Probability characterization method and system for design allowable value of thermoplastic composite material leading edge structure under small sample condition

Abstract

The invention belongs to the technical field of uncertainty probability characterization analysis, and discloses a thermoplastic composite material leading edge structure design allowable value probability characterization method and system under a small sample condition, and the method comprises the steps: defining a plurality of candidate probability distribution models; fitting each model based on the original sample data and calculating an AIC value and a BIC value; a dynamic weight factor alpha is calculated according to the sample size n, and then a hybrid information criterion HIC value is calculated; generating a plurality of sample sets through Bootstrap self-service sampling, recalculating the HIC value on each sample set, and counting the selected optimal frequency of each model; and determining an optimal probability distribution model according to the frequency, wherein the optimal probability distribution model is used for representing a design allowable value. According to the method, the dynamic weight factor alpha is introduced, AIC and BIC criteria are effectively unified, optimal balance between prediction precision and model complexity is achieved under the condition of small samples, and engineering practicability and robustness are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of uncertainty probability characterization and analysis technology, specifically involving a probabilistic characterization method and system for the design allowable value of thermoplastic composite leading edge structure under small sample conditions, focusing on obtaining the design allowable value of the wing leading edge structure. Background Technology

[0002] Thermoplastic composite leading-edge structures demonstrate enormous application potential. They exhibit superior impact toughness, effectively resisting impact loads such as bird strikes and hail during flight, thus improving flight safety. Compared to traditional thermoset composites, they possess unique weldability and reprocessability, enabling efficient and low-cost joining and repair, and facilitating recycling, aligning with green manufacturing trends. Furthermore, through thermoforming processes, complex curved surface structures can be rapidly formed within minutes, resulting in short production cycles suitable for large-scale manufacturing.

[0003] However, this structure also faces challenges in engineering applications. Its raw material costs are high, and the thermoforming process requires precise temperature and pressure control, placing stringent demands on mold design and process stability, leading to increased initial investment and production costs. Furthermore, long-term performance data (long-term creep, aging performance) under harsh environments such as high humidity and high temperature are still insufficient, resulting in significant dispersion in design allowable values ​​and hindering the precise setting of its safety boundaries. To reliably apply this structure in the development of new aircraft, it is urgent to establish an efficient probabilistic characterization method for design allowable values ​​based on limited experimental data.

[0004] Traditional probabilistic characterization methods (such as Markov random fields and Monte Carlo sampling) typically require massive sample sizes, resulting in high testing costs and long cycles, making them unsuitable for rapid iterative development needs. Therefore, introducing probabilistic characterization methods for small sample sizes is crucial. For example, model selection and bootstrap sampling techniques based on the AIC criterion can efficiently and robustly assess the overall probability distribution of material properties using limited experimental data, providing quantitative and reliable uncertainty analysis for determining core design allowable values.

[0005] In summary, to promote the mature application of thermoplastic composite leading edge structures in the aerospace field, this paper proposes and explores a small-sample probabilistic characterization method suitable for their characteristics, aiming to provide a solid theoretical basis and data support for the damage-tolerant design, reliability assessment, and ultimate successful application of this type of structure. Summary of the Invention

[0006] This invention addresses the problems of high production costs and large dispersion of design allowable values ​​for existing thermoplastic composite materials. It proposes a probabilistic characterization method and system for design allowable values ​​of thermoplastic composite leading edge structures under small sample conditions, solving the problems of large sample requirements, difficulty in model selection, and insufficient engineering applicability in existing technologies.

[0007] The technical solution of this invention is implemented as follows:

[0008] In a first aspect, the present invention provides a probabilistic characterization method for allowable values ​​of thermoplastic composite front-edge structure design under small sample conditions, which includes the following steps:

[0009] S1: Define multiple candidate probability distribution models for fitting the performance data of thermoplastic composites;

[0010] S2: Based on the original performance sample dataset, calculate the Mixed Information Criterion (HIC) value for each candidate probability distribution model; the HIC value is calculated using the formula HIC = α × AIC + (1-α) × BIC, where α is the weight parameter, calculated as α = 1 / (1 + log(n)), n is the sample size of the original performance sample dataset, AIC is the Akaike Information Criterion, and BIC is the Bayesian Information Criterion;

[0011] S3: Perform B bootstrap samplings with replacement on the original performance sample dataset to generate B bootstrap sample sets;

[0012] S4: For each bootstrap sample set generated in step S3, recalculate the HIC value of each candidate probability distribution model, and record the model with the smallest HIC value as the optimal distribution model under that bootstrap sample set.

[0013] S5: Calculate the frequency with which each candidate probability distribution model is selected as the optimal distribution model in B bootstrap samplings;

[0014] S6: Based on the frequency, determine the final probability distribution model from the candidate probability distribution models to characterize the allowable value of the thermoplastic composite leading edge structure design.

[0015] As a further technical solution of the present invention: the candidate probability distribution model mentioned in step S1 includes at least three of the following: normal distribution, log-normal distribution, Weiber distribution, gamma distribution and exponential distribution.

[0016] As a further technical solution of the present invention: In step S2, the AIC value and BIC value of each candidate probability distribution model are calculated, specifically as follows:

[0017] Based on the original performance sample dataset, each candidate probability distribution model is fitted using the maximum likelihood estimation method, and the maximum likelihood value L of the model is obtained.

[0018] The AIC value is calculated using the formula AIC = 2k - 2ln(L), where k is the number of parameters in the candidate probability distribution model.

[0019] Calculate the BIC value using the formula BIC = k × ln(n) - 2ln(L).

[0020] As a further technical solution of the present invention: the "determining the final probability distribution model according to the frequency" in step S6 specifically means: selecting the candidate probability distribution model with the highest frequency that is selected as the optimal distribution model as the final probability distribution model.

[0021] As a further technical solution of the present invention: the number of self-sampling times B in step S3 is not less than 1000.

[0022] As a further technical solution of the present invention: after determining the final probability distribution model, the method further includes the following steps:

[0023] S7: Based on the final probability distribution model, calculate the allowable mechanical properties of the thermoplastic composite leading edge structure at the required confidence level.

[0024] Secondly, the present invention provides a probabilistic characterization system for allowable values ​​of thermoplastic composite front structure design under small sample conditions, comprising:

[0025] The model definition module is used to define multiple candidate probability distribution models;

[0026] The fitting calculation module is used to fit each candidate distribution model based on the original sample data and calculate the AIC and BIC values.

[0027] The weight calculation module is used to calculate the dynamic weight factor α based on the sample size n.

[0028] The HIC calculation module is used to calculate the HIC value of each model based on the AIC value, BIC value, and weight factor α.

[0029] The self-sampling module is used to perform Bootstrap self-sampling and generate multiple self-sampling sample sets;

[0030] The frequency statistics module is used to repeatedly calculate HIC values ​​on the bootstrap sample set and count the frequency with which each model is selected as the optimal model.

[0031] The model determination module is used to determine the optimal probability distribution model based on frequency.

[0032] As a further technical solution of the present invention: the fitting calculation module is also used to calculate the maximum likelihood value L of each candidate distribution model.

[0033] As a further technical solution of the present invention: the number of Bootstrap samplings B performed by the self-service sampling module is not less than 1000.

[0034] As a further technical solution of the present invention: the model determination module selects the distribution model with the highest selected frequency as the optimal probability distribution model.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] 1. This invention unifies the AIC and BIC criteria through a dynamic weighting factor α, achieving an adaptive balance between prediction accuracy and model complexity;

[0037] 2. This invention is applicable to small sample situations, taking into account both engineering practicality and statistical robustness;

[0038] 3. The method of this invention has high scalability and is compatible with large sample scenarios after data accumulation;

[0039] 4. This invention provides a quantitative basis for the reliability design and safety assessment of thermoplastic composite leading edge structures.

[0040] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0041] Figure 1 A simplified diagram illustrating the Bootstrap resampling principle of this invention is shown. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some embodiments of this invention, but not all embodiments.

[0043] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0044] Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this invention.

[0045] The following is in conjunction with the appendix Figure 1 The embodiments of the present invention will be described in detail below.

[0046] Example 1

[0047] Existing thermoplastic composite materials suffer from high production costs and significant dispersion in design allowable values. This invention aims to develop a method for efficiently and accurately determining the design allowable values ​​of thermoplastic composite wing leading-edge structures, building upon existing probabilistic characterization methods for these values. To further advance the application of thermoplastic composite leading-edge structure design technology in the development of new aircraft models, this invention develops a method for characterizing the allowable values ​​of thermoplastic composite leading-edge structure design, providing theoretical support for the subsequent application of thermoplastic composite leading-edge structures.

[0048] This invention focuses on the leading edge structure of a thermoplastic composite wing. It presents a probabilistic characterization method for allowable design values ​​of thermoplastic composite structures under small sample conditions. The main implementation steps are as follows:

[0049] 1) Define the candidate distribution model:

[0050] List the potential probability distribution models to be evaluated (such as normal distribution, log-normal distribution, exponential distribution, gamma distribution, Weiber distribution, Poisson distribution, etc.).

[0051] 2) Fit the model to the original samples and calculate the AIC:

[0052] a. For the original sample data, fit each candidate distribution model and calculate the corresponding AIC value.

[0053] AIC formula: AIC = 2k - 2ln(L)

[0054] k: Number of model parameters (e.g., k=2 for a normal distribution), L: Maximum likelihood value of the model. The lower the AIC, the better the model fit.

[0055] b. For the original sample data, fit each candidate distribution model and calculate the corresponding BIC value.

[0056] BIC formula: BIC = kln(n) - 2ln(L)

[0057] k: Number of model parameters (e.g., k=2 for a normal distribution), L: Maximum likelihood value of the model. The lower the BIC, the better the model fit.

[0058] c. Calculate the weight parameter α = 1 / (1 + log(n))

[0059] d. Calculate the HIC value of the criterion parameter.

[0060] HIC formula: HIC= α × AIC + (1-α) × BIC

[0061] 3) Perform bootstrap sampling:

[0062] Samples are drawn with replacement from the original sample (bootstrap samples), and this is repeated B times (e.g., B=1000) to obtain B bootstrap sample sets.

[0063] 4) Repeat the calculation of HIC on the self-service sample:

[0064] For each bootstrap sample, refit all candidate distribution models and calculate the HIC value for each model;

[0065] 5) Select the model with the smallest HIC in the current bootstrap sample (i.e. the optimal distribution under the current resampling).

[0066] Frequency of selection of statistical models: Summarize the results of all bootstrap samples and calculate the proportion of each distribution model that is selected as "optimal".

[0067] The Bootstrap evaluation methods involved in this solution are as follows:

[0068] Suppose the initial experimental dataset is represented as ,in This represents the sample size. The corresponding sample mean and variance can be estimated using the following formula:

[0069] (1)

[0070] (2)

[0071] By randomly sampling with replacement from the original experimental sample set This process can be repeated to obtain a bootstrap sample set with the same sample size as the original dataset. The resulting Bootstrap sample set can be represented as Similarly, for each Bootstrap sample set, the sample mean and variance can be estimated:

[0072] (3)

[0073] (4)

[0074] A simplified diagram illustrating the basic principle of Bootstrap resampling technology is shown below. Figure 1 As shown, where This represents the sample statistics (such as mean and variance) estimated from the Bootstrap sample.

[0075] To address the current limitations of probabilistic characterization methods for allowable design values ​​of thermoplastic composite structures, where the use of a single AIC or BIC criterion results in a trade-off between predictive power and complexity, this invention, for the first time, unifies these two aspects in a probabilistic characterization method for allowable design values ​​of thermoplastic composite structures under small sample conditions by introducing a dynamic weighting factor α. This ultimately yields a prediction method that balances engineering practicality and accuracy. Therefore, the calculation and optimization method of the weighting factor α presented in this invention is its core content.

[0076] To address the high production costs and significant dispersion in design allowable values ​​of thermoplastic composite materials, a probabilistic characterization method for the design allowable values ​​of thermoplastic composite wing leading edge structures is proposed under small sample conditions. This method can efficiently and accurately determine the design allowable values ​​of thermoplastic composite wing leading edge structures, and has good practicality and theoretical guidance.

[0077] The weighted hybrid criterion used in this invention is not a simple superposition of AIC and BIC, but rather a novel and unified model selection framework constructed by introducing an adaptive weight coefficient α. Specific advantages are as follows:

[0078] 1) Breaking through the limitations of the traditional "either / or" principle, achieving the optimal balance between prediction accuracy and model simplicity.

[0079] In existing technologies, the AIC criterion tends to select models with stronger predictive power but potentially greater complexity, while the BIC criterion tends to select simpler models but potentially weaker predictive power. Engineers often face a dilemma when confronted with practical problems, lacking a unified, quantifiable basis for decision-making.

[0080] This approach transforms model selection from a discrete "either / or" decision into a continuously adjustable optimization process by constructing a hybrid criterion. The weight α, as an engineering adjustment factor, allows users to precisely balance "pursuing ultimate predictive performance" with "ensuring model simplicity and reliability" based on the specific task objectives.

[0081] 2) Introducing application-oriented dynamic adaptive capabilities significantly improves the engineering practicality and robustness of the method.

[0082] Traditional fixed criteria are a "one-size-fits-all" solution that cannot be adjusted according to specific changes in data characteristics and engineering scenarios.

[0083] In this scheme, the weight α can be designed as a dynamic variable rather than a fixed constant. When the sample size n is small, α automatically approaches 1, and the method approaches AIC to make full use of the information in the limited data for prediction; when the sample size n increases, α automatically decreases, and the method gradually introduces the strong penalty of BIC to effectively prevent overfitting. It is particularly suitable for the "small sample" starting point targeted by this invention, and is also compatible with large sample scenarios after data accumulation.

[0084] Example 2

[0085] This invention discloses a method and system for probabilistic characterization of allowable values ​​for the design of thermoplastic composite leading-edge structures under small sample conditions.

[0086] I. Overview of Methods and Procedures

[0087] The core of this invention lies in using a Hybrid Information Criterion (HIC) combined with Bootstrap resampling technology to robustly select the optimal probability distribution model under small sample conditions. The entire process can be divided into three stages:

[0088] Initial model evaluation phase: Based on the original small sample data, the candidate models are initially screened using the dynamically weighted HIC criterion.

[0089] Bootstrap robustness verification phase: Through repeated sampling, the randomness of the samples is simulated to evaluate the performance stability of each candidate model under different sample perturbations.

[0090] Optimal Model Determination Stage: Based on the Bootstrap results, the model most frequently selected as the optimal model is chosen as the final design allowable value probability representation model.

[0091] II. Detailed Implementation Steps

[0092] Step 1: Define the candidate distribution model library

[0093] Based on the data characteristics of the mechanical properties of thermoplastic composites (such as tensile strength, compressive strength, and post-impact compressive strength), a candidate probability distribution model library is predefined. These models should cover common distribution patterns. Typical candidate models include, but are not limited to:

[0094] Normal distribution

[0095] Lognormal Distribution

[0096] Weibull Distribution

[0097] Gamma Distribution

[0098] Logistic Distribution

[0099] In this embodiment, we selected the normal distribution, log-normal distribution, and Weibull distribution as candidate model libraries. The Weibull distribution is widely used in material strength statistics, the log-normal distribution is often used to process positively skewed data, and the normal distribution is used as the basic model for comparison.

[0100] Step 2: Fit the model to the original samples and calculate AIC and BIC.

[0101] Suppose that sample data for a key performance characteristic (e.g., residual strength after bird strike) of a thermoplastic composite leading-edge structure is obtained through experiments, denoted as X={x1,x2,...,x n}, where the sample size n=25 (small sample case).

[0102] a. Model Fitting and Maximum Likelihood Estimation: Using maximum likelihood estimation, the parameters of the normal, log-normal, and Weibull distributions are fitted to the original sample data X, respectively. For example, for the normal distribution, its mean μ and standard deviation σ are estimated; for the Weibull distribution, its shape parameter k and scale parameter λ are estimated.

[0103] b. Calculate AIC and BIC values: Based on the fitting results, calculate the maximum likelihood value L for each model, and then substitute it into the formula:

[0104] - AIC = 2k−2ln(L)

[0105] - BIC = k⋅ln(n)−2ln(L)

[0106] Where k is the number of model parameters (normal distribution k=2, log-normal distribution k=2, Weibull distribution k=2).

[0107] Step 3: Calculate the dynamic weighting factor α and the HIC value

[0108] a. Calculate the dynamic weighting factor α:

[0109]

[0110] This value reflects that, given the current sample size, the BIC criterion (with a stronger penalty) carries a higher weight than the AIC criterion in the mixed criteria.

[0111] b. Calculate the HIC value for each model: HIC = α × AIC + (1 − α) × BIC

[0112] Calculate the HIC values ​​for the three candidate models. Assume the calculation results are as follows: - Normal distribution: HIC~N~ = 125.6 - Log-normal distribution: HIC~LN~ = 122.3 - Weibull distribution: HIC~W~ = 120.1 On the original sample, the Weibull distribution has the smallest HIC value, indicating the best initial performance.

[0113] Step 4: Perform Bootstrap self-sampling

[0114] Set the number of resampling iterations to B = 5000 (to ensure statistical stability, it is recommended that B be no less than 1000). From the original sample set X, randomly draw n = 25 samples with replacement to form a Bootstrap sample set. Repeat this process 5000 times to obtain a Bootstrap sample set of 500. , ,..., .

[0115] Step 5: Repeat the calculation and frequency count on the Bootstrap sample.

[0116] This is a cyclical process, for the b-th Bootstrap sample set. (b From 1 to 5000) Perform the following operations:

[0117] 1. Fit the data using normal, log-normal, and Weibull distributions respectively. .

[0118] 2. Calculate the value of each model. The AIC and BIC values ​​on the screen.

[0119] 3. Using the same α value (α=0.237 calculated based on the original sample size n=25), calculate the HIC value for each model.

[0120] 4. Select the current Bootstrap sample set The model with the smallest HIC value is denoted as the "optimal model" in this sampling.

[0121] After the loop ends, the frequency with which each candidate model is selected as the "optimal model" is counted. Assume the statistical results are as follows:

[0122] The Weibull distribution was selected 3200 times, with a frequency of 3200 / 5000 = 64%.

[0123] The log-normal distribution was selected 1500 times, with a frequency of 30%.

[0124] The normal distribution was selected 300 times, with a frequency of 6%.

[0125] Step 6: Determine the optimal probability distribution model

[0126] Based on the Bootstrap frequency statistics, the Weibull distribution, with the highest selection frequency of 64%, was determined to be the optimal probability distribution model for characterizing the allowable design value of the leading edge structure of this thermoplastic composite material on this performance index.

[0127] Ultimately, designers can use a Weibull distribution model that has passed the goodness-of-fit test to determine the B-benchmark value (or other statistically permissible value) of the material's properties, providing a probabilistic input for structural design.

[0128] III. System Implementation

[0129] A system corresponding to the above method can be built as a software platform containing the following modules or as a toolkit integrated into an existing CAE system:

[0130] Data input module: Provides an interface for inputting sample data obtained from the experiment and setting parameters (such as candidate model selection, Bootstrap number B).

[0131] Model Management and Fitting Module: Embeds common probability distribution models and their parameter estimation algorithms.

[0132] Criterion Calculation Engine: The core calculation unit responsible for performing calculations of AIC, BIC, α, and HIC.

[0133] Bootstrap Sampling and Loop Control Module: Automates the resampling and loop calculation process.

[0134] Results Statistics and Visualization Module: Outputs frequency statistics tables, distribution curve comparison charts, Bootstrap sample distribution charts, etc. for each model, and highlights the finally selected optimal model.

[0135] Report generation module: Automatically generates analysis reports that include the data processing process, key intermediate results, and the basis for determining the final model.

[0136] Those skilled in the art can implement the above modules through programming (such as using Python, MATLAB, etc.) to form a complete analysis tool.

[0137] Thus, the objective of this invention has been achieved.

[0138] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A probabilistic characterization method for allowable values ​​in the design of thermoplastic composite leading-edge structures under small sample conditions, characterized in that, Includes the following steps: S1: Define multiple candidate probability distribution models for fitting the performance data of thermoplastic composites; S2: Based on the original performance sample dataset, calculate the Mixed Information Criterion (HIC) value for each candidate probability distribution model; The HIC value is calculated using the formula HIC = α × AIC + (1-α) × BIC, where α is the weight parameter, calculated as α = 1 / (1 + log(n)), n is the sample size of the original performance sample dataset, AIC is the Akaike information criterion, and BIC is the Bayesian information criterion. S3: Perform B bootstrap samplings with replacement on the original performance sample dataset to generate B bootstrap sample sets; S4: For each bootstrap sample set generated in step S3, recalculate the HIC value of each candidate probability distribution model, and record the model with the smallest HIC value as the optimal distribution model under that bootstrap sample set. S5: Calculate the frequency with which each candidate probability distribution model is selected as the optimal distribution model in B bootstrap samplings; S6: Based on the frequency, determine the final probability distribution model from the candidate probability distribution models to characterize the allowable value of the thermoplastic composite leading edge structure design.

2. The method according to claim 1, characterized in that, The candidate probability distribution model mentioned in step S1 includes at least three of the following: normal distribution, log-normal distribution, Weiber distribution, gamma distribution, and exponential distribution.

3. The method according to claim 1, characterized in that, In step S2, the AIC and BIC values ​​of each candidate probability distribution model are calculated, specifically as follows: Based on the original performance sample dataset, each candidate probability distribution model is fitted using the maximum likelihood estimation method, and the maximum likelihood value L of the model is obtained. The AIC value is calculated using the formula AIC = 2k - 2ln(L), where k is the number of parameters in the candidate probability distribution model. Calculate the BIC value using the formula BIC = k × ln(n) - 2ln(L).

4. The method according to claim 1, characterized in that, The step S6, "determining the final probability distribution model based on the frequency", specifically means: selecting the candidate probability distribution model with the highest frequency that is selected as the optimal distribution model, as the final probability distribution model.

5. The method according to claim 1, characterized in that, The number of self-sampling attempts B in step S3 shall not be less than 1000.

6. The method according to claim 1, characterized in that, After determining the final probability distribution model, the method further includes the following steps: S7: Based on the final probability distribution model, calculate the allowable mechanical properties of the thermoplastic composite leading edge structure at the required confidence level.

7. A probabilistic characterization system for allowable values ​​of thermoplastic composite front-edge structure design under small sample conditions, characterized in that, include: The model definition module is used to define multiple candidate probability distribution models; The fitting calculation module is used to fit each candidate distribution model based on the original sample data and calculate the AIC and BIC values. The weight calculation module is used to calculate the dynamic weight factor α based on the sample size n. The HIC calculation module is used to calculate the HIC value of each model based on the AIC value, BIC value, and weight factor α. The self-sampling module is used to perform Bootstrap self-sampling and generate multiple self-sampling sample sets; The frequency statistics module is used to repeatedly calculate HIC values ​​on the bootstrap sample set and count the frequency with which each model is selected as the optimal model. The model determination module is used to determine the optimal probability distribution model based on frequency.

8. The system according to claim 7, characterized in that, The fitting calculation module is also used to calculate the maximum likelihood value L for each candidate distribution model.

9. The system according to claim 7, characterized in that, The number of Bootstrap samplings B performed by the self-service sampling module is no less than 1000.

10. The system according to claim 7, characterized in that, The model determination module selects the distribution model with the highest selection frequency as the optimal probability distribution model.

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