the time variable transformation relationship, the semi-empirical performance degradation model is restructured to obtain a linear combination form of the semi-empirical performance degradation model; a linear regression model is identified from the linear combination form to obtain the linear regression model of the semi-empirical performance degradation model.

[0028] Furthermore, the step of solving the linear regression model using the least squares method to obtain the parameters η and β in the linear regression model includes: constructing a design matrix based on the independent and dependent variables in the linear regression model to obtain the design matrix of the linear regression model; and performing regularization processing on the design matrix to obtain the regularized design matrix.

[0029] Based on the regularized design matrix and the observed data vector, a least squares objective function is constructed to obtain the least squares optimization problem of the linear regression model; the least squares optimization problem is numerically solved to obtain the parameter solution vector of the linear regression model.

[0030] The linear parameters η and β are extracted from the parameter solution vector to obtain the linear parameters η and β in the linear regression model.

[0031] Furthermore, the global optimization of the nonlinear parameters λ and α based on the genetic algorithm to obtain optimized nonlinear parameters λ and α, and the error between the output of the model and the experimental data based on minimizing the optimized nonlinear parameters, includes: initializing the population for the value space of nonlinear parameters λ and α, setting the population size to 15 individuals to obtain an initial population; and performing selection, crossover, and mutation operations on the initial population, wherein the crossover probability is set to 0.8 and the mutation probability is set to 0.2 to obtain a new generation population.

[0032] The fitness of the new generation population is evaluated to obtain the optimal individual in the population; the values ​​of nonlinear parameters λ and α are extracted from the optimal individual to obtain the optimized nonlinear parameters λ and α.

[0033] Furthermore, the performance degradation model optimized based on the linear parameters η and β and the optimized nonlinear parameters λ and α, along with the preset failure criteria, calculates the material failure time under various temperature conditions, including: based on the strength requirements of fiber-reinforced composite materials in the national standard GB1447-2005, setting the material performance failure threshold to 100MPa, and obtaining the preset failure criteria.

[0034] Substituting the failure criterion into the performance degradation model that includes the linear parameters η and β, as well as the optimized nonlinear parameters λ and α, yields the performance termination equation regarding aging time; numerically solving the performance termination equation yields the material failure time under various temperature conditions.

[0035] Furthermore, the step of performing linear regression using the least squares method on the material failure time under each temperature condition to fit the Arrhenius model parameters and establish an Arrhenius model, and then establishing a temperature-lifetime relationship based on the Arrhenius model, includes: performing Arrhenius coordinate transformation on the material failure time series under each temperature condition, converting the thermodynamic temperature T to the reciprocal coordinate 1 / T, and the failure time L to the logarithmic coordinate ln(L), to obtain a linearized data point set in the Arrhenius coordinate system; and then performing linear regression analysis using the least squares method based on the linearized data point set in the Arrhenius coordinate system to obtain numerical solutions for the Arrhenius model parameters A and B.

[0036] Substitute the Arrhenius model parameters A and B into the Arrhenius model mathematical expression to establish a complete temperature-lifetime mathematical relationship model;

[0037] The specific form of the Arrhenius model is as follows:

[0038]

[0039] in, Indicates the storage life of composite materials. The thermodynamic temperature during material storage. , These are the parameters to be determined by fitting experimental data;

[0040] The fitting accuracy of the established temperature-lifetime mathematical model was verified, and a valid Arrhenius temperature-lifetime mathematical model was obtained, thus completing the establishment of the relationship between temperature and lifetime.

[0041] The relationship between temperature and lifespan is as follows:

[0042]

[0043] in, For lifespan, Thermodynamic temperature , The parameters are obtained by fitting the experimental data.

[0044] Furthermore, the method of predicting the storage life of composite materials at room temperature based on the temperature-life relationship includes: substituting the room temperature storage temperature into the verified Arrhenius temperature-life mathematical model to calculate the theoretical storage life of the composite material at room temperature and obtain the theoretical life value at room temperature; performing local sensitivity analysis on the Arrhenius temperature-life mathematical model to identify key parameters that affect the accuracy of life prediction and obtain a sensitivity ranking of key parameters.

[0045] Based on the sensitivity ranking of the key parameters, Monte Carlo simulation is used to perform multiple random samplings to calculate the statistical distribution of the model prediction results and obtain the lifetime prediction confidence interval. Based on the theoretical lifetime value at room temperature and the lifetime prediction confidence interval, a reliability assessment is performed to obtain a room temperature storage lifetime prediction result with guaranteed reliability.

[0046] (III) Beneficial Effects

[0047] This invention provides a method for predicting the storage life of composite materials based on variable transformation and genetic algorithms, which has the following beneficial effects:

[0048] 1. In this invention, composite material performance degradation data under different temperature conditions are obtained through accelerated aging tests. Combined with a semi-empirical degradation model, a nonlinear problem is transformed into a linear regression problem using variable transformation, and some parameters are quickly solved using the least squares method. Simultaneously, a genetic algorithm is introduced to optimize key nonlinear parameters, effectively overcoming the shortcomings of traditional methods that are prone to getting trapped in local optima.

[0049] 2. In this invention, by combining the Arrhenius model, the relationship between temperature and lifetime is established, further enabling the prediction of storage lifetime at room temperature. Furthermore, the method integrates sensitivity analysis and uncertainty quantification functions, providing a reliability assessment of the prediction results and improving the accuracy and stability of lifetime prediction. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the process for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to the present invention.

[0051] Figure 2 Curve of accelerated aging compressive strength change of high silica / phenolic composite material;

[0052] Figure 3 The fitting result of the Arrihenius model;

[0053] Figure 4 Figure 1 shows the compressive strength degradation model of high-silica phenolic short fiber molded parts; Figure 2 shows the performance degradation fitting curve at 90℃; Figure 3 shows the performance degradation fitting curve at 110℃; Figure 4 shows the performance degradation fitting curve at 130℃; and Figure 5 shows the performance degradation fitting curve at 150℃.

[0054] Figure 5 The lifetime prediction graph for high-silica phenolic resins at different temperatures; Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Please see Figures 1-5 This invention provides a method for predicting the storage life of composite materials based on variable transformation and genetic algorithms, comprising the following steps:

[0057] S1. The composite material samples were treated under different temperature conditions, and the performance degradation data related to the composite material properties were collected in real time.

[0058] In this embodiment, the process of treating the composite material samples under different temperature conditions and collecting performance degradation data related to the composite material properties in real time includes:

[0059] Standard samples of the composite material are prepared and initial performance is tested to obtain a sample group with initial performance parameters. Based on a preset temperature profile, the sample group is subjected to temperature grouping and accelerated aging treatment to obtain aged sample groups under different temperature conditions.

[0060] At preset aging time points, the performance parameters of the aging sample group are tested to obtain time-series performance test data; the time-series performance test data is aligned based on temperature group to obtain performance degradation data arranged in temperature sequence.

[0061] The detailed test data of uniaxial compressive strength of high-silica phenolic short fiber molded parts at different temperatures and aging times are shown in Table 1:

[0062] Table 1. Test data on uniaxial compressive strength of high-silica phenolic short fiber molded parts

[0063] Visualizing the experimental data in Table 1 yields a line graph showing the relationship between "accelerated aging time and compressive strength" at different temperatures (e.g., ...). Figure 2 As shown in the figure, this figure intuitively shows the degradation trend of material compressive strength with accelerated aging time under various temperature conditions. The horizontal axis is the accelerated aging time (days), and the vertical axis is the compressive strength (MPa). Different curves correspond to temperature conditions of 90℃, 110℃, 130℃, and 150℃, respectively.

[0064] Aging time points refer to predetermined test dates in accelerated aging tests, such as 0 days, 10 days, 30 days, and 60 days. An aging sample group refers to a collection of samples that have undergone accelerated aging treatment. Performance parameter testing refers to measuring the performance of the aged samples, including mechanical properties such as compressive strength, to quantify the degradation of material properties over time.

[0065] Specifically, the operational steps include removing samples from the constant temperature and humidity chamber at each preset aging time point, inspecting the sample's appearance and surface quality, and measuring its height and diameter using calipers. Then, the sample is placed in a uniaxial compression testing machine, the loading rate is set to 5 mm / min to start the test, and load-displacement curves are collected in real time to analyze the compressive strength and quantify the aging effect. The compressive strength is calculated based on the cross-sectional area of ​​the working section of the sample and the maximum load. The cross-sectional area is measured based on the sample's geometry or set according to standard sample specifications, and the maximum load is automatically recorded by the compression testing machine. Finally, through multiple tests and recordings, time-series performance test data are obtained, which reflect the trend of material properties changing over time.

[0066] The overall effect is to obtain time-series performance test data by conducting performance parameter tests at preset aging time points, such as the compressive strength values ​​of high silica phenolic short fiber molded parts at different time points at 90℃, 110℃, 130℃, and 150℃, thereby capturing the dynamic process of material performance degradation and providing time-series data support for establishing a performance degradation model.

[0067] In detail, a temperature profile refers to a pre-defined sequence or conditions of temperatures used to systematically simulate the thermal environment that composite materials may experience during storage. For example, multiple temperature points such as 90℃, 110℃, 130℃, and 150℃ may be set. A sample set refers to a collection of composite material samples after initial performance testing. Accelerated aging treatment refers to exposing samples to a high-temperature environment to accelerate the degradation process of material properties, thereby obtaining long-term aging data in a shorter time.

[0068] Preferably, in this step, the specific operations include dividing the composite material samples into multiple groups, such as 4 groups, each corresponding to different temperature conditions; then placing each group of samples into a constant temperature and humidity test chamber, which simulates temperature and humidity changes, with a temperature range of 0-100°C, humidity of 20-95%RH, and an accuracy of ±0.5°C / ±2%RH. The samples are gradually heated from room temperature to the target temperature at a preset heating rate, such as 5°C / min; aging treatment is continuously performed at the target temperature, and samples are taken at specific time points, such as 0 days, 10 days, 30 days, and 60 days, while recording macroscopic changes in the samples, such as color, mass, and size; after sampling, the samples are prepared for subsequent performance testing.

[0069] In detail, aging time points refer to predetermined test dates in accelerated aging tests, such as 0 days, 10 days, 30 days, and 60 days. An aging sample group refers to a collection of samples that have undergone accelerated aging treatment. Performance parameter testing refers to measuring the performance of the aged samples, including mechanical properties such as compressive strength, to quantify the degradation of material properties over time.

[0070] Preferably, in this step, the specific operational actions include: at each preset aging time point, removing the sample from the constant temperature and humidity test chamber, inspecting the sample's appearance and surface quality, and measuring its height and diameter using calipers; then placing the sample into a uniaxial compression testing machine, setting the loading rate to 5 mm / min to start the test, acquiring the load-displacement curve in real time, and analyzing the compressive strength to quantify the aging effect. The compressive strength is calculated based on the cross-sectional area of ​​the working section of the sample and the maximum load. The cross-sectional area is measured based on the sample's geometric dimensions or set according to standard sample specifications, and the maximum load is automatically recorded by the compression testing machine. Finally, through multiple tests and records, time-series performance test data are obtained, which reflect the trend of material properties changing over time.

[0071] More specifically, the overall effect is achieved by conducting performance parameter tests at preset aging time points to obtain time-series performance test data. For example, this includes the compressive strength values ​​of high-silica phenolic short fiber molded parts at different time points at 90℃, 110℃, 130℃, and 150℃. This captures the dynamic process of material performance degradation, providing time-series data support for establishing a performance degradation model. Specifically, temperature groups refer to experimental groups under different temperature conditions, such as 90℃, 110℃, 130℃, and 150℃ groups. Time-series performance test data refers to performance parameter data measured at different time points. Data alignment refers to organizing and arranging the time-series data from different temperature groups according to the temperature sequence to facilitate subsequent analysis.

[0072] Preferably, in this step, the specific operations include collecting performance test data for each temperature group at different time points, such as the compressive strength values ​​in Table 1; then sorting and organizing the data according to the temperature sequence from low to high temperature to ensure that the data for each temperature group matches the corresponding time point; for example, aligning the compressive strength data at 90℃, 110℃, 130℃, and 150℃ to their respective time series; finally, through systematic data alignment, performance degradation data arranged according to the temperature sequence is obtained, and these data can be corresponding to... Figure 2 The discrete data points of each curve can be directly used for performance degradation model fitting and lifetime prediction. More specifically, the overall effect is to obtain performance degradation data arranged in temperature sequence by aligning the data based on temperature groups, which facilitates the analysis of the impact of temperature on performance degradation and provides structured data input for building the Arrhenius model, thereby improving the accuracy of lifetime prediction.

[0073] S2. Construct a semi-empirical performance degradation model for composite material performance degradation based on performance degradation data;

[0074] In this embodiment, the construction of a semi-empirical performance degradation model for composite material performance degradation based on performance degradation data includes:

[0075] The performance degradation data is analyzed to obtain the material performance evolution characteristics of the performance degradation data; based on the material performance evolution characteristics, the competition mechanism is identified to obtain a competition mechanism model framework in which the enhancement effect and degradation effect of the material performance evolution characteristics are parallel.

[0076] A semi-empirical performance degradation model of the competition mechanism model framework is obtained by constructing a mathematical expression for the competition mechanism model framework; the parameters of the semi-empirical performance degradation model are initialized based on the statistical characteristics of the performance degradation data to obtain a semi-empirical performance degradation model with a physically meaningful initial value range.

[0077] In detail, performance degradation data refers to the quantitative record of the changes in the properties of composite materials over time under different temperature conditions obtained through accelerated aging tests, including mechanical property parameters such as compressive strength. Performance evolution analysis refers to the systematic analysis of performance degradation data to identify the trend characteristics of performance changes over time. Material performance evolution characteristics refer to the performance change patterns extracted from experimental data, including the characteristic manifestations of the performance enhancement stage and the performance degradation stage.

[0078] Preferably, in this step, the specific operational actions include first collecting performance degradation data under various temperature conditions, such as the compressive strength data of high-silica phenolic short fiber molded parts at 90℃, 110℃, 130℃, and 150℃ for 0 days, 10 days, 30 days, and 60 days; then plotting the curve of compressive strength versus aging time to observe the common pattern of performance changes at different temperatures. By analyzing the curve shape, the material performance evolution characteristics are identified, including the performance enhancement phenomenon in the early stage of aging and the subsequent performance degradation trend; for example, at 90℃, the compressive strength first increases from the initial value of 250.74MPa to 254.2MPa, and then gradually decreases to 213.6MPa; a similar pattern of first enhancement and then degradation is observed at different temperatures.

[0079] More specifically, the overall effect is to extract typical characteristics of material performance evolution from experimental data through performance evolution law analysis, providing a basis for subsequent competition mechanism identification and model construction. These characteristics reflect the inherent change law of composite materials during thermal aging.

[0080] To analyze compressive strength, the formula is as follows:

[0081]

[0082] in: Compressive strength; : Cross-sectional area of ​​the working section of the sample.

[0083] In this study, The values ​​are determined by actual measurement based on the specimen geometry, or set according to standard specimen specifications. The specimens are subjected to compression performance tests under different accelerated aging temperature conditions (e.g., 90℃, 110℃, 130℃, and 150℃), with the maximum load... The data was automatically recorded by the compression testing machine. Table 1 summarizes the compression performance test results under various test temperature conditions, reflecting the variation of compressive strength with aging time and temperature. This data provides a basis for subsequent performance degradation analysis and the establishment of a life prediction model.

[0084] In detail, material performance evolution characteristics refer to the performance change patterns extracted from experimental data, including the characteristic manifestations of performance enhancement and performance degradation stages. Competition mechanism identification refers to analyzing the physicochemical processes leading to performance changes and identifying competing mechanisms. Enhancement and degradation effects refer to two opposing effects existing simultaneously during material aging; the enhancement effect improves material performance, while the degradation effect reduces it. Preferably, in this step, specific operational actions include first analyzing the performance enhancement phenomenon in the material performance evolution characteristics and identifying the physical mechanisms leading to performance enhancement, such as the temporary increase in compressive strength caused by the crosslinking reaction in the early stages of aging of high-silica phenolic composite materials.

[0085] Then, the performance degradation phenomenon is analyzed, and the physical mechanisms leading to performance deterioration, such as molecular chain breakage and interfacial degradation, are identified. Next, a competitive mechanism model framework is established, describing the simultaneous and independent influence of these two effects on material properties during the aging process. Finally, a complete competitive mechanism model framework is formed, providing a theoretical foundation for the construction of mathematical expressions. More specifically, the overall effect is to establish a physical model framework that can explain experimentally observed phenomena through the identification of competitive mechanisms. This framework accurately describes the competitive relationship between reinforcement and degradation effects during the aging process of composite materials, laying the physical foundation for constructing a semi-empirical performance degradation model.

[0086] In detail, for high-silica phenolic short fiber composites, the regular degradation of their mechanical properties over time in long-term service environments constitutes the core of storage life assessment. To establish a physical-statistical coupling model based on measured aging data, and further quantify the storage life of materials under different stress and temperature fields, thus providing a theoretical basis for the reliability design of engineering structures, the following semi-empirical mathematical model is introduced:

[0087]

[0088] in: These are the initial values ​​for the material properties; This refers to the aging time. Indicates the aging time Performance values ​​below; , Describe the upper limit and rate of the enhancement effect; , This reflects the rate and curvature of performance degradation.

[0089] This model is essentially an abstract expression of the "competitive mechanism" aging process, where reinforcement and degradation mechanisms operate in parallel and independently during aging, and their superposition determines the remaining properties of the material. Preferably, the semi-empirical mathematical model refers to a mathematical expression constructed based on physical mechanisms and experimental data to describe the performance degradation process of composite materials. This formula represents the performance value as a linear combination of initial performance, reinforcement terms, and degradation terms. The reinforcement term captures the initial performance increase, while the degradation term describes the later decline in performance.

[0090] More specifically, the source and purpose of each factor in the formula are as follows:

[0091] Indicates the aging time The performance values, such as compressive strength, are the dependent variables of the model and are used to quantify the material's performance over aging time. The current state. The initial values ​​of material properties, such as the initial compressive strength of 250.74 MPa for high-silica phenolic short fiber molded parts, are determined experimentally and used as the model benchmark.

[0092] The aging time is the independent variable of the model, representing the exposure time of the material in the accelerated aging test, such as 0 days, 10 days, 30 days, and 60 days. , Describe the upper limit and rate of the enhancement effect, where Control the maximum magnitude of the enhancement. Adjusting the exponential saturation rate of enhancement terms affects the rapid climb of early performance improvements. , The rate and curvature that reflect performance degradation, among which Control the weight of the decay term. Adjusting the logarithmic gradual curvature of the attenuation term affects the slow accumulation of performance degradation in the later stages.

[0093] More specifically, the purpose of this formula is to abstractly represent the competition mechanism in the material aging process through mathematical form, and to enhance the term. The temporary performance improvement caused by the simulated cross-linking reaction, and the degradation term This simulation addresses performance degradation caused by molecular chain breakage. The overall effect is to provide a model framework that can fit experimental data, laying the foundation for subsequent variable transformations and parameter optimization.

[0094] In detail, the competition mechanism model framework refers to a physical model framework that describes the parallel effects of enhancement and degradation. Mathematical expression construction refers to the process of transforming the physical model into a mathematical formula. A semi-empirical performance degradation model is a mathematical model that combines physical mechanisms with experimental data.

[0095] Preferably, in this step, the specific operational actions include first, according to the competition mechanism model framework, expressing the enhancement effect as a mathematical expression, using an exponential saturation form to describe the upper limit and rate of performance enhancement; then, expressing the degradation effect as a mathematical expression, using a logarithmic form to describe the rate and curvature of performance degradation. Next, the enhancement and degradation terms are combined to form a complete performance degradation model; finally, the specific mathematical expression of the semi-empirical performance degradation model is obtained, which includes the initial values ​​of material properties, aging time, and parameters describing the enhancement and degradation effects.

[0096] Specifically, the performance degradation data of high-silica phenolic short fiber molded parts at different temperatures were fitted, and the resulting performance degradation model (i.e., the fitting curve) is as follows: Figure 4 As shown, it intuitively demonstrates the model's ability to capture experimental data (the change in compressive strength over aging time). Figure 4 Subplots (a), (b), (c), and (d) correspond to the fitting curves of compressive strength degradation under conditions of 90℃, 110℃, 130℃, and 150℃, respectively, verifying the applicability of the constructed model.

[0097] More specifically, the overall effect is achieved by constructing a mathematical expression that transforms the competition mechanism model framework into a computable mathematical model. This model accurately describes the evolution of composite material properties over time, particularly capturing the complex changes between early performance enhancement and later performance degradation. In detail, the statistical characteristics of performance degradation data refer to the numerical distribution characteristics of the experimental data, including statistics such as mean, variance, and extreme values. The parameters of the semi-empirical performance degradation model refer to the coefficients that need to be determined in the model, including parameters describing the enhancement and degradation effects. Initial value setting refers to setting a reasonable initial range of values ​​for the model parameters based on the characteristics of the experimental data.

[0098] Preferably, in this step, the specific operations include first analyzing the statistical characteristics of the performance degradation data, calculating the mean and range of compressive strength under various temperature conditions, and then setting initial values ​​for the parameters of the semi-empirical performance degradation model based on the data characteristics. For example, setting the upper limit of the enhancement effect parameter based on the magnitude of performance enhancement, and setting the initial value of the degradation effect parameter based on the rate of performance degradation.

[0099] Ensure that all parameters have clear physical meaning, such as the enhancement effect parameter reflecting the degree of cross-linking reaction and the degradation effect parameter reflecting the rate of molecular chain breakage; finally, obtain a semi-empirical performance degradation model with a physically meaningful initial value range, providing a good starting point for subsequent parameter optimization.

[0100] Specifically, after completing the model construction and parameter optimization process, an optimized semi-empirical performance degradation model was obtained based on the performance degradation data of high-silica phenolic short fiber molded parts at 90℃, 110℃, 130℃, and 150℃. The specific mathematical expression of this model (including the optimized parameters η, β, λ, α and the initial value P0) is listed in Table 2, namely, "Degradation Model of Compressive Strength of High-Silica Phenolic Short Fiber Molded Parts". This table summarizes the final quantifiable performance degradation model under different accelerated aging temperature conditions, which is a key output of the method of this invention applied to specific material systems.

[0101] Table 2. Model for compressive strength degradation of high-silica phenolic short fiber molded parts

[0102] More specifically, the overall effect is to ensure that the semi-empirical performance degradation model is physically reasonable and numerically stable by setting the initial values ​​of parameters based on statistical characteristics, thereby improving the convergence and efficiency of the subsequent parameter optimization process and laying the foundation for accurate lifetime prediction.

[0103] S3. Introduce a specific variable transformation method to transform the semi-empirical performance degradation model into a linear regression model;

[0104] In this embodiment, the introduction of a specific variable transformation method to transform the semi-empirical performance degradation model into a linear regression model includes:

[0105] The time variables in the semi-empirical performance degradation model are defined by a function transformation to obtain the time variable transformation relationship of the semi-empirical performance degradation model;

[0106] The transformation formula is: and

[0107] in, and For the nonlinear parameters to be determined, This refers to the aging time.

[0108] Based on the time variable transformation relationship, the semi-empirical performance degradation model is restructured to obtain a linear combination form of the semi-empirical performance degradation model; a linear regression model is identified from the linear combination form to obtain the linear regression model of the semi-empirical performance degradation model.

[0109] In detail, the identifiability of model parameters refers to the degree to which parameters can be uniquely determined within the model, while the stability of the fit refers to the model's ability to resist data fluctuations and noise interference during parameter estimation. Preserving the original structure of the degradation model means keeping the basic mathematical form of the semi-empirical performance degradation model unchanged, i.e., not changing the core physical meaning of the model. Time variable function transformation refers to converting aging time into new variables through mathematical operations to simplify the model structure.

[0110] Preferably, in this step, the specific operations include, to improve the identifiability and fitting stability of the model parameters, performing a functional transformation on the time variable while preserving the original structure of the semi-empirical performance degradation model, and defining two intermediate variables. This process, by introducing a transformation formula, converts the nonlinear model into a linear form, thereby enhancing the robustness and efficiency of parameter estimation. For example, for accelerated aging data of high-silica phenolic short fiber composite materials, this transformation helps solve the nonlinear optimization problem and improve the accuracy of lifetime prediction.

[0111] More specifically, the overall effect is that, through function transformation, model parameters are made easier to identify and estimate, reducing numerical instability during the fitting process. This provides a solid foundation for subsequent least squares and genetic algorithm optimization, ensuring the reliability of composite material storage life prediction. In detail, in this step, to improve the identifiability and fitting stability of model parameters, this paper performs a function transformation on the time variable while preserving the original structure of the degraded model, defining the intermediate variables as follows:

[0112] and

[0113] In detail, intermediate variables and By adjusting time variables The new variables obtained by performing mathematical transformations are used to linearize the original nonlinear model.

[0114] Preferably, the source and purpose of each factor in the formula are as follows: It is a nonlinear parameter to be determined, which controls the exponential saturation rate of the enhancement term and affects the rapid climb of early performance improvement. Genetic algorithms were used to optimize and capture the performance enhancement phenomenon of high silica-phenolic composite materials in the early stage of aging, such as the compressive strength increasing from the initial value of 250.74 MPa to 254.2 MPa.

[0115] It is a nonlinear parameter to be determined. Adjusting the logarithmic gradual curvature of the attenuation term affects the slow accumulation of performance degradation in the later stages. Similarly, genetic algorithms are used to optimize and describe the performance degradation of materials during long-term aging, such as the compressive strength decreasing to 213.6 MPa after 60 days. This refers to the aging time, which represents the duration of material exposure in accelerated aging tests, such as test points at 90℃, 110℃, 130℃, and 150℃ for 0 days, 10 days, 30 days, and 60 days, respectively. The transformation formula simplifies the model solution by performing exponential and logarithmic operations on the time variable, transforming the nonlinear dependency into a linearly fitable form.

[0116] More specifically, the overall effect is to transform the nonlinear terms in the original model into linear terms by defining intermediate variables, so that the model can be represented as a linear combination, which facilitates parameter estimation using the least squares method, thereby improving computational efficiency and the accuracy of model fitting.

[0117] Substituting this into the performance degradation model, it can be rewritten in the following form:

[0118]

[0119] in, Indicates the material in time Initial performance values ​​at that time and These correspond to the influence weights of the performance growth and decay terms, respectively. To improve the stability of the model solution, In this study, parameters determined experimentally are not treated as fitting parameters. Specifically, among them... Indicates the aging time The performance values, such as compressive strength, are given. Preferably, the source and purpose of each factor in the formula are as follows:

[0120] Indicates the material in time The initial performance values ​​are obtained through performance tests prior to accelerated aging to ensure the accuracy of the model baseline. For example, the initial compressive strength of the high-silica phenolic short fiber molded part is 250.74 MPa. In the document, Experiments have shown that these parameters are not treated as fitting parameters in order to improve the stability of the model solution. This is a linear parameter, corresponding to the weight of the performance growth term, describing the upper limit of the enhancement effect. In the document, The least squares method is used to solve for the magnitude of the performance enhancement, such as the maximum contribution of the enhancement term.

[0121] It is a linear parameter, corresponding to the influence weight of the performance degradation term, reflecting the rate of performance degradation. In the document, Similarly, the least squares method is used to solve for the degree of performance degradation, such as the dominant effect of the decay term. and These are intermediate variables, defined by the transformation formula, representing the transformed forms of the enhancement and attenuation terms, respectively. More specifically, the overall effect is to transform the nonlinear problem into a linear regression problem by rewriting the model, making the parameters... and The least squares method can be used to solve the problem quickly, thereby improving the solution efficiency and accuracy of the entire model and providing a reliable tool for predicting the storage life of composite materials.

[0122] S4. Solve the linear regression model using the least squares method to obtain the parameters η and β in the linear regression model;

[0123] In this embodiment, the step of solving the linear regression model using the least squares method to obtain the parameters η and β in the linear regression model includes:

[0124] The design matrix of the linear regression model is constructed based on the independent and dependent variables in the linear regression model; the design matrix is ​​then regularized to obtain the regularized design matrix.

[0125] Based on the regularized design matrix and the observed data vector, a least squares objective function is constructed to obtain the least squares optimization problem of the linear regression model; the least squares optimization problem is numerically solved to obtain the parameter solution vector of the linear regression model.

[0126] The linear parameters η and β are extracted from the parameter solution vector to obtain the linear parameters η and β in the linear regression model. The detailed overall process is as follows: at a given temperature Next, collect Group experimental data The corresponding triples can be calculated. The model predicts the following values:

[0127]

[0128] To ensure that the model predictions are as consistent as possible with the experimental values, the objective function of the residual sum of squares is constructed as follows:

[0129]

[0130] , ,

[0131] The covariance term is defined as:

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] According to the principle of least squares, let the partial derivative of the objective function with respect to the parameters be zero:

[0138]

[0139]

[0140] The analytical solution can be obtained by solving the system of equations:

[0141]

[0142] in Given the determinant of the covariance matrix, the uniqueness of the solution is guaranteed. Based on this solution, the model's predictions can be further calculated according to the mean relationship. : .

[0143] However, in this study, Since the experimental data is known, this formula is mainly used for result consistency verification or model back-calculation. To ensure the physical interpretability and stability of the model in practical engineering applications, the following constraints need to be imposed on the parameters:

[0144]

[0145] in, and Control the mapping curvature of the time variable; and These represent the dominant effects of performance growth and degradation mechanisms, respectively.

[0146] In detail, the model predictions are derived from the formula:

[0147]

[0148] In detail, Indicates the aging time point At this point, the model-predicted values ​​of composite material properties, such as compressive strength; These are the initial values ​​of material properties, determined experimentally, and are not used as parameters to be fitted. These are linear parameters, representing the influence weights of the performance growth mechanism and the degradation mechanism, respectively; These are intermediate variables obtained through variable transformation. Specifically, and ,in These are nonlinear parameters, optimized by a genetic algorithm. It refers to the aging time.

[0149] More specifically, in the context of composite material storage life prediction, this prediction model is used to describe the performance changes of high-silica phenolic short fiber molded parts during accelerated aging tests, such as the evolution of compressive strength over time at temperatures of 90°C, 110°C, 130°C, and 150°C. The calculation of the model's predicted values ​​is based on least squares fitting, which simplifies the parameter solution process by linearizing the nonlinear problem. Overall, this formula decomposes the complex performance degradation process into a linear combination, allowing for rapid parameter estimation via least squares, improving computational efficiency, and providing model support for subsequent life prediction. The residual sum of squares objective function is given by the formula... definition.

[0150] In detail, It is the sum of squared residuals, used to quantify the model's predicted values. Compared with experimental values Overall deviation between; It refers to the number of test data points, such as the number of samples at different aging time points in accelerated aging tests. These are the experimentally measured composite material properties, such as compressive strength, with specific values ​​obtained from Table 1.

[0151] More specifically, in the context of composite material storage life prediction, this objective function is used to ensure that the model is as consistent as possible with experimental data. This is achieved by minimizing... Parameters can be optimized. and The estimated value is used to accurately capture performance degradation trends. When constructing this function, it is first based on the triples after variable transformation. The residuals between predicted and experimental values ​​are calculated, and then the sum of squares of these residuals is taken to amplify the impact of larger errors and improve fitting accuracy. Overall, this objective function is the core of the least squares method. By minimizing the sum of squared residuals, the model can better fit the experimental data, providing a reliable description of the performance degradation of composite materials under high-temperature conditions and laying the foundation for extrapolating storage life at room temperature. The mean is calculated using the formula... and definition.

[0152] In detail, It is an intermediate variable The arithmetic mean, It is an intermediate variable The arithmetic mean, These are experimental values. The arithmetic mean; It represents the number of data points; the summation symbol. This indicates that all data points are summed. More specifically, in composite material storage life prediction environments, these means are used to center the data and reduce calculation bias. For example, in accelerated aging tests of high-silica phenolic short fiber molded parts, the mean value corresponding to each aging time point is first calculated according to the variable transformation formula. Then, their mean is calculated for use in the subsequent calculation of the covariance term. The mean reflects the central tendency of the dataset, which helps to simplify the solution process of the least squares method.

[0153] In terms of overall effectiveness, calculating the mean transforms the data into a decentralized form, facilitating the construction of the covariance matrix, improving the stability and accuracy of parameter estimation, and ensuring model consistency under different temperature conditions. The covariance term is expressed by the formula... definition.

[0154] In detail, It is a variable variance, a measure The degree of dispersion; It is a variable variance, a measure The degree of dispersion; It is a variable and The covariance describes the linear relationship between them; It is a variable and experimental values covariance, describing right The impact; It is a variable and experimental values covariance, describing The impact; among them .

[0155] More specifically, in the context of composite material storage life prediction, these covariance terms are used to quantify the correlations between variables, thereby constructing a system of linear equations in the least squares solution. For example, calculating these terms based on aging test data at a given temperature can capture the interaction between enhancement and degradation mechanisms during performance degradation. In the calculation, the data is first centered using the mean, and then the sum of squares or product sums are calculated. Overall, the covariance terms form the basis of the least squares analytical solution, from which parameters can be derived. and The expression ensures the mathematical rigor of the model fit and provides support for subsequent optimization of nonlinear parameters using genetic algorithms. The partial derivatives are zero according to the formula. Provided.

[0156] In detail, It is the sum of squared residuals For parameters The partial derivatives, It is the sum of squared residuals For parameters The partial derivatives; setting these partial derivatives to zero is based on the least squares principle, minimizing the residual sum of squares by solving for the extreme points. More specifically, in the context of composite material storage life prediction, this step is crucial for parameter estimation. First, the residual sum of squares function... Regarding respectively Taking partial derivatives yields two equations; then, these equations are combined to form a system of linear equations, allowing for analytical solution of the parameters. This process ensures the optimality of the model parameters, minimizing the error between predicted and experimental values.

[0157] In terms of overall effectiveness, by using the condition that the partial derivatives are zero, the nonlinear optimization problem is transformed into a linear solution, which improves computational efficiency and provides a theoretical basis for the least squares part of the hybrid optimization strategy, ensuring the accuracy of the composite material performance degradation model.

[0158] Analytical solution from formula .

[0159] In detail, These are estimates of the linear parameters; It is a variable and experimental values The covariance, i.e. ; It is a variable and experimental values The covariance, i.e.

[0160] ; and It is the aforementioned covariance term; This is the determinant of the covariance matrix, used to ensure the uniqueness of the solution. More specifically, in the context of composite material storage life prediction, this analytical solution directly provides parameter values ​​through algebraic operations, avoiding iterative calculations. For example, in fitting high-silica phenolic short fiber molded parts, the covariance term is calculated using accelerated aging test data, and then substituted into the formula to solve. This process is based on the principle of least squares, ensuring that parameter estimation is unbiased and efficient.

[0161] In terms of overall performance, the analytical solution provides a fast estimate of linear parameters, simplifying the model fitting process. Combined with the genetic algorithm to optimize nonlinear parameters, a hybrid optimization strategy is formed, improving the accuracy and reliability of composite material storage life prediction. The initial values ​​of the model are given by the formula... Calculation. In detail, These are the initial values ​​of the material properties; These are experimental values. The mean; These are the linear parameters that have already been solved; It is the mean of the intermediate variables.

[0162] More specifically, in the context of composite material storage life prediction, this formula is used to inversely deduce from parameter estimation results. However, in this invention, Since the experimental data is known (e.g., the initial compressive strength is obtained from Table 1), this calculation is primarily used for model consistency checks or backtesting. For example, after fitting is complete, this formula can be used to check... To assess model reliability, this step checks whether the values ​​match experimental values. Overall, this step ensures the inherent consistency of model parameters, enhances physical interpretability, and provides a foundation for failure time calculations in subsequent lifetime predictions. The parameter constraints are as follows: .

[0163] In detail, These are the initial values ​​of material properties and must be positive to represent actual strength. These are linear parameters, representing the dominant effects of performance growth and degradation mechanisms, respectively, with positive constraints ensuring the correct physical meaning; It is a nonlinear parameter that controls the mapping curvature of the time variable, and positive constraints ensure the effectiveness of variable transformation.

[0164] More specifically, in the context of composite material storage life prediction, these constraints are used to ensure the physical interpretability and numerical stability of the model in practical engineering applications. For example, in the degradation model of high-silica phenolic short fiber molded parts, positive parameters ensure that performance values ​​do not exhibit non-physical negative values, and transforming variables... The parameters change monotonically with aging time. When applying constraints, the parameters are checked after the least squares solution or verified during the validation phase. Overall, parameter constraints enhance the robustness of the model, prevent overfitting or non-physical solutions, and ensure the reliability and practicality of the prediction results in the assessment of the storage life of composite materials.

[0165] In detail, the design matrix contains independent variables. The matrix form is used to represent the structure of the linear model. More specifically, in the composite material storage life prediction environment, a design matrix is ​​first constructed based on the transformed data, where each row corresponds to an experimental point and the columns correspond to variables. Thus, the model This is represented as a matrix equation. This step organizes the data to provide input for the least squares solution. Overall, designing the matrix simplifies the computation and facilitates subsequent regularization and numerical solutions.

[0166] In detail, regularization improves the condition number of the matrix by adding regularization terms, preventing overfitting or numerical instability. More specifically, in the context of composite material storage life prediction, experimental data may contain noise or multicollinearity, such as under high-temperature accelerated aging conditions where performance data fluctuates significantly. Regularization improves the stability of the solution by adjusting the matrix eigenvalues. This step may use Tikhonov regularization or similar methods. Overall, regularization ensures the robustness of parameter estimation, enabling the model to reliably fit even under sparse data conditions.

[0167] In detail, the least squares objective function is in matrix form of the sum of squared residuals, i.e. ,in It is a design matrix. It is a parameter vector. This is the observed data vector. More specifically, in the context of composite material storage life prediction, this function is constructed based on experimental data and minimizes prediction error through regularized matrix calculations. Overall, this step transforms the problem into a convex optimization problem, ensuring the existence of a global optimum, which facilitates numerical solution. In detail, numerical solution involves calculating the parameter vector using algorithms such as normal equations or QR decomposition. .

[0168] More specifically, in the context of composite material storage life prediction, numerical methods are used to solve linear systems, such as analytical solutions based on covariance terms or iterative algorithms, to obtain... The estimated values ​​are obtained. This step ensures efficient and accurate computation, especially suitable for large-scale data. Overall, the numerical solution provides specific numerical values ​​for the parameters, laying the foundation for model prediction and subsequent optimization. Linear parameters are extracted from the parameter solution vector. To obtain the linear parameters in the linear regression model .

[0169] In detail, the parameter solution vector Include and The estimated values ​​are extracted and directly used in the linear model. More specifically, in the context of composite material storage life prediction, this step is the final output of the least squares method, for example, the performance degradation model parameters at various temperatures are given in Table 2. After extraction, the parameters are used to calculate the predicted values ​​and perform model validation. Overall, this step completes the parameter estimation of the linear part, and combined with the nonlinear parameters optimized by the genetic algorithm, achieves hybrid optimization, improving the overall accuracy of composite material storage life prediction.

[0170] S5. Based on the genetic algorithm, global optimization is performed on the nonlinear parameters λ and α to be determined to obtain the optimized nonlinear parameters λ and α. Based on the optimized nonlinear parameters, the error between the model output and the experimental data is minimized.

[0171] In this embodiment, the global optimization of the nonlinear parameters λ and α based on the genetic algorithm yields optimized nonlinear parameters λ and α. The error between the output of the model and the experimental data is minimized based on the optimized nonlinear parameters, including:

[0172] Population initialization is performed on the value space of nonlinear parameters λ and α, with the population size set to 15 individuals to obtain an initial population; selection, crossover, and mutation operations are performed on the initial population, with the crossover probability set to 0.8 and the mutation probability set to 0.2 to obtain a new generation population;

[0173] The fitness of the new generation population is evaluated to obtain the optimal individual in the population; the values ​​of nonlinear parameters λ and α are extracted from the optimal individual to obtain the optimized nonlinear parameters λ and α.

[0174] In detail, population initialization is the starting step for the genetic algorithm to perform a global search. Specifically, this invention addresses the optimization of nonlinear parameters in the problem of predicting the storage life of composite materials, and sets up an initial population containing fifteen parameter individuals.

[0175] Each individual is composed of a pair of nonlinear parameters λ and α. λ is a parameter that regulates the exponential saturation rate of the performance enhancement term and affects intermediate variables. The rapid increase in α is the dominant factor in the early performance improvement of composite materials. α is a parameter that adjusts the logarithmically gradual curvature of the performance degradation term, affecting intermediate variables. The slow growth is used to capture the cumulative degradation of composite material properties in later stages. These individuals are generated through uniform random sampling within pre-defined physical constraint boundaries.

[0176] The typical range of λ is 0.01 to 10, ensuring that the model can cover different aging timescales of composite materials, from short-term rapid changes to long-term slow evolution. The typical range of α is 0.001 to 1, and the primary purpose of this constraint is to ensure the function in variable transformations:

[0177]

[0178] It is valid within its domain, preventing singularities in the logarithmic function. Through the above operations, an initial population with diversity within the feasible solution space is obtained, laying the foundation for simulating biological evolution to find the global optimum.

[0179] Preferably, the initial population undergoes selection, crossover, and mutation operations, with the crossover probability set to 0.8 and the mutation probability set to 0.2, to obtain a new generation population. Selection, crossover, and mutation are the core operations driving population evolution, aiming to improve the fitness of individuals in the population through iteration. In this invention, the crossover probability is set to 0.8, meaning that when generating offspring individuals, there is an 80% probability that some parameter codes of two parent individuals will be exchanged. This setting aims to strengthen the transmission and combination of excellent genetic traits and promote the diffusion of information about superior solutions in the population.

[0180] The mutation probability is set to 0.2, meaning that when generating offspring individuals, there is a 20% probability of randomly perturbing the individual's parameter encoding. This operation aims to introduce new genetic characteristics into the population, enhance the algorithm's ability to explore the parameter space, and prevent the algorithm from prematurely converging to a local optimum and falling into a local trap. This invention employs a tournament selection mechanism to maintain population diversity and avoid premature convergence. Through this series of selection, crossover, and mutation operations, the initial population evolves, producing a new generation. More specifically, the fitness of this new generation is evaluated to obtain the optimal individual in the population. Fitness evaluation is a crucial step in measuring the quality of each individual in the population; its standard is whether the parameter value corresponding to the individual minimizes the error between the model's predicted value and the measured value in the accelerated aging experiment of the composite material. Specifically, the fitness function is defined as the residual sum of squares objective function:

[0181]

[0182] in, , The objective function The model's predicted values ​​and measured performance values ​​were directly quantified after linearization by variable transformation. The overall deviation between them. For each individual in the population, i.e., each specific group First, fix the parameter combination and calculate all corresponding aging time points. Transformation variables .

[0183] Subsequently, construction Design Matrix Furthermore, it uses embedded non-intercept linear regression to help predict the optimal linear parameters at this point. ,

[0184] The calculation formula is as follows:

[0185]

[0186] The obtained And the calculations derived therefrom Substitute them together into the objective function Calculate its value .this The value represents the fitness of the individual in the problem of predicting the storage life of composite materials involved in this invention. The smaller the value, the better for this set of parameters. The better the fitness value, the smaller the error between the model output and the experimental data. By comparing the fitness values ​​of all individuals in the population, the optimal individual in the current population, corresponding to the minimum fitness value, can be identified. The set of parameters with values. Because the parameters λ and α are implicitly coupled through nonlinear transformations, the optimization problem exhibits non-convex multimodal characteristics. Therefore, this population-level global search strategy of the genetic algorithm is significantly better than the single-point gradient method.

[0187] In detail, this step is the final output stage of the genetic algorithm optimization process. After a set number of iterations or when the convergence criterion is met, the algorithm terminates. At this point, the values ​​of λ and α are extracted from the individual with the best fitness in the final generation population, or from the best individual recorded throughout the entire evolutionary history. These extracted values ​​are the optimization nonlinear parameters obtained from the global optimization process. The mathematical expression of this process is to find the objective function. Minimize the combination of parameters:

[0188]

[0189] get Then, the nonlinear component in the composite material performance degradation model was fixed. Specifically, the optimized nonlinear parameters were obtained. Subsequently, independent non-intercept linear regression was introduced to accurately solve for the linear parameters. This step is a crucial one in the hybrid optimization strategy, immediately following the global optimization of the genetic algorithm. Its aim is to accurately determine the linear parameters in the composite material performance degradation model. Specifically, the nonlinear parameters obtained by the genetic algorithm optimization are first fixed. and Subsequently, all aging time points were recalculated using these two parameters. Corresponding intermediate variables .

[0190] Next, construct It should be noted that in the design matrix, The symbols corresponding to the columns and those in the model The terms match. The final linear regression model is expressed as follows: ,in It is the measured performance vector. The initial properties of the material are known. The optimal linear parameters can be obtained in one step by solving the following matrix equation:

[0191]

[0192] This formula is an analytical solution for non-intercept multiple linear regression, which can efficiently and accurately determine the weights of the enhancement terms simultaneously. and the weight of the decay term .

[0193] Preferably, matrix The positive definiteness is determined by the intermediate variable. The mathematical properties of the matrix ensure this. The invertibility and positive definiteness of the matrix are the mathematical basis for the existence and uniqueness of the linear regression solution. In this invention, this property is ensured by the intermediate variable. This is guaranteed by the mathematical properties of the variables. Specifically, the variables... It is the aging time. The function whose derivative with respect to time is... Always greater than zero, which indicates It is a function that is strictly monotonically increasing with time.

[0194] variable Similarly, aging time The function whose derivative with respect to time It is also always greater than zero, which indicates that It is also a strictly monotonically increasing function over time. The strict monotonicity of these two variables, and their typically low correlation, ensures the design matrix... The full rank property of the matrix ensures that the matrix has a column rank. It is an invertible positive definite matrix such that the analytical solution of the linear parameters is... and It can solve problems stably and reliably. Among them, The weights of the performance enhancement effect were quantified, and their upper limits were set. With saturation rate Synergistic effect; This characterizes the weight of the performance degradation effect and its degradation rate. With curvature parameters Mutual balance.

[0195] More specifically, in obtaining the complete parameter set Subsequently, the composite material performance degradation model was constructed. This model was then used for prediction. Specifically, each aging time point was... Substitute the values ​​into the model to calculate the corresponding performance predictions. This forms a complete prediction sequence. The calculation formula is:

[0196]

[0197] in By fixed The results were obtained through calculation. To objectively evaluate the goodness of fit between the prediction model and the experimental data, i.e., the model's goodness of fit and prediction accuracy, three key validation statistics need to be calculated: the coefficient of determination. This is used to measure the extent to which a model explains the variability of experimental data, and its calculation formula is:

[0198]

[0199] Root mean square error This is used to quantify the average deviation between model predictions and experimental values, and its calculation formula is:

[0200]

[0201] Mean Absolute Error It is also used to quantify prediction error, but it is less sensitive to outliers than RMSE. Its calculation formula is:

[0202]

[0203] These statistical indicators collectively provide a quantitative basis for evaluating the accuracy and reliability of the established composite material performance degradation model. Specifically, to ensure that the composite material storage life prediction model is not only mathematically valid but also physically reliable, and to guarantee the numerical stability of the calculation process, strict constraints must be imposed on all model parameters. These constraints specifically include:

[0204]

[0205] These constraints have clear physical and mathematical significance. This indicates that the initial properties of the composite material must be positive. This ensures that the performance enhancement effect is a positive, saturated process. This ensures that the performance degradation effect is a positive and gradual process. Specifically, constraints... In practice, by setting It is crucial, as it directly guarantees the transformation of variables. The logarithmic function in this model avoids mathematical singularities caused by parameters being zero or negative, ensuring the physical validity of the transformation. This genetic algorithm framework is designed for nonlinear target objects. The optimization, by embedding the aforementioned physical constraints, significantly improves the robustness of the model and independently constructs a coupled model that combines physical meaning with statistical methods, providing a powerful parameter optimization tool for predicting the storage life of composite materials.

[0206] S6. Based on the performance degradation model optimized by the linear parameters η and β and the optimized nonlinear parameters λ and α, and the preset failure criteria, calculate the material failure time under each temperature condition.

[0207] In this embodiment, the calculation of material failure time under various temperature conditions based on the performance degradation model optimized by the linear parameters η and β and the optimized nonlinear parameters λ and α, and the preset failure criterion, includes:

[0208] Based on the strength requirements of fiber-reinforced composite materials in the national standard GB1447-2005, the material performance failure threshold is set to 100MPa, and the preset failure criterion is obtained.

[0209] Substituting the failure criterion into the performance degradation model that includes the linear parameters η and β, as well as the optimized nonlinear parameters λ and α, yields the performance termination equation regarding aging time; numerically solving the performance termination equation yields the material failure time under various temperature conditions.

[0210] In detail, based on the strength requirements of fiber-reinforced composite materials in the national standard GB1447-2005, the material performance failure threshold is set to 100MPa, and the preset failure criterion is obtained.

[0211] Failure criteria are key standards for determining whether a composite material has reached its end-of-life. Specifically, this invention sets a clear performance failure threshold based on the relevant provisions of the national standard GB1447-2005 regarding the strength of fiber-reinforced composite materials. This standard provides a basis for ensuring the safety and reliability of materials in engineering applications.

[0212] In a specific embodiment of the present invention for high-silica phenolic composite materials, the failure threshold is set to 100 MPa. This means that when the properties of the composite material, such as compressive strength, decrease to 100 MPa during aging, the material is considered to no longer meet the usage requirements and has reached the end of its service life. This threshold setting provides a unified and objective benchmark for the subsequent accurate calculation of the material's failure time under different temperature conditions.

[0213] Preferably, the failure criterion is substituted into a performance degradation model that includes the linear parameters η and β, as well as the optimized nonlinear parameters λ and α, to obtain a performance termination equation regarding aging time. After obtaining a clear failure criterion, it needs to be combined with the established and optimized performance degradation model. Specifically, the performance degradation model is:

[0214]

[0215] in, These are the initial property values ​​of the material. The optimization parameters are obtained through the aforementioned hybrid optimization algorithm combining genetic algorithm and least squares method. The failure criterion, i.e., the performance threshold, is set. MPa, substitute into the model, let Thus, we obtain information about aging time. The equation:

[0216]

[0217] This equation is the performance termination equation, and its solution represents the aging time corresponding to the material's performance degradation to the failure threshold. Because this equation combines exponential and logarithmic terms, it is a complex nonlinear equation and cannot be solved analytically directly; numerical methods are required. More specifically, the performance termination equation is solved numerically to obtain the material failure time under various temperature conditions. Numerical solution is the key calculation step for obtaining the specific failure time of the material at each test temperature. Specifically, for each accelerated aging test temperature, such as 90℃, 110℃, 130℃, and 150℃, there is a set of independently optimized model parameters. For each temperature, substitute its corresponding optimized parameters into the performance termination equation described above.

[0218] Subsequently, numerical solution algorithms, such as the bisection method or Newton's iteration method, are used to search for roots satisfying the equation in the time domain. This root This represents the aging time required for the composite material's properties to degrade to the 100 MPa failure threshold under a specific temperature condition, i.e., the material failure time at that temperature. This method allows for the systematic calculation of the failure time corresponding to all accelerated aging temperatures.

[0219] Specifically, the failure times of the high-silica phenolic composite material calculated above at four accelerated aging temperatures of 90℃, 110℃, 130℃, and 150℃ were summarized to form a table of "pseudo-failure lifetime under accelerated aging conditions," namely Table 3. As shown in Table 3, the corresponding material failure times at 90℃, 110℃, 130℃, and 150℃ are approximately 708.67 days, 227.48 days, 114.04 days, and 65.82 days, respectively. This table clearly and quantitatively demonstrates the accelerating effect of temperature on material failure time, providing a core data sequence for the subsequent establishment of the Arrhenius model.

[0220] Table 3. Pseudo-failure lifetime under accelerated aging conditions

[0221] In detail, the calculated material failure times under various temperature conditions play a crucial role in bridging the gap between earlier and later calculations. These short-term failure data obtained at different high temperatures directly reflect the accelerating effect of temperature on the material aging rate. Specifically, these failure time data will be correlated with the reciprocal of the corresponding absolute temperature. Together, they are used to fit the Arrhenius model. This establishes a quantitative relationship between temperature and lifespan.

[0222] Finally, through this extrapolation model, the long-term storage life of the composite material under ambient temperature storage conditions, such as 25 degrees Celsius, can be predicted. In the high-silica phenolic composite material embodiment of the present invention, the extrapolated predicted ambient temperature storage life is 23,809.08 days, equivalent to 65.19 years. This result fully demonstrates the effectiveness and engineering application value of the method of the present invention in predicting the storage life of composite materials.

[0223] S7. Based on the material failure time under the aforementioned temperature conditions, perform linear regression using the least squares method to fit the Arrhenius model parameters, establish the Arrhenius model, and establish the temperature-lifetime relationship based on the Arrhenius model.

[0224] In this embodiment, the Arrhenius model parameters are obtained by performing linear regression on the material failure time under each temperature condition and the least squares method, and an Arrhenius model is established. Based on the Arrhenius model, the temperature-lifetime relationship is established, including:

[0225] The material failure time series under each temperature condition are subjected to Arrhenius coordinate transformation, converting the thermodynamic temperature T to the reciprocal coordinate 1 / T and the failure time L to the logarithmic coordinate ln(L), resulting in a linearized data point set in the Arrhenius coordinate system. Based on the linearized data point set in the Arrhenius coordinate system, the least squares method is used to perform linear regression analysis to obtain the numerical solutions of the Arrhenius model parameters A and B.

[0226] Substituting the Arrhenius model parameters A and B into the Arrhenius model mathematical expression, a complete temperature-lifetime mathematical relationship model is established; the specific form of the Arrhenius model is as follows:

[0227]

[0228] in, Indicates the storage life of composite materials. The thermodynamic temperature during material storage. , These are the parameters to be determined by fitting experimental data;

[0229] The fitting accuracy of the established temperature-lifetime mathematical model was verified, and a valid Arrhenius temperature-lifetime mathematical model was obtained, thus completing the establishment of the relationship between temperature and lifetime.

[0230] The relationship between temperature and lifespan is as follows:

[0231]

[0232] in, For lifespan, Thermodynamic temperature , The parameters are obtained by fitting the experimental data.

[0233] In detail, the material failure time series under each temperature condition are subjected to Arrhenius coordinate transformation, converting the thermodynamic temperature T into reciprocal coordinates. Convert the failure time L to logarithmic coordinates This yields a linearized set of data points in the Arrhenius coordinate system.

[0234] Coordinate transformation is the first step in establishing the Arrhenius model. Its purpose is to convert the nonlinear temperature-life relationship into a linear one to facilitate regression analysis. Specifically, firstly, the material failure times under various temperature conditions calculated using the performance degradation model and failure criteria are aggregated. Next, two crucial coordinate transformations are performed: First, each test temperature is converted from Celsius to thermodynamic temperature in Kelvin, and then its reciprocal is calculated. .

[0235] The second step is to take the natural logarithm of the failure time L corresponding to each temperature. After this transformation, the original nonlinear data points The data points are transformed into a set that is expected to be linearly distributed in the Arrhenius coordinate system. This prepares the ground for subsequent linear regression. The results of this coordinate transformation and the subsequent fitted linear relationship have been visualized. Figure 3 In the (Arrhenius model fitting effect diagram), the scatter points represent the transformed experimental data points (1 / T, ln(L)).

[0236] Preferably, based on the linearized data point set in the Arrhenius coordinate system, the least squares method is used to perform linear regression analysis to obtain the numerical solutions of the Arrhenius model parameters A and B.

[0237] Linear regression analysis is the core step in determining the specific parameters of the Arrhenius model using transformed data. Specifically, the mathematical expression of the Arrhenius model under transformed coordinates is:

[0238]

[0239] This is a univariate linear equation. The least squares method is used to fit this linearized data set, with the goal of finding a straight line that minimizes the sum of the squares of the perpendicular distances (i.e., residuals) from all data points to this line. The optimal numerical solutions for model parameters A and B can be obtained using the standard least squares calculation procedure. Parameter A represents the intercept of the line, an empirical constant related to the material itself and the aging reaction mechanism. Parameter B represents the slope of the line, its physical meaning related to the activation energy of the aging reaction, specifically: ,in The activation energy for the aging reaction. Here, represents the Boltzmann constant. In a specific embodiment of the invention, the value of parameter A is obtained as 1.17 and the value of parameter B is 6044.90 through fitting, thus yielding the specific Arrhenius equation:

[0240]

[0241] The fitting process and the resulting straight line (i.e., the fitting model) have been... Figure 3 As clearly shown in the figure, the straight line is the Arrhenius fitting line drawn based on the parameters mentioned.

[0242] More specifically, by substituting the Arrhenius model parameters A and B into the Arrhenius model mathematical expression, a complete temperature-lifetime mathematical relationship model is established. After obtaining the accurate model parameters A and B, a temperature-lifetime relationship model that can be used for quantitative prediction can be constructed. Specifically, the numerical values ​​of the solved parameters A and B are substituted into the standard mathematical expression of the Arrhenius model:

[0243]

[0244] Thus, a complete and parameter-defined temperature-lifetime mathematical model was established. This model clearly reveals the quantitative relationship between the storage life L of the composite material and its ambient thermodynamic temperature T: the logarithm of the lifespan. The reciprocal of thermodynamic temperature The relationship is linear. This model is based on accelerated aging experimental data (high temperature, short lifespan), but its significance lies in its ability to extrapolate and predict the long-term storage life of materials at lower temperatures (such as room temperature) based on this relationship. In detail, the fitting accuracy of the established temperature-lifespan mathematical relationship model is verified, resulting in a validated Arrhenius temperature-lifespan mathematical model, thus completing the establishment of the temperature-lifespan relationship.

[0245] Model validation is a necessary step to ensure the reliability and accuracy of the established temperature-lifetime relationship. Specifically, it is necessary to validate the fitting accuracy of the Arrhenius model obtained in the aforementioned steps. In an embodiment of the present invention, by analyzing the data points and the fitted line, the coefficient of determination R² = 0.9841 is calculated. Figure 3 As indicated by the annotation, this value is extremely close to 1, indicating that the fitted line can explain more than 98% of the variability in the experimental data, thus confirming that the model has high fitting accuracy and passes the verification. Finally, the relationship between temperature and lifetime was established as follows:

[0246]

[0247] Where L represents lifetime, T represents thermodynamic temperature, and A and B are parameters obtained by fitting experimental data. The establishment of this validated Arrhenius temperature-lifetime mathematical model marks the successful construction of a quantitative relationship between temperature and lifetime. It provides a core theoretical foundation and computational tool for extrapolating high-temperature accelerated aging test results to room-temperature conditions and achieving accurate prediction of the room-temperature storage lifetime of composite materials.

[0248] S8. Predict the storage life of composite materials at room temperature based on the temperature-life relationship.

[0249] In this embodiment, predicting the storage life of the composite material at room temperature based on the temperature-lifetime relationship includes:

[0250] Substitute the room temperature storage temperature into the verified Arrhenius temperature-life mathematical model to calculate the theoretical storage life of the composite material at room temperature and obtain the theoretical life value at room temperature; perform local sensitivity analysis on the Arrhenius temperature-life mathematical model to identify key parameters affecting the accuracy of life prediction and obtain the sensitivity ranking of key parameters.

[0251] Based on the sensitivity ranking of the key parameters, Monte Carlo simulation is used to perform multiple random samplings to calculate the statistical distribution of the model prediction results and obtain the lifetime prediction confidence interval. Based on the theoretical lifetime value at room temperature and the lifetime prediction confidence interval, a reliability assessment is performed to obtain a room temperature storage lifetime prediction result with guaranteed reliability.

[0252] In detail, calculating the theoretical lifetime value at room temperature is the core output step of lifetime prediction. Specifically, the actual room temperature of the composite material during storage is substituted into the validated Arrhenius temperature-lifetime mathematical model for calculation. The specific form of the Arrhenius model is as follows: ,in For lifespan, Thermodynamic temperature These are the model parameters obtained by fitting accelerated aging test data.

[0253] In the embodiment of the high-silica phenolic composite material of the present invention, the room temperature storage temperature is set to 25 degrees Celsius, which translates to a thermodynamic temperature of 298 Kelvin. and the parameters obtained from the fitting , Substituting into the model, the calculation process is as follows:

[0254]

[0255] Calculation After obtaining the value, the lifespan is obtained by inverse calculation using exponentiation. This yields the theoretical storage life of the composite material at room temperature. A visual representation of this prediction is shown below. Figure 5 As shown in the figure (prediction of lifetime of high-silica phenolic resin at different temperatures), the predicted lifetime at 25°C (298 K) is clearly marked as 23809.08 days (65.19 years). This figure is the final visualization result of the Arrhenius model extrapolating from high temperature to room temperature prediction.

[0256] Preferably, local sensitivity analysis is an important means of evaluating model reliability and identifying key influencing factors. Specifically, for the established Arrhenius model... Local sensitivity analysis was performed. This analysis aimed to quantify the model input parameters, including the model parameters. and invalidation criteria When small changes occur, the output result, i.e., the predicted lifetime, is affected. The degree of influence. Local sensitivity can be assessed by calculating the partial derivative of the output lifetime with respect to each input parameter. The larger the absolute value of the sensitivity coefficient, the more significant the impact of the uncertainty of that parameter on the final lifetime prediction result.

[0257] By comparing the sensitivity coefficients of each parameter, a ranking of the sensitivity of key parameters can be obtained. For example, the analysis results may show the parameters... The sensitivity is the highest, followed by the parameter. The invalidation criterion This could also be an important influencing factor. This ranking clarifies the core parameters that need to be focused on in model application and subsequent uncertainty quantification, pointing the way to optimizing prediction accuracy.

[0258] More specifically, Monte Carlo simulation is a crucial step in quantifying the statistical uncertainty of lifetime prediction results. Specifically, based on the key parameters identified through the aforementioned sensitivity analysis, their probability distribution characteristics are defined. For example, assuming key parameters... and The parameters follow a normal distribution with a mean of 0.5 and a certain standard deviation. Subsequently, Monte Carlo simulation is used to perform thousands of random samplings within the distribution range of the key parameters.

[0259] For each sampling, a random combination of parameters is generated and substituted into the Arrhenius model to calculate a corresponding room-temperature storage lifetime value. By repeating this process extensively, a large set of predicted room-temperature storage lifetime values ​​can be obtained, which constitutes the statistical distribution of the predicted lifetime. Based on this distribution, its statistical characteristics, such as the mean, median, and percentiles, can be calculated. Finally, by taking specific percentiles, such as 2.5% and 97.5%, a 95% confidence interval is determined. This confidence interval, in the form of a numerical range, quantifies the range of uncertainty that the theoretical room-temperature storage lifetime value may fluctuate, providing important statistical reliability information for the prediction results.

[0260] In detail, reliability assessment is the final step in integrating point estimation and uncertainty information to arrive at the final engineering applicability conclusion. Specifically, the calculated theoretical lifespan at room temperature is used as the most probable lifespan prediction, while the lifespan prediction confidence interval obtained from Monte Carlo simulation is used as the reliability boundary of this prediction. The final prediction result should report both of these parts simultaneously.

[0261] For example, it can be stated that the predicted storage life of high-silica phenolic composite materials at room temperature of 25 degrees Celsius is about 65.19 years, and at a 95% confidence level, its lifespan confidence interval is several years to several years. Figure 5 The key prediction results based on the Arrhenius model are presented graphically, showcasing the temperature-lifetime relationship curves extrapolated from high-temperature accelerated aging conditions (such as 90℃, 110℃, 130℃, and 150℃). The predicted lifetime point corresponding to room temperature (25℃) is clearly marked on the curves. This presentation not only provides a clear lifetime expectation but, more importantly, reveals the inherent uncertainty of the prediction through confidence intervals, offering a scientific basis for engineering decision-makers to assess risks, formulate maintenance strategies, or set safety factors.

[0262] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0263] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0264] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the storage life of composite materials based on variable transformation and genetic algorithm, characterized in that, The method includes: S1. The composite material samples were treated under different temperature conditions, and the performance degradation data related to the composite material properties were collected in real time. S2. Construct a semi-empirical performance degradation model for composite material performance degradation based on performance degradation data; S3. Introduce a specific variable transformation method to transform the semi-empirical performance degradation model into a linear regression model; S4. Solve the linear regression model using the least squares method to obtain the parameters η and β in the linear regression model; S5. Based on the genetic algorithm, global optimization is performed on the nonlinear parameters λ and α to be determined to obtain the optimized nonlinear parameters λ and α. Based on the optimized nonlinear parameters, the error between the model output and the experimental data is minimized. S6. Based on the performance degradation model optimized by the linear parameters η and β and the optimized nonlinear parameters λ and α, and the preset failure criteria, calculate the material failure time under each temperature condition. S7. Based on the material failure time under the aforementioned temperature conditions, perform linear regression using the least squares method to fit the Arrhenius model parameters, establish the Arrhenius model, and establish the temperature-lifetime relationship based on the Arrhenius model. S8. Predict the storage life of composite materials at room temperature based on the temperature-life relationship.

2. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1, characterized in that, The process of treating composite material samples under different temperature conditions and collecting performance degradation data related to the composite material properties in real time includes: Standard specimens of the composite material were prepared and initial performance tests were performed to obtain a set of specimens with initial performance parameters. Based on a preset temperature profile, the sample group is subjected to temperature grouping and accelerated aging treatment to obtain aged sample groups under different temperature conditions. At preset aging time points, the performance parameters of the aging sample group are tested to obtain time-series performance test data. The time-series performance test data are aligned based on temperature groups to obtain performance degradation data arranged in temperature sequence. The performance degradation data includes mechanical performance data, thermal performance data, and electrical performance data.

3. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1, characterized in that, The semi-empirical performance degradation model for composite material performance degradation based on performance degradation data includes: The performance degradation data is analyzed to determine the material property evolution characteristics. Based on the material performance evolution characteristics, a competition mechanism identification is performed to obtain a competition mechanism model framework in which the enhancement effect and degradation effect of the material performance evolution characteristics are parallel. A semi-empirical performance degradation model of the competition mechanism model framework is obtained by constructing a mathematical expression for the competition mechanism model framework. Based on the statistical characteristics of the performance degradation data, the parameters of the semi-empirical performance degradation model are initialized to obtain a semi-empirical performance degradation model with a physically meaningful initial value range.

4. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1, characterized in that, The method of introducing specific variable transformation to convert the semi-empirical performance degradation model into a linear regression model includes: The time variables in the semi-empirical performance degradation model are defined by a function transformation to obtain the time variable transformation relationship of the semi-empirical performance degradation model; The transformation formula is: and in, and For the nonlinear parameters to be determined, This refers to the aging time. Based on the time variable transformation relationship, the semi-empirical performance degradation model is restructured to obtain a linear combination form of the semi-empirical performance degradation model; Linear regression model identification is performed on the linear combination form to obtain the linear regression model of the semi-empirical performance degradation model.

5. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1, characterized in that, The least squares method is used to solve the linear regression model to obtain the parameters η and β in the linear regression model, including: The design matrix of the linear regression model is obtained by constructing a design matrix based on the independent and dependent variables in the linear regression model. The design matrix is ​​regularized to obtain the regularized design matrix; Based on the regularized design matrix and the observed data vector, the least squares objective function is constructed to obtain the least squares optimization problem of the linear regression model; The least squares optimization problem is solved numerically to obtain the parameter solution vector of the linear regression model; The linear parameters η and β are extracted from the parameter solution vector to obtain the linear parameters η and β in the linear regression model.

6. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1, characterized in that, The genetic algorithm is used to globally optimize the nonlinear parameters λ and α to obtain optimized nonlinear parameters λ and α. The error between the output of the model that minimizes the optimized nonlinear parameters and the experimental data includes: Population initialization is performed on the value space of nonlinear parameters λ and α, with the population size set to 15 individuals to obtain the initial population; The initial population is subjected to selection, crossover, and mutation operations, with the crossover probability set to 0.8 and the mutation probability set to 0.2, to obtain a new generation population. Fitness assessment was performed on the new generation population to obtain the optimal individual in the population; The values ​​of nonlinear parameters λ and α are extracted from the optimal individual to obtain the optimized nonlinear parameters λ and α.

7. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1, characterized in that, The performance degradation model optimized based on the linear parameters η and β, and the optimized nonlinear parameters λ and α, along with the preset failure criteria, calculates the material failure time under various temperature conditions, including: Based on the strength requirements of fiber-reinforced composite materials in the national standard GB1447-2005, the material performance failure threshold is set to 100MPa, and the preset failure criterion is obtained. Substituting the failure criterion into the performance degradation model that includes the linear parameters η and β, as well as the optimized nonlinear parameters λ and α, yields the performance termination equation for aging time. The performance termination equation is numerically solved to obtain the material failure time under various temperature conditions.

8. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1, characterized in that, The material failure time under each temperature condition is linearly regressed using the least squares method to obtain Arrhenius model parameters, and an Arrhenius model is established. Based on the Arrhenius model, a temperature-lifetime relationship is established, including: The material failure time series under the aforementioned temperature conditions are subjected to Arrhenius coordinate transformation, converting the thermodynamic temperature T to the reciprocal coordinate 1 / T and the failure time L to the logarithmic coordinate ln(L), resulting in a linearized data point set in the Arrhenius coordinate system. Based on the linearized data point set in the Arrhenius coordinate system, the least squares method is used to perform linear regression analysis to obtain the numerical solutions of the Arrhenius model parameters A and B. Substitute the Arrhenius model parameters A and B into the Arrhenius model mathematical expression to establish a complete temperature-lifetime mathematical relationship model; The specific form of the Arrhenius model is as follows: in, Indicates the storage life of composite materials. The thermodynamic temperature during material storage. , These are the parameters to be determined by fitting experimental data; The fitting accuracy of the established temperature-lifetime mathematical model was verified, and a valid Arrhenius temperature-lifetime mathematical model was obtained, thus completing the establishment of the relationship between temperature and lifetime. The relationship between temperature and lifespan is as follows: in, For lifespan, Thermodynamic temperature , The parameters are obtained by fitting the experimental data.

9. The method for predicting the storage life of composite materials based on variable transformation and genetic algorithm according to claim 1 or 8, characterized in that, The method for predicting the storage life of composite materials at room temperature based on the temperature-life relationship includes: Substitute the room temperature storage temperature into the validated Arrhenius temperature-life mathematical model to calculate the theoretical storage life of the composite material at room temperature and obtain the room temperature theoretical life value. Local sensitivity analysis was performed on the Arrhenius temperature-lifetime mathematical model to identify key parameters affecting the accuracy of lifetime prediction and to obtain a sensitivity ranking of the key parameters. Based on the sensitivity ranking of the key parameters, Monte Carlo simulation method is used to perform multiple random samplings, calculate the statistical distribution of the model prediction results, and obtain the lifetime prediction confidence interval. A reliability assessment is performed based on the theoretical lifetime value at room temperature and the lifetime prediction confidence interval to obtain a reliable room temperature storage lifetime prediction result.

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