Limit load modeling method and device for high-temperature adhesive, storage medium and equipment

Abstract

The invention relates to the technical field of uncertainty probability modeling, and provides a limit load modeling method and device for a high-temperature adhesive, a computer readable storage medium and electronic device.The method comprises the steps that self-service sampling processing is conducted on an original limit load sample set of the high-temperature adhesive, and N self-service sample sets are obtained; n is an integer greater than 1; fitting each candidate probability distribution model by using each self-service sample set, and calculating a Bayesian information criterion value corresponding to each candidate probability distribution model; under each self-service sample set, selecting an optimal model based on a Bayesian information criterion value; and counting the frequency of each candidate probability distribution model selected as an optimal model under the N self-service sample sets, and determining the candidate probability distribution model with the highest frequency as an optimal fitting distribution model of the limit load data of the high-temperature adhesive. The invention provides a scientific and reliable method for high-temperature adhesive limit load distribution modeling.

Description

Technical Field

[0001] This disclosure relates to the field of uncertainty probability modeling technology, and in particular to a method for modeling the ultimate load of high-temperature adhesives, a device for modeling the ultimate load of high-temperature adhesives, a computer-readable storage medium, and an electronic device. Background Technology

[0002] High-temperature adhesives for roof tiles are functional bonding materials specifically designed for high-temperature environments. They maintain excellent structural stability and bonding performance even at extreme temperatures exceeding 500℃ or 1000℃, and are not prone to melting, carbonization, or decomposition. These adhesives are widely used for bonding and fixing high-temperature components such as ceramic tiles, refractory tiles, and metal tiles. They not only achieve a strong connection between substrates, preventing detachment due to thermal expansion, contraction, or mechanical vibration, but also effectively fill joints, forming a high-temperature sealed structure. This prevents leakage of gas, liquid, or dust, improving the overall airtightness and operational safety of the equipment.

[0003] Although high-temperature adhesives for roofing exhibit excellent physicochemical properties at high temperatures, their application in engineering still faces certain limitations. On the one hand, inorganic high-temperature adhesives, particularly those suitable for ultra-high temperature environments (e.g., above 1000℃), are significantly more expensive than conventional adhesives due to high raw material costs and complex manufacturing processes, limiting their large-scale application. On the other hand, the ultimate load capacity of these adhesives exhibits considerable dispersion, and their distribution characteristics are not yet fully understood, introducing significant uncertainties into structural strength design and safety assessment, thus affecting their reliable use in critical high-temperature components.

[0004] Traditional studies on ultimate load distribution primarily rely on statistical methods based on physical experiments. This involves acquiring strength data through numerous destructive tests on a large number of specimens and establishing statistical models based on assumed population distributions (such as normal or Weiber distributions). However, this method not only consumes significant human, material, and time resources but also struggles to accurately determine the distribution type when the sample size is limited. Consequently, the analysis results suffer from low reliability and efficiency, failing to meet the practical needs of rapid development and reliability design for modern high-temperature structural components.

[0005] Therefore, there is an urgent need in the field to develop a new method and apparatus for modeling the ultimate load of high-temperature adhesives.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure. Summary of the Invention

[0007] The purpose of this disclosure is to provide a method, apparatus, computer-readable storage medium, and electronic device for modeling the ultimate load of high-temperature adhesives, thereby overcoming, to some extent, the technical problems caused by the limitations of related technologies, such as the high cost of manpower and resources and the difficulty in obtaining accurate analytical results when the number of samples is limited.

[0008] Other features and advantages of this disclosure will become apparent from the following detailed description, or may be learned in part from practice of this disclosure.

[0009] According to a first aspect of this disclosure, a method for modeling the ultimate load of a high-temperature adhesive is provided, comprising:

[0010] The original ultimate load sample set of the high-temperature adhesive is subjected to bootstrap sampling to obtain N bootstrap sample sets; N is an integer greater than 1.

[0011] Each candidate probability distribution model is fitted using each of the aforementioned bootstrap sample sets, and the Bayesian information criterion value corresponding to each candidate probability distribution model is calculated;

[0012] For each self-service sample set, the optimal model is selected based on the Bayesian information criterion value;

[0013] The frequency with which each candidate probability distribution model is selected as the optimal model in the N bootstrap sample sets is counted, and the candidate probability distribution model with the highest frequency is determined as the best-fit distribution model for the ultimate load data of the high-temperature adhesive.

[0014] In an exemplary embodiment of this disclosure, the candidate probability distribution model includes at least two of the following:

[0015] Normal distribution, exponential distribution, gamma distribution, and Weiber distribution.

[0016] In an exemplary embodiment of this disclosure, the step of performing bootstrap sampling on the original ultimate load sample set of the high-temperature adhesive to obtain N bootstrap sample sets includes:

[0017] From the original ultimate load sample set, samples are randomly drawn with replacement, and the number of samples drawn each time is the same as the number of samples in the original ultimate load sample set, to obtain a bootstrap sample set.

[0018] The sampling process is repeated N times to obtain the N bootstrap sample sets.

[0019] In an exemplary embodiment of this disclosure, the Bayesian information criterion value corresponding to each candidate probability distribution model is calculated based on the following formula:

[0020] BIC = kln(n) - 2ln(L)

[0021] Wherein, BIC represents the Bayesian information criterion value; k represents the number of model parameters corresponding to each candidate probability distribution model; n represents the sample size corresponding to the current bootstrap sample set; and L represents the maximum likelihood value of each candidate probability distribution model under the current bootstrap sample set.

[0022] In an exemplary embodiment of this disclosure, the maximum likelihood value of each candidate probability distribution model under the current bootstrap sample set is determined in the following manner:

[0023] For each candidate probability distribution model, a likelihood function corresponding to the candidate probability distribution model is constructed based on the current bootstrap sample set;

[0024] The likelihood function is optimized using the maximum likelihood estimation method to find the model parameter estimates that maximize the likelihood function value.

[0025] Substituting the estimated model parameters into the likelihood function, the maximum likelihood value of the candidate probability distribution model under the current bootstrap sample set is calculated.

[0026] In an exemplary embodiment of this disclosure, selecting the optimal model based on the Bayesian information criterion value includes:

[0027] The candidate probability distribution model with the smallest Bayesian information criterion value is selected as the optimal model.

[0028] In an exemplary embodiment of this disclosure, N is an integer greater than or equal to 1000.

[0029] According to a second aspect of this disclosure, a device for modeling the ultimate load of a high-temperature adhesive is provided, comprising:

[0030] The self-sampling module is used to perform self-sampling processing on the original ultimate load sample set of the high-temperature adhesive to obtain N self-sampling sample sets; N is an integer greater than 1.

[0031] The fitting module is used to fit each candidate probability distribution model using each of the bootstrap sample sets, and to calculate the Bayesian information criterion value corresponding to each candidate probability distribution model.

[0032] The model selection module is used to select the optimal model based on the Bayesian information criterion value for each bootstrap sample set.

[0033] The statistics module is used to count the frequency with which each of the candidate probability distribution models is selected as the optimal model under the N bootstrap sample sets, and to determine the candidate probability distribution model with the highest frequency as the best-fit distribution model for the ultimate load data of the high-temperature adhesive.

[0034] According to a third aspect of this disclosure, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the ultimate load modeling method for high-temperature adhesives described in the first aspect above.

[0035] According to a fourth aspect of this disclosure, an electronic device is provided, comprising: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to perform the extreme load modeling method for high-temperature adhesives described in the first aspect by executing the executable instructions.

[0036] As can be seen from the above technical solutions, the ultimate load modeling method, ultimate load modeling device, computer-readable storage medium, and electronic device of the exemplary embodiments of this disclosure have at least the following advantages and positive effects:

[0037] In some embodiments of this disclosure, a systematic and scientific method for selecting the best-fit distribution model for ultimate load data of high-temperature adhesives is provided by combining bootstrap sampling and Bayesian information criterion (BIC). First, bootstrap sampling is used to generate multiple sample sets, which helps overcome the problem of limited original data volume and better reflects the true distribution characteristics of the data, increasing the robustness of the analysis. Next, by fitting each candidate probability distribution model to each bootstrap sample set and calculating the corresponding BIC value, this process not only considers the model fit but also penalizes model complexity, ensuring that the selected model can both well describe the data characteristics and avoid overfitting. Then, based on each bootstrap sample set, the optimal model is selected based on the BIC value. This method effectively identifies the model most suitable for describing the characteristics of the current sample set. Finally, by performing frequency statistics on the optimal models selected in all bootstrap sample sets, the model with the highest frequency is determined as the best-fit distribution model. This method not only improves the reliability of model selection but also effectively addresses the variability between different sample sets. Overall, this approach provides a scientific and systematic method for determining the best-fit distribution model of the ultimate load of high-temperature adhesives, which is of great significance for improving product quality, optimizing design parameters, and ensuring safe use.

[0038] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0039] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0040] Figure 1 A flowchart illustrating the ultimate load modeling method for high-temperature adhesives in embodiments of this disclosure is shown.

[0041] Figure 2 This diagram illustrates the basic principle of Bootstrap resampling technology.

[0042] Figure 3 A comparison chart of BIC values ​​for candidate probability distribution models under the original sample set is shown.

[0043] Figure 4 This shows a frequency plot of different distribution models selected as the optimal model in Bootstrap sampling;

[0044] Figures 5-8 This diagram shows the BIC value distribution of each candidate probability distribution model in the embodiments of this disclosure;

[0045] Figure 9 This diagram shows a comparison between the original data histogram and the gamma distribution fitting curve in an embodiment of this disclosure.

[0046] Figure 10 A schematic diagram of the ultimate load modeling apparatus for high-temperature adhesives in an exemplary embodiment of this disclosure is shown.

[0047] Figure 11 A schematic diagram of the structure of an electronic device in an exemplary embodiment of this disclosure is shown. Detailed Implementation

[0048] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make this disclosure more comprehensive and complete, and to fully convey the concept of the example embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced with one or more of the specific details omitted, or other methods, components, apparatus, steps, etc., can be employed. In other instances, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0049] The terms “a,” “an,” “the,” and “the” are used in this specification to indicate the presence of one or more elements / components / etc.; the terms “including” and “having” are used to indicate an open-ended inclusion and to mean that there may be other elements / components / etc. in addition to the listed elements / components / etc.; the terms “first” and “second” are used only as markings and are not a limitation on the number of objects.

[0050] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0051] Traditional research on ultimate load distribution relies on statistical methods of physical experiments, which establishes a strength distribution database through a large number of specimen failure tests and requires knowledge of the overall distribution of the samples. This results in a large number of specimen tests, which is costly, time-consuming, and inefficient.

[0052] With the development of technology and the increasing demand for efficiency, the method of studying the distribution characteristics of ultimate loads based on the BIC criterion and bootstrap sampling has become an emerging statistical data method. It can evaluate the ultimate load of a product with fewer samples and in the shortest time, greatly improving the efficiency and economy of testing.

[0053] To further promote the application of high-temperature adhesives for roofing tiles in the development of new aircraft models, based on the comprehensive environmental and durability performance test results of high-temperature adhesives for roofing tiles, the ultimate load distribution characteristics of high-temperature adhesives for roofing tiles under small sample conditions were obtained, providing theoretical support for the subsequent application of high-temperature adhesives for roofing tiles.

[0054] In the embodiments of this disclosure, a method for modeling the ultimate load of high-temperature adhesives is first provided, which at least to some extent overcomes the shortcomings of related technologies that are labor-intensive and difficult to obtain accurate analysis results when the number of samples is limited.

[0055] Figure 1 The flowchart of the ultimate load modeling method for high-temperature adhesives in this embodiment is shown. The execution subject of the ultimate load modeling method for high-temperature adhesives can be a server that evaluates material properties.

[0056] refer to Figure 1 A method for modeling the ultimate load of a high-temperature adhesive according to an embodiment of the present disclosure includes the following steps:

[0057] Step S110: Perform bootstrap sampling on the original ultimate load sample set of high-temperature adhesives to obtain N bootstrap sample sets; N is an integer greater than 1.

[0058] Step S120: Fit each candidate probability distribution model to each bootstrap sample set and calculate the Bayesian information criterion value corresponding to each candidate probability distribution model.

[0059] Step S130: Select the optimal model based on the Bayesian information criterion value for each bootstrap sample set;

[0060] Step S140: Count the frequency with which each candidate probability distribution model is selected as the optimal model in N bootstrap sample sets, and determine the candidate probability distribution model with the highest frequency as the best-fit distribution model for the ultimate load data of high-temperature adhesives.

[0061] exist Figure 1 The technical solution provided in the illustrated embodiment offers a systematic and scientific method for selecting the best-fit distribution model for ultimate load data of high-temperature adhesives by combining bootstrap sampling and the Bayesian Information Criterion (BIC). First, bootstrap sampling is used to generate multiple sample sets, which helps overcome the problem of limited original data volume and better reflects the true distribution characteristics of the data, increasing the robustness of the analysis. Next, each candidate probability distribution model is fitted to each bootstrap sample set, and the corresponding BIC value is calculated. This process not only considers the model fit but also penalizes model complexity, ensuring that the selected model can both well describe the data characteristics and avoid overfitting. Then, based on each bootstrap sample set, the optimal model is selected based on the BIC value. This method effectively identifies the model most suitable for describing the characteristics of the current sample set. Finally, by performing frequency statistics on the optimal models selected in all bootstrap sample sets, the model with the highest frequency is determined as the best-fit distribution model. This method not only improves the reliability of model selection but also effectively addresses the variability between different sample sets. Overall, this approach provides a scientific and systematic method for determining the best-fit distribution model of the ultimate load of high-temperature adhesives, which is of great significance for improving product quality, optimizing design parameters, and ensuring safe use.

[0062] The following are Figure 1 The specific implementation process of each step in the process will be explained in detail:

[0063] In step S110, the original ultimate load sample set of the high-temperature adhesive is subjected to self-sampling to obtain N self-sampling sample sets.

[0064] In this step, the original ultimate load sample set of the high-temperature adhesive (hereinafter also referred to as the original sample set) can be subjected to bootstrap sampling to obtain N bootstrap sample sets. N is an integer greater than 1, preferably an integer greater than 1000, for example: 5000.

[0065] High-temperature adhesives refer to special adhesives used for bonding tile structures in high-temperature environments. Their ultimate load data reflects the maximum load value that the adhesive can withstand under high-temperature conditions.

[0066] The original ultimate load sample set for high-temperature adhesives refers to a set of ultimate load data obtained through experimental testing, used to describe the load-bearing capacity of the adhesive under specific test conditions. For example, the original sample set may contain the following data points: 1698.557, 1648.823, 2435.112, 2024.190, 2424.971, 1464.319, 1274.029. This sample set contains a total of 7 data points, which is a small sample dataset, making it difficult to accurately fit the distribution using traditional statistical methods.

[0067] To enhance the robustness and reliability of the modeling, this step employs bootstrap sampling to randomly draw samples with replacement from the original sample set. Each sample draw contains the same number of data points as the original sample set (7 data points), forming a bootstrap sample set. This sampling process is repeated N = 5000 times, resulting in 5000 bootstrap sample sets, which are then used for subsequent distribution fitting and model evaluation.

[0068] refer to Figure 2 , Figure 2 The diagram illustrates the basic principle of the Bootstrap resampling technique described above. Figure 2 As shown:

[0069] This figure illustrates the application of the Bootstrap method in statistical analysis. The original sample set consists of a series of observations, represented as x = {x...} (1) x (1) ,x (1) ,……,x (N)} where N is the total number of observations. Using the Bootstrap method, we randomly draw samples with replacement from the original sample set to generate multiple Bootstrap sample sets, as shown in the figure. Until Each sample set also contains N observations, but these observations are randomly selected from the original sample set, and therefore may include duplicate observations, or some observations may not have been selected. For each Bootstrap sample set, we calculate the corresponding statistic. This can be any statistical indicator of interest, such as the mean, variance, or median. Through this series of bootstrap statistics, we can estimate the distribution characteristics of the statistics, and then assess their variability or construct confidence intervals. This is crucial for understanding data uncertainty and conducting hypothesis testing. The entire process demonstrates the powerful role of the bootstrap method in nonparametric statistical inference; it provides reliable results without requiring strict assumptions about the data distribution.

[0070] Next, refer to Figure 1 In step S120, each candidate probability distribution model is fitted using each bootstrap sample set, and the Bayesian information criterion value corresponding to each candidate probability distribution model is calculated.

[0071] In this step, each bootstrap sample set can be used to fit each candidate probability distribution model, and the Bayesian information criterion value corresponding to each candidate probability distribution model can be calculated.

[0072] Among them, the above-mentioned candidate probability distribution models can include at least two of the following: normal distribution, exponential distribution, gamma distribution, and Weibull distribution.

[0073] For each bootstrap sample set, the parameters of the above candidate probability distribution model are estimated and fitted, and the corresponding BIC value is calculated based on the following Bayesian Information Criterion (BIC) Formula 1:

[0074] BIC = kln(n) - 2ln(L) Formula 1

[0075] Wherein, BIC represents the Bayesian Information Criterion value; where: k represents the number of parameters of the candidate probability distribution model (for example, the normal distribution has 2 parameters: mean and standard deviation); m represents the sample size of the current bootstrap sample set (7 in this embodiment); L represents the maximum likelihood value of the candidate probability distribution model under the current bootstrap sample set.

[0076] The maximum likelihood value L is calculated as follows:

[0077] The likelihood function for constructing a candidate probability distribution model based on the current bootstrap sample set;

[0078] The maximum likelihood estimation method (MLE) is used to optimize the likelihood function, and the estimated model parameters that maximize the likelihood function value are obtained.

[0079] Substitute the estimated parameters into the likelihood function to calculate the maximum likelihood value L.

[0080] By following the steps above, the corresponding BIC value can be calculated for each bootstrap sample set and each candidate probability distribution model.

[0081] In step S130, the optimal model is selected based on the Bayesian information criterion value for each bootstrap sample set.

[0082] In this step, a smaller BIC value indicates a better balance between fit and model complexity. Therefore, for each bootstrap sample set, the candidate probability distribution model with the smallest BIC value is selected as the optimal model for that sample set. This process is repeated for each bootstrap sample set to obtain the optimal model for each set.

[0083] For example, taking the original sample set as an example, the BIC of each candidate probability distribution model can be referred to in Table 1:

[0084] Table 1

[0085] Candidate probability distribution model BIC value normal distribution 108.469 Exponential distribution 121.289 Gamma distribution 108.127 Weiber distribution 108.466

[0086] As shown in Table 1, the gamma distribution has the smallest BIC value, therefore the optimal model for the original sample set is the gamma distribution.

[0087] refer to Figure 3 , Figure 3 The graph shows a comparison of the BIC values ​​of the candidate probability distribution models under the original sample set, as shown below. Figure 3 As shown, Figure 3 A bar chart is presented to compare the BIC values ​​of candidate probability distribution models for the original data, in order to determine the optimal distribution model for the ultimate load distribution characteristics of high-temperature adhesives used in tiles. The horizontal axis represents different probability distribution models (including normal, exponential, gamma, and Weiber distributions), and the vertical axis corresponds to the BIC values ​​of these models. The chart shows that the normal distribution has a BIC value of 108.5, the exponential distribution has the highest BIC value of 121.3, significantly higher than the other three distribution models, and the gamma distribution has the lowest BIC value of 108.1, marked with an asterisk (*) to indicate that it is the optimal distribution model selected based on the BIC criterion. The Weiber distribution... The BIC value is the same as that of the normal distribution, at 108.5. Since a lower BIC value implies a better fit and takes into account the influence of model complexity, the gamma distribution is identified as the optimal distribution among the four candidate probability distribution models due to its lowest BIC value. This is consistent with the conclusion in the scheme description, that is, the allowable ultimate load is more likely to follow the gamma distribution. The text above the chart, "Optimal distribution: gamma (marked with an asterisk)," further emphasizes this conclusion. This result has important guiding significance for subsequent analysis and application, especially in the case of small samples, where selecting an appropriate distribution model is crucial for accurately evaluating the ultimate load characteristics of high-temperature adhesives for tiles.

[0088] Next, refer to Figure 1 In step S140, the frequency of each candidate probability distribution model being selected as the optimal model in N bootstrap sample sets is counted, and the candidate probability distribution model with the highest frequency is determined as the best-fit distribution model for the ultimate load data of high-temperature adhesives.

[0089] In this step, the frequency with which each candidate probability distribution model is selected as the optimal model in the above 5000 bootstrap sample set can be counted, and the candidate probability distribution model with the highest frequency can be determined as the best fit distribution model for the ultimate load data of high temperature adhesives.

[0090] For example, the statistical results can be found in Table 2 below:

[0091] Table 2

[0092] Candidate probability distribution model Frequency of being selected as the optimal model percentage normal distribution 9 0.18％ Exponential distribution 0 0.00％ Gamma distribution 3208 64.16％ Weiber distribution 1783 35.66％

[0093] As shown in Table 2, the gamma distribution was selected as the optimal model most frequently in 5000 bootstrapping experiments, accounting for 64.16%, which is much higher than other distribution models.

[0094] refer to Figure 4 , Figure 4 This shows a frequency plot of different distribution models selected as the optimal model in Bootstrap sampling. For example... Figure 4 As shown, Figure 4 A bar chart is presented to reflect the frequency with which different candidate probability distribution models (normal, exponential, gamma, and Weiber distributions) were selected as the optimal distribution during the Bootstrap sampling process. The horizontal axis represents the probability distribution model, and the vertical axis represents the percentage of each model selected. The normal distribution was selected with a frequency of only 0.2%, which is almost negligible; the exponential distribution was never selected as the optimal model in the entire 5000 bootstrap sampling process, with a frequency of 0.0%; the gamma distribution was the most frequently selected model with a selection frequency of 63.4%, indicating that it had the best fit in most bootstrap samples; the Weiber distribution was selected with a selection frequency of 36.4%, which, although lower than the gamma distribution, still shows its high fit as a candidate probability distribution model. This result is highly consistent with the data in the scheme description, where the gamma distribution was selected 64.16% of the time in 5000 bootstrap samplings, the Weiber distribution 35.66%, the normal distribution 0.18%, and the exponential distribution 0.00%.

[0095] The Bootstrap sampling method allows for a more robust evaluation of the applicability of various distribution models under different samples, especially under small sample conditions. The gamma distribution, due to its high-frequency adaptability and stability exhibited in multiple resampling processes, has been identified as the most probable ultimate load distribution model. This conclusion has significant guiding implications for subsequent analysis and prediction of load characteristics in engineering practice and theoretical research.

[0096] Optionally, the average BIC value of each distribution model can be further calculated across all bootstrap sample sets, as shown in Table 3:

[0097] Table 3

[0098] Candidate probability distribution model Average BIC value normal distribution 106.7 Exponential distribution 121.2 Gamma distribution 106.4 Weiber distribution 106.7

[0099] As shown in Table 3, the average BIC value of the gamma distribution is the lowest, further verifying that it is the optimal model. Therefore, it can be finally determined that the ultimate load data of high-temperature adhesives for tiles are more likely to follow the gamma distribution.

[0100] refer to Figures 5-8 , Figures 5-8 This diagram shows the BIC value distribution of each candidate probability distribution model in the embodiments of this disclosure. Specifically, Figure 5 This demonstrates the distribution of BIC values ​​for a normal distribution during Bootstrap sampling. Figure 6 This demonstrates the distribution of BIC values ​​under the exponential distribution during Bootstrap sampling. Figure 7 This demonstrates the distribution of BIC values ​​in the gamma distribution during the Bootstrap sampling process. Figure 8 This illustrates the distribution of the BIC values ​​according to the Weibull distribution during the bootstrap sampling process. The horizontal axis represents the BIC value, and the vertical axis represents the frequency, i.e., the number of times each different BIC value occurs in 5000 bootstrap samplings. Specifically:

[0101] Normal distribution: BIC values ​​are concentrated between 100 and 110, showing a certain left skewness (negative skewness of -1.92), with a mean and median of 106.7, a standard deviation of 3.4, a minimum of 82.2, and a maximum of 112.3.

[0102] Exponential distribution: The BIC value range is relatively narrow, concentrated between 117 and 125, with a mean of 121.2, a median of 121.3, a small standard deviation (1.2), and a skewness close to zero, indicating that its fit is relatively stable in all bootstrap samples. However, since the BIC mean is significantly higher than other distributions, it is not the optimal choice.

[0103] Gamma distribution: BIC values ​​are also concentrated between 100 and 110, showing a left-skewed distribution (skewness of -1.69), with a mean of 106.4, slightly lower than the normal distribution, a median of 107.0, a standard deviation of 3.4, a minimum of 81.7, and a maximum of 112.8.

[0104] The Weiber distribution: The BIC values ​​are also concentrated between 100 and 110, but its skewness is greater (-2.48), showing a more obvious left-skewed distribution. The mean is 106.7, the same as the normal distribution, the median is 107.4, the standard deviation is also 3.4, the minimum is 80.7, and the maximum is 112.4.

[0105] In summary, the gamma distribution is considered the most likely ultimate load distribution model due to its lowest mean BIC value and high stability across multiple resampling tests. While the Weiber distribution performs well in some samples, it is less stable overall than the gamma distribution. The normal and exponential distributions are not considered optimal choices due to their high mean BIC values.

[0106] refer to Figure 9 , Figure 9 This diagram shows a comparison between the original data histogram and the gamma distribution fitting curve in an embodiment of this disclosure. Specifically, Figure 9 A probability density plot is presented to compare the histogram of the original data with the fitting curve of the gamma distribution—the optimal distribution model selected according to the BIC criterion—to verify the effectiveness and accuracy of the model in describing the ultimate load data. The horizontal axis represents the observed values ​​(ultimate load), and the vertical axis represents the probability density. The histogram represents the frequency distribution of the original data, showing that the observed values ​​are mainly concentrated between 1200 and 2400, especially with a higher frequency in the 2000 to 2400 range. The curve represents the fitting result of the gamma distribution, with parameters α = 19.3217 and β = 95.8949, the best estimates obtained through the fitting process. The shape of the curve is basically consistent with the distribution trend of the original data, especially showing a high degree of fit in the high-frequency range. In the low-frequency range (e.g., 1200 to 1600), the gamma distribution curve can capture the trend of the original data well without significant deviation; in the high-frequency range (2000 to 2400), the fitted curve is very close to the histogram, further verifying its good fitting effect. Furthermore, in the right side of the high-frequency range (above 2400), despite the limited amount of original data, the gamma distribution curve can still reasonably predict the trend of probability density changes, demonstrating a certain extrapolation ability. This comparative analysis shows that the gamma distribution, as the optimal distribution model, not only accurately describes the main distribution characteristics of the original data but also possesses a certain predictive ability. This has significant reference value for subsequent evaluation of ultimate load characteristics in engineering applications and theoretical research.

[0107] Based on the above technical solution, this disclosure has at least the following technical effects:

[0108] To address the unclear ultimate load distribution characteristics of high-temperature adhesives for roofing tiles, a method for judging the ultimate load distribution characteristics of high-temperature adhesives for roofing tiles based on the BIC criterion and bootstrap sampling under small sample conditions is proposed. This method can efficiently and accurately grasp the ultimate load distribution characteristics of high-temperature adhesives and has good practicality and theoretical guidance.

[0109] This disclosure also provides a device for modeling the ultimate load of high-temperature adhesives. Figure 10 This diagram illustrates the structure of the ultimate load modeling apparatus for high-temperature adhesives in an exemplary embodiment of this disclosure; as shown below. Figure 10 As shown, the ultimate load modeling device 1000 for high-temperature adhesives may include a self-sampling module 1010, a fitting module 1020, a model selection module 1030, and a statistical module 1040. Wherein:

[0110] The self-sampling module 1010 is used to perform self-sampling processing on the original ultimate load sample set of the high-temperature adhesive to obtain N self-sampling sample sets; N is an integer greater than 1.

[0111] The fitting module 1020 is used to fit each candidate probability distribution model using each of the bootstrap sample sets, and to calculate the Bayesian information criterion value corresponding to each candidate probability distribution model.

[0112] The model selection module 1030 is used to select the optimal model based on the Bayesian information criterion value for each bootstrap sample set.

[0113] The statistics module 1040 is used to count the frequency of each candidate probability distribution model being selected as the optimal model under the N bootstrap sample sets, and to determine the candidate probability distribution model with the highest frequency as the best-fit distribution model for the ultimate load data of the high-temperature adhesive.

[0114] In an exemplary embodiment of this disclosure, the candidate probability distribution model includes at least two of the following:

[0115] Normal distribution, exponential distribution, gamma distribution, and Weiber distribution.

[0116] In an exemplary embodiment of this disclosure, the self-sampling module 710 performs self-sampling processing on the original ultimate load sample set of the high-temperature adhesive to obtain N self-sampling sample sets, including:

[0117] From the original ultimate load sample set, samples are randomly drawn with replacement, and the number of samples drawn each time is the same as the number of samples in the original ultimate load sample set, to obtain a bootstrap sample set.

[0118] The sampling process is repeated N times to obtain the N bootstrap sample sets.

[0119] In an exemplary embodiment of this disclosure, the fitting module 720 calculates the Bayesian information criterion value corresponding to each candidate probability distribution model based on the following formula:

[0120] BIC = kln(n) - 2ln(L)

[0121] Wherein, BIC represents the Bayesian information criterion value; k represents the number of model parameters corresponding to each candidate probability distribution model; n represents the sample size corresponding to the current bootstrap sample set; and L represents the maximum likelihood value of each candidate probability distribution model under the current bootstrap sample set.

[0122] In an exemplary embodiment of this disclosure, the maximum likelihood value of each candidate probability distribution model under the current bootstrap sample set is determined in the following manner:

[0123] For each candidate probability distribution model, a likelihood function corresponding to the candidate probability distribution model is constructed based on the current bootstrap sample set;

[0124] The likelihood function is optimized using the maximum likelihood estimation method to find the model parameter estimates that maximize the likelihood function value.

[0125] Substituting the estimated model parameters into the likelihood function, the maximum likelihood value of the candidate probability distribution model under the current bootstrap sample set is calculated.

[0126] In an exemplary embodiment of this disclosure, the model selection module 730 selects the optimal model based on the Bayesian information criterion value, including:

[0127] The candidate probability distribution model with the smallest Bayesian information criterion value is selected as the optimal model.

[0128] In an exemplary embodiment of this disclosure, N is an integer greater than or equal to 1000.

[0129] The specific details of each module in the above-mentioned ultimate load modeling device for high-temperature adhesives have been described in detail in the corresponding ultimate load modeling method for high-temperature adhesives, so they will not be repeated here.

[0130] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0131] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0132] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0133] This disclosure also provides a computer-readable storage medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device.

[0134] Computer-readable storage media can be, for example—but not limited to—electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0135] A computer-readable storage medium can be sent, propagated, or transmitted for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable storage medium can be transmitted using any suitable medium, including but not limited to: wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0136] A computer-readable storage medium carries one or more programs that, when executed by an electronic device, cause the electronic device to perform the methods described in the above embodiments.

[0137] Furthermore, this disclosure also provides an electronic device capable of implementing the above-described method.

[0138] Those skilled in the art will understand that various aspects of this disclosure can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0139] The following reference Figure 11 To describe an electronic device 1100 according to such an embodiment of the present disclosure. Figure 11 The electronic device 1100 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0140] like Figure 11 As shown, the electronic device 1100 is presented in the form of a general-purpose computing device. The components of the electronic device 1100 may include, but are not limited to: at least one processor 1110, at least one memory 1120, a bus 1130 connecting different system components (including memory 1120 and processor 1110), and a display 1140.

[0141] The memory stores program code that can be executed by the processor 1110, causing the processor 1110 to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of this disclosure. For example, the processor 1110 can perform actions such as... Figure 1As shown: Step S110, perform bootstrap sampling on the original ultimate load sample set of the high-temperature adhesive to obtain N bootstrap sample sets; N is an integer greater than 1; Step S120, fit each candidate probability distribution model using each bootstrap sample set, and calculate the Bayesian information criterion value corresponding to each candidate probability distribution model; Step S130, select the optimal model based on the Bayesian information criterion value under each bootstrap sample set; Step S140, count the frequency of each candidate probability distribution model being selected as the optimal model under the N bootstrap sample sets, and determine the candidate probability distribution model with the highest frequency as the best-fit distribution model for the ultimate load data of the high-temperature adhesive.

[0142] The memory 1120 may include a readable medium in the form of volatile storage, such as random access memory (RAM) 11201 and / or cache memory 11202, and may further include read-only memory (ROM) 11203.

[0143] The memory 1120 may also include a program / utility 11204 having a set (at least one) of program modules 11205, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0144] Bus 1130 can represent one or more of several types of bus structures, including a memory bus or memory controller, peripheral bus, graphics acceleration port, processor, or a local bus using any of the various bus structures.

[0145] Electronic device 1100 can also communicate with one or more external devices 1200 (e.g., keyboard, pointing device, Bluetooth device, etc.), one or more devices that enable a user to interact with electronic device 1100, and / or any device that enables electronic device 1100 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 1150. Furthermore, electronic device 1100 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 1160. As shown, network adapter 1160 communicates with other modules of electronic device 1100 via bus 1130. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 1100, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0146] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This disclosure is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

Claims

1. A method for modeling the ultimate load of high-temperature adhesives, characterized in that, include: The original ultimate load sample set of the high-temperature adhesive is subjected to bootstrap sampling to obtain N bootstrap sample sets; N is an integer greater than 1. Each candidate probability distribution model is fitted using each of the aforementioned bootstrap sample sets, and the Bayesian information criterion value corresponding to each candidate probability distribution model is calculated; For each self-service sample set, the optimal model is selected based on the Bayesian information criterion value; The frequency with which each candidate probability distribution model is selected as the optimal model in the N bootstrap sample sets is counted, and the candidate probability distribution model with the highest frequency is determined as the best-fit distribution model for the ultimate load data of the high-temperature adhesive.

2. The method according to claim 1, characterized in that, The candidate probability distribution model includes at least two of the following: Normal distribution, exponential distribution, gamma distribution, and Weiber distribution.

3. The method according to claim 1 or 2, characterized in that, The original ultimate load sample set of the high-temperature adhesive is subjected to bootstrap sampling to obtain N bootstrap sample sets, including: From the original ultimate load sample set, samples are randomly drawn with replacement, and the number of samples drawn each time is the same as the number of samples in the original ultimate load sample set, to obtain a bootstrap sample set. The sampling process is repeated N times to obtain the N bootstrap sample sets.

4. The method according to claim 3, characterized in that, The Bayesian information criterion value for each candidate probability distribution model is calculated based on the following formula: BIC = kln(n) - 2ln(L) Wherein, BIC represents the Bayesian information criterion value; k represents the number of model parameters corresponding to each candidate probability distribution model; n represents the sample size corresponding to the current bootstrap sample set; and L represents the maximum likelihood value of each candidate probability distribution model under the current bootstrap sample set.

5. The method according to claim 4, characterized in that, The maximum likelihood value of each candidate probability distribution model under the current bootstrap sample set is determined by the following method: For each candidate probability distribution model, a likelihood function corresponding to the candidate probability distribution model is constructed based on the current bootstrap sample set; The likelihood function is optimized using the maximum likelihood estimation method to find the model parameter estimates that maximize the likelihood function value. Substituting the estimated model parameters into the likelihood function, the maximum likelihood value of the candidate probability distribution model under the current bootstrap sample set is calculated.

6. The method according to claim 1, characterized in that, The selection of the optimal model based on the Bayesian information criterion value includes: The candidate probability distribution model with the smallest Bayesian information criterion value is selected as the optimal model.

7. The method according to claim 1, characterized in that, N is an integer greater than or equal to 1000.

8. A device for modeling the ultimate load of a high-temperature adhesive, characterized in that, include: The self-sampling module is used to perform self-sampling processing on the original ultimate load sample set of the high-temperature adhesive to obtain N self-sampling sample sets; N is an integer greater than 1. The fitting module is used to fit each candidate probability distribution model using each of the bootstrap sample sets, and to calculate the Bayesian information criterion value corresponding to each candidate probability distribution model. The model selection module is used to select the optimal model based on the Bayesian information criterion value for each bootstrap sample set. The statistics module is used to count the frequency with which each of the candidate probability distribution models is selected as the optimal model under the N bootstrap sample sets, and to determine the candidate probability distribution model with the highest frequency as the best-fit distribution model for the ultimate load data of the high-temperature adhesive.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the ultimate load modeling method for high-temperature adhesives according to any one of claims 1 to 7.

10. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the ultimate load modeling method for high-temperature adhesives according to any one of claims 1 to 7 by executing the executable instructions.

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