Method for calculating fire endurance of concrete filled steel tubular column in fire

Abstract

The invention provides a method for calculating the fire endurance of a concrete filled steel tubular column in a fire disaster, which belongs to the technical field of safety risk assessment, and specifically comprises the following steps of: carrying out numeralization and normalization processing on collected literature data, analyzing an obtained data parameter group by adopting a Spearman correlation coefficient method, determining important parameters according to the correlation level, and calculating the fire endurance of the concrete filled steel tubular column in the fire disaster; according to the determined important parameter data, establishing a fire endurance prediction model, establishing a database, performing single-parameter analysis on the determined important parameters, and fitting a result to correct a calculation formula; the method has the beneficial effects that the calculation formula can more comprehensively reflect the fire resistance of an actual structure, so that the applicability and the accuracy of the formula are improved, the formula not only shows good applicability in different sample data, but also has relatively high calculation precision, and a reliable basis is provided for fire resistance design in actual engineering.

Description

Technical Field

[0001] The invention belongs to the technical field of safety risk assessment, and in particular relates to a method for calculating the fire resistance limit of a steel tube concrete column under fire. Background Art

[0002] In recent years, steel tube concrete columns have been widely used in high-rise buildings due to their high bearing capacity, good stiffness and excellent seismic performance. However, when encountering a serious fire, the mechanical properties of steel tube concrete columns are significantly reduced, which may lead to local damage or overall collapse of the structure. With the development of the field of fire resistance, many scholars have proposed a variety of calculation formulas for the fire resistance limit of steel tube concrete columns based on test results and simulation data. However, due to differences in the parameters considered, research methods, heating curves, etc., these calculation formulas are not unified and it is difficult to provide a reliable reference for fire resistance design. Therefore, a unified calculation formula for the fire resistance limit of steel tube concrete columns should be proposed to improve the accuracy and safety of fire resistance design.

[0003] At present, a variety of fire resistance calculation formulas for concrete-filled steel tube columns have been proposed, as follows: Based on the numerical analysis results, the fire resistance calculation formula of concrete-filled steel tube columns under fire was regressed. This formula takes into account the effects of section width, load eccentricity, load eccentricity angle, slenderness ratio and load ratio on the fire resistance limit.

[0004] In the above formula, is the fire resistance limit, (min); B is the section width, (mm); is the load eccentricity angle, (°) is the slenderness ratio, n is the load ratio; e is the eccentricity.

[0005] An analysis of the existing technologies revealed the following problems: Currently, most of the existing fire resistance calculation formulas for steel tube concrete columns are based on a small amount of test data or finite element simulation results, and only consider limited parameters such as load ratio, steel tube thickness and cross-sectional size. These calculation formulas are usually proposed based on specific test samples, so their accuracy and reliability are low when applied to other samples. Summary of the invention

[0006] In view of this, the present invention proposes a method for calculating the fire resistance limit of steel tube concrete columns under fire, which solves the problems of limited consideration parameters and insufficient calculation data when calculating the fire resistance limit of concrete columns, and also solves the problems of low applicability and accuracy of current experimental analysis formulas.

[0007] The present invention proposes a method for calculating the fire resistance limit of a steel tube concrete column under fire, which specifically includes the following steps: S1 digitizes and normalizes the collected literature data to obtain a data parameter group; S2 uses the Spearman correlation coefficient method to analyze the data parameter group obtained in step S1, determines the correlation between the data group and the fire resistance limit, and determines the important parameters according to the correlation; S3 uses data training and testing machine learning algorithms to establish a fire resistance prediction model based on the important parameter data determined in step S2; S4 uses an integrated model to predict fire resistance by expanding input parameters and establishing a database; S5: using the database established in step 4, performing single parameter analysis on the important parameters determined in step S2 to determine the functional relationship between the important parameters and the fire resistance limit; S6 adopts a nonlinear regression analysis method to fit the functional relationship obtained in S5 to obtain a calculation formula for the fire resistance limit of the steel tube concrete column; S7 verifies the fire resistance calculation formula obtained in S6 according to the data in the original database, and modifies the calculation formula according to the fitting result.

[0008] On the basis of the above technical solution, the fire resistance calculation method of a steel tube concrete column under fire of the present invention can also be improved as follows: Further, the specific steps of S1 are as follows: Existing literature data were collected to determine 10 parameters, including 9 numerical parameters and 1 classification parameter; For numerical parameters, they are directly saved in their numerical form; for categorical parameters, they are assigned values ​​of 0-1 according to the categorical form, thus converting them into numerical form; Subsequently, the parameter results in numerical form are divided by the corresponding maximum value to complete the normalization of the literature parameter data, and the processing result range is limited to between 0 and 1 to obtain the processed data parameter group.

[0009] Further, the specific steps of S2 are as follows: Using Python software, Spearman correlation analysis was performed on the data parameter group obtained after the S1 step, and a heat map of the correlation between each corresponding parameter and the fire resistance limit was generated; The thermodynamic diagram was analyzed to identify five key parameters with a correlation greater than 0.25 with the fire resistance limit, which are considered to be important parameters affecting the fire resistance limit; specifically, cross-sectional dimensions, steel pipe thickness, load ratio, cross-sectional shape, and load eccentricity.

[0010] Further, the specific steps of S3 are as follows: Using Python software, the data sorted in steps S1 and S2 are divided into a training set and a test set in a ratio of 7:3, and the training set and the test set are respectively input into the Random Forest Regression, XGBoost Regression, and MLP Regression algorithms; By debugging the basic parameters of each algorithm, optimizing the performance of the algorithm, and performing weighted integration on the prediction results of the algorithm, the corresponding fire resistance limit prediction model is obtained.

[0011] The specific steps of S4 are as follows: The data range of the five key parameters determined in step S2 is consulted, and the value of each parameter is adjusted one by one. One of the parameters is selected as a variable, and the remaining parameters are set as fixed values. Different parameter combinations are input into the prediction model to predict the fire resistance limit of these components and obtain a fire resistance limit database.

[0012] Further, the specific steps of S5 are as follows: Using Origin software, single parameter analysis was performed on the five important parameters according to the database established in step S4 to determine the best fitting function relationship between each parameter and the fire resistance limit. In order to further improve the accuracy of the method, the functional relationship between various parameters and fire resistance limit in other literatures was collected, the collected functional relationship was compared with the calculated best fitting functional relationship, and the comparison results were analyzed; at the same time, the parameter data collected from other literatures were input into the best fitting function to obtain the verified functional relationship results, and the verified results were compared and analyzed with the original functional relationship.

[0013] Further, the specific steps of S6 are as follows: Using Origin software, we adopted the form of adding parameter function relationship to reduce parameter error, performed nonlinear regression analysis on the overall database, obtained the fitting accuracy under different combination forms, and used the performance index R2 for evaluation; The combination form with R2 of 0.911 showed the highest accuracy, and the corresponding formula was adopted as the calculation formula for the fire resistance limit of steel tube concrete columns.

[0014] Compared with the prior art, the method for calculating the fire resistance limit of a steel tube concrete column under fire proposed by the present invention has the following beneficial effects: Optimize important parameters: The Spearman correlation coefficient analysis method was used to determine five parameters that have an important impact on the fire resistance limit, breaking through the limitation of only considering a small number of parameters in the existing technology. This method has no requirements for data distribution and is suitable for collected test data. This improvement enables the calculation formula to more comprehensively reflect the fire resistance performance of the actual structure, thereby improving the applicability and accuracy of the formula.

[0015] Take the integrated model for data enhancement: Through the integration method, a prediction model with good generalization performance was established, and a large amount of data was predicted to establish a huge fire resistance limit database, which solved the accuracy problem caused by insufficient data in the existing technology. The establishment of this database has enhanced the calculation accuracy of the regression formula under multiple parameter combinations, thereby improving the reliability of the fire resistance limit calculation formula.

[0016] Improve the applicability and accuracy of formulas: The formula form of parameter addition is adopted to reduce the error. The fire resistance calculation formula established based on nonlinear regression analysis combines the relationship between multiple important parameters and overcomes the shortcomings of the existing formula in terms of applicability. This formula not only shows good applicability in different sample data, but also has high calculation accuracy, providing a reliable basis for fire resistance design in actual engineering.

[0017] Enhanced safety of fire-resistant design: Through the above improvements, the present invention can provide designers with more accurate fire resistance limit data, thereby enhancing the safety of buildings under fire conditions, reducing the risk of local damage or overall collapse, and promoting safety standardization in the construction industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Heatmaps for Spearman correlation analysis; Figure 2 It is a single parameter analysis of cross-sectional size and fire resistance; Figure 3 It is a single parameter analysis of steel pipe thickness and fire resistance; Figure 4 It is a single parameter analysis of load ratio and fire resistance; Figure 5 It is a single parameter analysis of cross-sectional shape and fire resistance; Figure 6 Single parameter analysis of load eccentricity and fire resistance Figure 7 To verify the fire resistance calculation formula results. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0020] like Figure 2-7 , is the analysis result of a method for calculating the fire resistance limit of a steel tube concrete column under fire proposed by the present invention. The specific steps of the present invention include: S1 digitizes and normalizes the collected literature data.

[0021] By collecting literature data, a total of 10 parameters were considered, including 9 numerical parameters and 1 categorical parameter. The numerical parameters were directly saved in their numerical form. For the categorical parameters, i.e., the cross-sectional form, different cross-sectional forms were assigned values ​​of 0-1, thus converting them into numerical form. Subsequently, the numerical parameter results were divided by their maximum value to achieve data normalization processing, so that the result range was limited to between 0 and 1.

[0022] S2 uses the Spearman correlation coefficient method to analyze the correlation between various parameters and fire resistance limit to optimize important parameters, among which important parameters such as Figure 2-6 shown.

[0023] Using Python software, the processed literature data was analyzed for correlation, and a heat map of the correlation between each parameter and the fire resistance limit was generated. By analyzing the bottom row of the heat map, five key parameters with a correlation greater than 0.25 with the fire resistance limit can be identified. These parameters are considered to be important parameters affecting the fire resistance limit, including section size, steel pipe thickness, load ratio, section shape, and load eccentricity.

[0024] Based on the data of steel tube concrete columns, Spearman correlation analysis is used to optimize parameters. In Spearman correlation analysis, there is no requirement for whether the data is normally distributed, and the requirements for data distribution are lower, which is more suitable for the collected test data, and the final correlation results are more consistent with the data law.

[0025] S3 uses data to train and test machine learning algorithms to build fire resistance prediction models.

[0026] Using Python software, the data sorted in step 2 was divided into training set and test set in a ratio of 7:3, and input into random forest (Random Forest Regression), extreme gradient boosting (XGBoostRegression), and multi-layer perceptron algorithm (MLP Regression) respectively, and the prediction results were weighted integrated to complete the establishment of the fire resistance limit prediction model.

[0027] Based on the test data, an integrated model of three machine learning algorithms was adopted to predict the fire resistance limit. This method selected three machine learning models with high prediction accuracy, namely extreme gradient boosting, multi-layer perceptron and random forest algorithm. After the training was completed, the prediction results of the three algorithms were weighted and integrated (Ensemble), and finally the prediction value was input. Through weighted integration, the results of the three algorithms were weighted averaged, which can significantly improve the generalization of the prediction results and enable the model to maintain a high accuracy for data outside the training samples.

[0028] Since the random forest, extreme gradient boosting and multi-layer perceptron algorithms have a certain overfitting phenomenon when predicting the fire resistance limit, which is specifically manifested as higher accuracy on the training set and lower accuracy on the test set, the model is only effective for training samples and has poor generalization ability. To solve this problem, this patent adopts a weighted integration method to improve the generalization performance of the model. By assigning different weights according to the prediction accuracy of the three algorithms and taking a weighted average of their prediction results, the overfitting phenomenon can be effectively alleviated. Therefore, the integrated model can improve the prediction accuracy and stability, enhance the generalization ability of the model, and enable it to maintain a high accuracy when predicting data outside the training samples.

[0029] S4 uses an integrated model to predict fire resistance by expanding input parameters to establish a database.

[0030] First, the data range of the five key parameters was consulted, and the values ​​of each parameter were adjusted one by one. In this process, one parameter was selected as a variable, and the remaining parameters were set to fixed values. In this way, different parameter combinations were input into the prediction model to predict the fire resistance limits of these components. Among them, 67 components considered the cross-sectional size, 36 components considered the steel pipe thickness, 41 components considered the load ratio, 36 components considered the cross-sectional shape, and 21 components considered the load eccentricity. Finally, a fire resistance limit database containing 201 components was constructed, which provided important data support for the establishment of subsequent fire resistance limit calculation formulas.

[0031] S5 performs single parameter analysis on important parameters to determine the functional relationship between each parameter and the fire resistance limit.

[0032] Using Origin software, single parameter analysis was performed on five important parameters based on the established database to determine the best fitting functional relationship between each parameter and the fire resistance limit. In addition, in order to further improve the accuracy of the method, the functional relationship between each parameter and the fire resistance limit in other literature was also collected.

[0033] S6 adopts nonlinear regression analysis to fit the fire resistance calculation formula of steel tube concrete column.

[0034] Using Origin software, the parameter function relationship is added in a continuous manner to reduce the parameter error, and the database is subjected to nonlinear regression analysis to obtain the fitting accuracy under different combinations, and the performance index R2 is used for evaluation. After many attempts, it was found that the combination with R2 of 0.911 showed the highest accuracy. Therefore, this formula is used as the fire resistance calculation formula for steel tube concrete columns. The specific formula is shown below.

[0035] (1) (2) (3) (4) (5) (6) In the above formula, is the fire resistance limit (min); Cross-sectional dimensions; is the thickness of the steel pipe; is the load ratio; is the cross-sectional shape; is the load eccentricity.

[0036] Based on the same prediction results, the parameter function relationship is added and the calculation formula is obtained through nonlinear regression fitting, as shown in formulas (1) to (6), and its fitting R2 is 0.91. This method adds the error of each parameter in the form of parameter addition, thereby significantly reducing the impact of the error on the fitting formula and improving the accuracy of the fire resistance calculation formula. This method further improves the accuracy of the calculation formula by effectively reducing the error.

[0037] S7 verifies the fire resistance calculation formula, verifies the calculation formula with the database and collected test data, and corrects the calculation formula based on the local database data. Finally, it uses big data to search the network database and extracts other test data corresponding to this field to re-verify the calculation formula. It is found that it has high calculation accuracy and good applicability. The calculation results are verified according to the original database. Figure 7 shown.

[0038] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the fire resistance limit of a steel tube concrete column under fire, characterized in that: The specific steps include: S1 digitizes and normalizes the collected literature data to obtain a data parameter group; S2 uses the Spearman correlation coefficient method to analyze the data parameter group obtained in step S1 to determine the correlation between the data parameter group and the fire resistance limit, and determines the important parameters according to the correlation level; S3 uses data training and testing machine learning algorithms to establish a fire resistance prediction model based on the important parameter data determined in step S2; S4 uses an integrated model to predict fire resistance by expanding input parameters and establishing a database; S5, using the database established in step S4, performs single parameter analysis on the important parameters determined in step S2 to determine the functional relationship between the important parameters and the fire resistance limit; S6 adopts the method of nonlinear regression analysis to fit the functional relationship obtained in S5 and obtains the calculation formula of the fire resistance limit of the steel tube concrete column; S7 verifies the fire resistance calculation formula obtained by S6 based on the data in the original database, and modifies the calculation formula based on the fitting results.

2. The method for calculating the fire resistance limit of a concrete-filled steel tube column under fire according to claim 1, characterized in that: The specific steps of S1 are as follows: Existing literature data were collected to determine 10 parameters, including 9 numerical parameters and 1 classification parameter; For numerical parameters, they are directly saved in their numerical form; for categorical parameters, they are assigned values ​​of 0-1 according to the categorical form, thus converting them into numerical form; Subsequently, the parameter results in numerical form are divided by the corresponding maximum value to complete the normalization of the literature parameter data, and the processing result range is limited to between 0 and 1 to obtain the processed data parameter group.

3. The method for calculating the fire resistance limit of a steel tube concrete column under fire according to claim 2, characterized in that: The specific steps of S2 are as follows: Using Python software, the correlation analysis of the data parameter group obtained after the S1 step is performed, and the correlation heat map of each corresponding parameter and the fire resistance limit is generated; The thermodynamic diagram was analyzed to identify five key parameters with a correlation greater than 0.25 with the fire resistance limit, which are considered to be important parameters affecting the fire resistance limit; specifically: cross-sectional size, steel pipe thickness, load ratio, cross-sectional shape, and load eccentricity.

4. The method for calculating the fire resistance limit of a concrete-filled steel tube column under fire according to claim 3, characterized in that: The specific steps of S3 are as follows: Using Python software, the data sorted in steps S1 and S2 are divided into a training set and a test set in a ratio of 7:3, and the training set and the test set are respectively input into the random forest, extreme gradient boosting, and multilayer perceptron algorithms; By debugging the basic parameters of each algorithm, optimizing the performance of the algorithm, and performing weighted integration on the prediction results of the algorithm, the corresponding fire resistance limit prediction model is obtained.

5. The method for calculating the fire resistance limit of a concrete-filled steel tube column under fire according to claim 3, characterized in that: The specific steps of S4 are as follows: The data range of the five key parameters determined in step S2 is consulted, and the value of each parameter is adjusted one by one. One of the parameters is selected as a variable, and the remaining parameters are set as fixed values. Different parameter combinations are input into the prediction model to predict the fire resistance limit of these components and obtain a fire resistance limit database.

6. A method for calculating the fire resistance limit of a concrete-filled steel tube column under fire according to claim 5, characterized in that: The specific steps of S5 are as follows: Using Origin software, single parameter analysis was performed on the five important parameters according to the database established in step S4 to determine the best fitting function relationship between each parameter and the fire resistance limit. In order to further improve the accuracy of the method, the functional relationship between various parameters and fire resistance limit in other literatures was collected, the collected functional relationship was compared with the calculated best fitting functional relationship, and the comparison results were analyzed; at the same time, the parameter data collected from other literatures were input into the best fitting function to obtain the verified functional relationship results, and the verified results were compared and analyzed with the original functional relationship.

7. The method for calculating the fire resistance limit of a concrete-filled steel tube column under fire according to claim 1, characterized in that: The specific steps of S6 are as follows: Using Origin software, we adopted the form of adding parameter function relationship to reduce parameter error, performed nonlinear regression analysis on the overall database, obtained the fitting accuracy under different combination forms, and used the performance index R2 for evaluation; The combination form with R2 of 0.911 showed the highest accuracy, and the corresponding formula was adopted as the calculation formula for the fire resistance limit of steel tube concrete columns.

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