A monte carlo-based method and system for optimizing cracks in reinforced concrete beams

Abstract

This invention relates to the field of civil engineering structural design technology, and particularly to a Monte Carlo-based method and system for optimizing cracks in reinforced concrete beams. The method includes: S1, selecting associated design parameters for cracks in reinforced concrete beams and establishing a parameter set; S2, constructing a crack width model based on the parameter set established in step S1; S3, performing correlation coefficient-Monte Carlo sensitivity analysis on the crack widths obtained from the parameter set and crack width model to obtain the correlation value of each associated design parameter and the probability value of the crack width; S4, constructing a histogram for the correlation values ​​of the associated design parameters and a distribution map for the probability values ​​of the crack width; S5, determining the associated design parameters to be optimized based on the histogram and distribution map, and optimizing the determined associated design parameters. This method improves the sensitivity analysis of design parameters, effectively guides optimization design, and provides a quantitative analysis of the effectiveness of optimization measures.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural design technology, and in particular to a Monte Carlo-based method and system for optimizing cracks in reinforced concrete beams. Background Technology

[0002] Reinforced concrete beams are prone to cracking under load, and crack width is an important indicator for assessing structural durability and safety. Traditional crack prediction methods often employ deterministic models, which struggle to account for material properties, geometric parameters, and the randomness of loads, leading to significant discrepancies between predicted and actual results.

[0003] The prior art CN116842620A discloses an intelligent prediction method and system for cracks in reinforced concrete bridges. The method includes: connecting a simulation system to model the first target bridge using the structural parameters of the first target bridge, outputting the first bridge simulation model for simulation, collecting a set of bridge sample images for model training, outputting a crack prediction dual-channel model, acquiring images of the first target bridge using an image acquisition device to obtain a set of real-time crack images, inputting the real-time crack image set and a preset target period into the crack prediction dual-channel model, and outputting the risk prediction result.

[0004] However, the aforementioned crack prediction methods lack sufficient sensitivity analysis of design parameters, cannot effectively guide optimized design, and lack quantitative analysis of the effects of optimization measures.

[0005] Therefore, there is an urgent need to provide a Monte Carlo-based method and system for optimizing cracks in reinforced concrete beams. Compared with existing technologies, this method improves the sensitivity analysis of design parameters, effectively guides optimization design, and provides quantitative analysis of the effects of optimization measures. Summary of the Invention

[0006] This invention addresses the technical problems existing in the prior art by providing a Monte Carlo-based method and system for optimizing cracks in reinforced concrete beams.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A Monte Carlo-based crack optimization method for reinforced concrete beams includes the following steps:

[0009] S1. Select the associated design parameters for cracks in reinforced concrete beams and establish a parameter set;

[0010] S2. Based on the parameter set established in step S1, construct a crack width model;

[0011] S3. Perform correlation coefficient-Monte Carlo sensitivity analysis on the crack width obtained from the parameter set and crack width model to obtain the correlation value of each associated design parameter and the probability value of the crack width.

[0012] S4. Construct histograms for the relevant values ​​of the associated design parameters and construct distribution maps for the probability values ​​of crack widths;

[0013] S5. Based on the histogram and distribution map, determine the correlation design parameters to be optimized, and optimize the determined correlation design parameters.

[0014] Furthermore, the associated design parameters in step S1 include concrete strength, steel reinforcement strength, bending moment, cover thickness, section height, and reinforcement ratio; N parameter sets are generated using the Latin hypercube sampling method, and each parameter set is represented by the following formula:

[0015] ;

[0016] In the above formula, Represents a set of parameters. Indicates concrete strength. Indicates the strength of the reinforcing steel. Indicates bending moment, Indicates the thickness of the protective layer. Indicates the cross-sectional height. This indicates the reinforcement ratio.

[0017] Furthermore, S2 specifically includes the following steps:

[0018] S21. Construct a steel reinforcement stress model based on the associated design parameters;

[0019] S22. Based on the steel reinforcement stress model, construct the crack width model.

[0020] Furthermore, the steel reinforcement stress model constructed in step S21 is expressed by the following formula:

[0021] ;

[0022] ;

[0023] In the above formula, Indicates the stress in the reinforcing steel. This represents the cross-sectional area of ​​the longitudinal reinforcement in the tension zone. Indicates the effective height of a reinforced concrete beam. Indicates taking , The minimum value after algebraic calculation of both.

[0024] Furthermore, the crack width model constructed in step S22 is expressed by the following formula:

[0025] ;

[0026] In the above formula, Indicates the crack width. , These all represent parameters related to concrete strength. Represents the elastic modulus of steel bars, for The value is 2.1.

[0027] Furthermore, the relevant value of each associated design parameter is calculated using the following formula:

[0028] ;

[0029] In the above formula, This represents the relevant value of the i-th associated design parameter, where i ranges from 1 to 6. This represents the value of the i-th associated design parameter in the k-th Monte Carlo trial, where k ranges from 1 to N. This represents the output value of the crack width in the k-th test. Let represent the mean of the i-th associated design parameter. This represents the average crack width.

[0030] Furthermore, the probability value of the crack width was calculated using MATLAB programming.

[0031] Furthermore, the association design parameters to be optimized include the association design parameters with the strongest negative correlation, the association design parameters with the second strongest negative correlation, and the association design parameters with the strongest positive correlation in the histogram.

[0032] Furthermore, step S6 is included, in which the association design parameter with the strongest negative correlation, the association design parameter with the second strongest negative correlation, and the association design parameter with the strongest positive correlation in the histogram are optimized in sequence. Steps S1-S4 are then repeated for the optimized association design parameter and the unoptimized association design parameter to obtain the crack width probability value range for each optimized association design parameter. The association design parameter with the largest number of peak frames and the smallest crack width probability value corresponding to the peak is selected as the association design parameter with the best optimization effect.

[0033] A Monte Carlo-based crack optimization system for reinforced concrete beams includes a parameter set module, a model generation module, a sensitivity analysis module, an optimization decision module, and a visualization module.

[0034] The parameter set module is used to input the associated design parameters of the selected reinforced concrete beam cracks and generate a parameter set; the model generation module is used to generate a crack width model based on the associated design parameters; the sensitivity analysis module is used to perform correlation coefficient-Monte Carlo sensitivity analysis to calculate the correlation coefficient of the associated design parameters and the probability value of the crack width; the optimization decision module is used to generate the associated design parameters to be optimized based on the correlation coefficient sorting; the visualization module is used to display the correlation coefficient sorting histogram and the crack width probability distribution map.

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

[0036] (1) The present invention takes into account the randomness of the values ​​of the associated design parameters of cracks in reinforced concrete beams. It uses the correlation coefficient-Monte Carlo method to perform sensitivity analysis on the associated design parameters and crack width, which significantly improves the accuracy of crack width prediction. Compared with the prior art, the present invention can improve the sensitivity analysis of design parameters, effectively guide the optimization design, and perform quantitative analysis on the effect of optimization measures.

[0037] (2) Based on the sensitivity of the associated design parameters, the present invention proposes targeted optimization measures to effectively reduce the probability of cracks exceeding the standard.

[0038] (3) This invention is applicable to the prediction of cracks in reinforced concrete beams under different specifications, materials and load conditions. By applying this method to different projects, different associated design parameters are input according to the characteristics of different projects, the sensitivity between the associated design parameters and crack width under different project characteristics can be quickly simulated, and the crack width of reinforced concrete beams can be quickly and accurately simulated.

[0039] (4) The present invention can sort according to the correlation coefficient, provide optimization measures, select economical and efficient optimization schemes, save construction costs and improve project quality. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method of the present invention.

[0041] Figure 2 This is a histogram of the relevant values ​​of each associated design parameter in Embodiment 3 of the present invention.

[0042] Figure 3 This is a distribution diagram of the probability value of each crack width in Embodiment 3 of the present invention.

[0043] Figure 4 This is a comparison chart in Embodiment 3 of the present invention showing the range of crack width probability values ​​between the optimized reinforcement, optimized bending moment, optimized section height and the original scheme. Detailed Implementation

[0044] The technical solution of the present invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are not all embodiments of the present invention. All other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0045] Example 1

[0046] like Figure 1 As shown, this embodiment provides a Monte Carlo-based crack optimization method for reinforced concrete beams, including the following steps:

[0047] S1. Select the associated design parameters for cracks in reinforced concrete beams and establish a parameter set.

[0048] The associated design parameters in this embodiment include concrete strength, steel reinforcement strength, bending moment, cover thickness, section height, and reinforcement ratio. Among them, bending moment, cover thickness, and section height are the bending moment, cover thickness, and section height of the reinforced concrete beam, respectively; the reinforcement ratio is the ratio of the cross-sectional area of ​​the longitudinal reinforcing steel bars in the reinforced concrete beam to the effective cross-sectional area of ​​the reinforced concrete beam.

[0049] The associated design parameters all conform to a normal distribution. A Latin hypercube sampling method is used to generate N samples to account for parameter uncertainty, resulting in N parameter sets. Each parameter set is represented by the following formula:

[0050] ;

[0051] In the above formula, Represents a set of parameters. Indicates concrete strength. Indicates the strength of the reinforcing steel. Indicates bending moment, Indicates the thickness of the protective layer. Indicates the cross-sectional height. This indicates the reinforcement ratio.

[0052] S2. Construct the corresponding crack width model for each parameter set. This includes the following steps:

[0053] S21. Construct a steel reinforcement stress model, which is specifically represented by the following formula:

[0054] ;

[0055] ;

[0056] In the above formula, Indicates the stress in the reinforcing steel. This represents the cross-sectional area of ​​the longitudinal reinforcement in the tension zone. Indicates the effective height of a reinforced concrete beam. Indicates taking , The minimum value after algebraic calculation of both.

[0057] S22. Construct a crack width model based on the steel reinforcement stress model. The crack width model is specifically expressed by the following formula:

[0058] ;

[0059] In the above formula, Indicates the crack width. , These all represent parameters related to concrete strength. This indicates the elastic modulus of the steel reinforcement.

[0060] To simplify calculations, the effect of concrete strength is ignored in the crack width model of this embodiment. The value is 2.1, but this does not affect the optimization analysis of concrete strength. The optimization of concrete strength in relation to crack width can be achieved by adjusting the steel reinforcement stress. The value is .

[0061] The crack widths calculated using the crack width model in this step all follow a normal distribution.

[0062] S3. Perform correlation coefficient-Monte Carlo sensitivity analysis on the parameter set and crack width. Specifically, use Monte Carlo sampling simulation technology to perform correlation coefficient sensitivity analysis on each associated design parameter and crack width to obtain the correlation value of each associated design parameter and the probability value of crack width.

[0063] The specific value of each associated design parameter is calculated using the following formula:

[0064] ;

[0065] In the above formula, This represents the relevant value of the i-th associated design parameter, where i ranges from 1 to 6. This represents the value of the i-th associated design parameter in the k-th Monte Carlo trial, where k ranges from 1 to N. This represents the output value of the crack width in the k-th test. Let represent the mean of the i-th associated design parameter. The mean crack width is represented by N, which represents the number of Monte Carlo simulations, and N is greater than or equal to 10000.

[0066] The probability value of the crack width was calculated using MATLAB programming.

[0067] S4. Sort the correlation coefficients between the associated design parameters and the crack width; construct a histogram for the correlation value of each associated design parameter, and construct a distribution map for each crack width and probability value. The histogram shows the sorting of the correlation values ​​of different associated design parameters, and the distribution map shows the probability of different crack width values.

[0068] S5. Based on the ranking of correlation coefficients, optimize the values ​​of the association design parameters. The association design parameters to be optimized include the association design parameters with the strongest negative correlation, the association design parameters with the second strongest negative correlation, and the association design parameters with the strongest positive correlation in the histogram.

[0069] S6. Optimize the association design parameter with the strongest negative correlation, the second strongest negative correlation, and the strongest positive correlation in the histogram in sequence. Then, repeat steps S1-S4 with the optimized association design parameter and the unoptimized association design parameter to obtain the crack width probability value range of each optimized association design parameter. Compare multiple crack width probability value ranges and select the association design parameter with the largest peak frame number and the smallest crack width probability value corresponding to the peak as the association design parameter with the best optimization effect.

[0070] Specifically, the process begins by optimizing the correlation design parameter with the strongest negative correlation, while leaving other correlation design parameters unoptimized. Steps S1-S4 are then performed to obtain a range of crack width probability values. Next, the correlation design parameter with the second strongest negative correlation is optimized, while leaving other correlation design parameters unoptimized. Steps S1-S4 are then performed again to obtain another range of crack width probability values. Finally, the correlation design parameter with the strongest positive correlation is optimized, while leaving other correlation design parameters unoptimized, resulting in another range of crack width probability values. The peak frame count and the corresponding crack width probability value for each of the three crack width probability value ranges are then compared. The correlation design parameter with the largest peak frame count and the smallest corresponding crack width probability value is selected as the correlation design parameter with the best optimization effect.

[0071] Example 2

[0072] This embodiment also provides a Monte Carlo-based crack optimization system for reinforced concrete beams, comprising a parameter set module, a model generation module, a sensitivity analysis module, an optimization decision module, and a visualization module. The parameter set module is used to input the selected associated design parameters of the reinforced concrete beam cracks and generate a parameter set. The model generation module is used to generate a crack width model based on the associated design parameters. The sensitivity analysis module is used to perform correlation coefficient-Monte Carlo sensitivity analysis to calculate the correlation coefficient of the associated design parameters and the probability value of the crack width. The optimization decision module is used to generate the associated design parameters to be optimized based on the correlation coefficient ranking. The visualization module is used to display the correlation coefficient ranking histogram and the crack width probability distribution map.

[0073] Example 3

[0074] A detailed analysis was performed using the method described in Example 1:

[0075] The values ​​of the associated design parameters are shown in the table below:

[0076]

[0077] The histogram of the correlation values ​​of each associated design parameter obtained from the data in the table above is shown below. Figure 2 As shown in the figure, the distribution of the probability value of each crack width is as follows: Figure 3 As shown, the correlation design parameters to be optimized are: the strongest negative correlation is the reinforcement ratio, the second strongest negative correlation is the section height, and the strongest positive correlation is the bending moment. Therefore, it is necessary to increase the reinforcement ratio, increase the section height, and control the bending moment load. Increasing the reinforcement ratio can effectively reduce the crack width, increasing the section height can reduce the crack propagation rate, and controlling the bending moment load can prevent the cracks from exceeding the standard.

[0078] Following the method in step S6, the crack width ranges were obtained after optimizing only the reinforcement ratio, only the bending moment, and only the section height, respectively. Figure 4 As shown, the crack width range corresponding to increasing the reinforcement ratio, decreasing the bending moment, and increasing the section height are all considered. Among them, the crack width range with the highest peak value and the smallest corresponding crack width value is obtained by increasing the reinforcement ratio. Therefore, the reinforcement ratio is the best-performing associated design parameter for optimization.

[0079] This invention considers the randomness of the values ​​of the associated design parameters for cracks in reinforced concrete beams. By using correlation coefficient-Monte Carlo analysis to assess the sensitivity of these parameters to crack width, the accuracy of crack width prediction is significantly improved. Based on the sensitivity of the associated design parameters, this invention proposes targeted optimization measures to effectively reduce the probability of cracks exceeding standards. This invention is applicable to crack prediction in reinforced concrete beams under different specifications, materials, and load conditions. By adapting this method to different projects and inputting different associated design parameters based on project characteristics, it can quickly simulate the sensitivity between the associated design parameters and crack width under different project characteristics, and rapidly and accurately simulate the crack width of reinforced concrete beams. This invention can provide optimization measures based on correlation coefficient ranking, selecting economical and efficient optimization schemes, saving construction costs, and improving project quality. Compared to existing technologies, this invention improves the sensitivity analysis of design parameters, effectively guides optimization design, and provides quantitative analysis of the effects of optimization measures.

[0080] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A Monte Carlo-based method for optimizing cracks in reinforced concrete beams, characterized in that, Includes the following steps: S1. Select the associated design parameters for cracks in reinforced concrete beams and establish a parameter set; S2. Based on the parameter set established in step S1, construct the crack width model; specifically including the following steps: S21. Construct a reinforcement stress model based on the associated design parameters; expressed by the following formula: ； ； In the above formula, Indicates the stress in the reinforcing steel. This represents the cross-sectional area of ​​the longitudinal reinforcement in the tension zone. Indicates the effective height of a reinforced concrete beam. Indicates taking , The minimum value after algebraic calculation of both; S22. Based on the steel reinforcement stress model, construct the crack width model; expressed by the following formula: ； In the above formula, Indicates the crack width. , These all represent parameters related to concrete strength. Represents the elastic modulus of steel bars, for The value is 2.1; S3. Perform a correlation coefficient-Monte Carlo sensitivity analysis on the crack widths obtained from the parameter set and crack width model to obtain the correlation value of each associated design parameter and the probability value of the crack width; the correlation value of each associated design parameter is calculated by the following formula: ； In the above formula, This represents the relevant value of the i-th associated design parameter, where i ranges from 1 to 6. This represents the value of the i-th associated design parameter in the k-th Monte Carlo trial, where k ranges from 1 to N. This represents the output value of the crack width in the k-th test. Let represent the mean of the i-th associated design parameter. This represents the average crack width. S4. Construct histograms for the relevant values ​​of the associated design parameters and construct distribution maps for the probability values ​​of crack widths; S5. Based on the histogram and distribution map, determine the correlation design parameters to be optimized, and optimize the determined correlation design parameters.

2. The Monte Carlo-based crack optimization method for reinforced concrete beams according to claim 1, characterized in that, The associated design parameters in step S1 include concrete strength, steel reinforcement strength, bending moment, cover thickness, section height, and reinforcement ratio. N parameter sets are generated using the Latin hypercube sampling method, and each parameter set is represented by the following formula: ； In the above formula, Represents a set of parameters. Indicates concrete strength. Indicates the strength of the reinforcing steel. Indicates bending moment, Indicates the thickness of the protective layer. Indicates the cross-sectional height. This indicates the reinforcement ratio.

3. A Monte Carlo-based crack optimization method for reinforced concrete beams according to any one of claims 1 or 2, characterized in that, The probability value of the crack width was calculated using MATLAB programming.

4. The Monte Carlo-based crack optimization method for reinforced concrete beams according to claim 1, characterized in that, The association design parameters to be optimized include the association design parameters with the strongest negative correlation, the association design parameters with the second strongest negative correlation, and the association design parameters with the strongest positive correlation in the histogram.

5. The Monte Carlo-based crack optimization method for reinforced concrete beams according to claim 4, characterized in that, The process also includes step S6, which sequentially optimizes the association design parameter with the strongest negative correlation, the association design parameter with the second strongest negative correlation, and the association design parameter with the strongest positive correlation in the histogram. Steps S1-S4 are then repeated for the optimized association design parameter and the unoptimized association design parameter to obtain the crack width probability value range for each optimized association design parameter. The association design parameter with the largest number of peak frames and the smallest crack width probability value corresponding to the peak is selected as the optimized association design parameter.

6. A Monte Carlo-based crack optimization system for reinforced concrete beams, characterized in that, The method for optimizing cracks in reinforced concrete beams based on Monte Carlo simulation, as described in any one of claims 1-5, includes a parameter set module, a model generation module, a sensitivity analysis module, an optimization decision module, and a visualization module. The parameter set module is used to input the associated design parameters of the selected reinforced concrete beam cracks and generate a parameter set; the model generation module is used to generate a crack width model based on the associated design parameters; the sensitivity analysis module is used to perform correlation coefficient-Monte Carlo sensitivity analysis to calculate the correlation coefficient of the associated design parameters and the probability value of the crack width; the optimization decision module is used to generate the associated design parameters to be optimized based on the correlation coefficient sorting; the visualization module is used to display the correlation coefficient sorting histogram and the crack width probability distribution map.

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