Monte Carlo-based reinforced concrete beam crack optimization method and system

Abstract

The invention relates to the technical field of civil engineering structure design, in particular to a reinforced concrete beam crack optimization method and system based on Monte Carlo. The method comprises the steps that S1, associated design parameters of reinforced concrete beam cracks are selected, and a parameter set is established; s2, constructing a crack width model according to the parameter set established in the step S1; s3, performing correlation coefficient-Monte Carlo sensitivity analysis on the crack width obtained by the parameter set and the crack width model to obtain a correlation value of each associated design parameter and a probability value of the crack width; s4, constructing a histogram for the correlation values of the associated design parameters, and constructing a distribution diagram for the probability values of the crack width; s5, determining associated design parameters to be optimized according to the histogram and the distribution diagram, and optimizing the determined associated design parameters; the sensitivity analysis on design parameters is improved, the optimization design is effectively guided, and the optimization measure effect is quantitatively analyzed.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering structure design, and in particular to a Monte Carlo-based reinforced concrete beam crack optimization method and system. Background Art

[0002] Reinforced concrete beams are prone to cracking under load, and crack width is a key indicator for assessing structural durability and safety. Traditional crack prediction methods often use deterministic models, which fail to account for the randomness of material properties, geometric parameters, and loads, resulting in significant deviations 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, performing image acquisition on the first target bridge according to an image acquisition device, obtaining a real-time crack image set, inputting the real-time crack image set and a preset target period into the crack prediction dual-channel model, and outputting a risk prediction result.

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

[0005] Therefore, there is an urgent need to provide a Monte Carlo-based reinforced concrete beam crack optimization method and system, which can improve the sensitivity analysis of design parameters compared with the existing technology, effectively guide the optimization design, and quantitatively analyze the effects of optimization measures. Summary of the Invention

[0006] The present invention solves the technical problems existing in the prior art and provides a reinforced concrete beam crack optimization method and system based on Monte Carlo.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows: A Monte Carlo-based crack optimization method for reinforced concrete beams comprises the following steps: S1. Select the associated design parameters of reinforced concrete beam cracks and establish a parameter set; S2. constructing a crack width model based on the parameter set established in step S1; S3. performing a correlation coefficient-Monte Carlo sensitivity analysis on the parameter set and the crack width obtained by the 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 constructing a distribution diagram for the probability values ​​of the crack width; S5. Determine the associated design parameters to be optimized based on the histogram and the distribution diagram, and optimize the determined associated design parameters.

[0008] Furthermore, the associated design parameters in step S1 include concrete strength, steel strength, bending moment, cover thickness, section height, and reinforcement ratio. The Latin hypercube sampling method is used to generate N parameter sets, each of which is represented by the following formula: ; In the above formula, Represents a set of parameters, Indicates the strength of concrete, Indicates the strength of steel bars, represents the bending moment, Indicates the thickness of the protective layer, Indicates the section height, Indicates the reinforcement ratio.

[0009] Furthermore, S2 specifically includes the following steps: S21. Constructing a steel bar stress model based on associated design parameters; S22. Construct a crack width model based on the steel bar stress model.

[0010] Furthermore, the steel bar stress model constructed in step S21 is expressed by the following formula: ; ; In the above formula, represents the steel bar stress, represents the cross-sectional area of ​​the longitudinal reinforcement in the tension zone, represents the effective height of the reinforced concrete beam, Indicates taking 、 The minimum value of the two after algebraic calculation.

[0011] Furthermore, the crack width model constructed in step S22 is expressed by the following formula: ; In the above formula, represents the crack width, 、 All of them represent parameters related to concrete strength. represents the elastic modulus of steel bars. The value of is 2.1.

[0012] Furthermore, the correlation value of each associated design parameter is calculated as follows: ; In the above formula, Represents the correlation value of the i-th associated design parameter, i ranges from 1 to 6, Indicates the value of the i-th associated design parameter in the k-th Monte Carlo test, where k ranges from 1 to N. represents the crack width output value of the kth test, represents the mean value of the i-th associated design parameter, represents the mean crack width.

[0013] Furthermore, the probability value of the crack width is calculated using Matlab programming.

[0014] Furthermore, the associated design parameters to be optimized include the associated design parameter with the strongest negative correlation, the associated design parameter with the second strongest negative correlation, and the associated design parameter with the strongest positive correlation in the histogram.

[0015] Furthermore, step S6 is also included, in which the associated design parameters with the strongest negative correlation, the associated design parameters with the second strongest negative correlation, and the associated design parameters with the strongest positive correlation in the histogram are optimized in turn, and the optimized associated design parameters and the unoptimized associated design parameters are re-performed with steps S1-S4 to obtain the crack width probability value range of each optimized associated design parameter, and the associated design parameter with the largest number of peak frames and the smallest crack width probability value corresponding to the peak is selected as the associated design parameter with the best optimization effect.

[0016] A Monte Carlo-based reinforced concrete beam crack optimization system 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 ranking; the visualization module is used to display the correlation coefficient ranking histogram and the crack width probability distribution diagram.

[0017] Compared with the prior art, the present invention has the following beneficial effects: (1) Taking into account the randomness of the values ​​of the associated design parameters of reinforced concrete beam cracks, the present invention conducts sensitivity analysis on the associated design parameters and crack width through correlation coefficient-Monte Carlo, which significantly improves the accuracy of crack width prediction. Compared with the existing technology, the present invention can improve the sensitivity analysis of design parameters, effectively guide the optimization design, and quantitatively analyze the effects of optimization measures.

[0018] (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.

[0019] (3) The present invention is applicable to the crack prediction of reinforced concrete beams under different specifications, materials and load conditions. The method is transplanted to different projects, and different associated design parameters are input according to the characteristics of different projects. The sensitivity between the associated design parameters and the crack width under different project characteristics is quickly simulated, and the crack width of the reinforced concrete beam is simulated quickly and accurately.

[0020] (4) The present invention can provide optimization measures based on the correlation coefficient ranking, select economical and efficient optimization solutions, save construction costs, and improve project quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of the method of the present invention.

[0022] Figure 2 It is a histogram of the correlation values ​​of each associated design parameter in Example 3 of the present invention.

[0023] Figure 3 3 is a distribution diagram of the probability value of each crack width in Example 3 of the present invention.

[0024] Figure 4 This is a comparison chart showing the crack width probability value ranges between the optimized reinforcement, optimized bending moment, optimized section height and the original solution in Example 3 of the present invention. DETAILED DESCRIPTION

[0025] The technical solution of the present invention will be clearly described below in conjunction with the accompanying drawings. Obviously, the described embodiments are not all embodiments of the present invention. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0026] Example 1 like Figure 1 As shown, this embodiment provides a Monte Carlo-based reinforced concrete beam crack optimization method, comprising the following steps: S1. Select the associated design parameters of reinforced concrete beam cracks and establish a parameter set.

[0027] The associated design parameters in this embodiment include concrete strength, steel strength, bending moment, protective layer thickness, cross-sectional height and reinforcement ratio, wherein the bending moment, protective layer thickness and cross-sectional height are all the bending moment, protective layer thickness and cross-sectional height of the reinforced concrete beam; the reinforcement ratio is the ratio of the cross-sectional area of ​​the longitudinal stress-bearing steel bars in the reinforced concrete beam to the effective cross-sectional area of ​​the reinforced concrete beam.

[0028] The associated design parameters all conform to the normal distribution. The Latin hypercube sampling method is used to generate N samples to consider the uncertainty of the parameters, that is, to generate N parameter sets. Each parameter set is expressed by the following formula: ; In the above formula, Represents a set of parameters, Indicates the strength of concrete, Indicates the strength of steel bars, represents the bending moment, Indicates the thickness of the protective layer, Indicates the section height, Indicates the reinforcement ratio.

[0029] S2. Construct the corresponding crack width model based on each parameter set. Specifically, the following steps are included: S21. Construct a steel bar stress model. The steel bar stress model is specifically expressed by the following formula: ; ; In the above formula, represents the steel bar stress, represents the cross-sectional area of ​​the longitudinal reinforcement in the tension zone, represents the effective height of the reinforced concrete beam, Indicates taking 、 The minimum value of the two after algebraic calculation.

[0030] S22. Construct a crack width model based on the steel bar stress model. The crack width model is specifically expressed by the following formula: ; In the above formula, represents the crack width, 、 All of them represent parameters related to concrete strength. Represents the elastic modulus of steel bars.

[0031] In order to simplify the calculation, the crack width model in this embodiment ignores the influence of concrete strength, so The value is 2.1, but it does not affect the optimization analysis of concrete strength. The optimization of concrete strength to crack width can be achieved by adjusting the steel bar stress. The value of .

[0032] The crack widths calculated by the crack width model in this step all obey the normal distribution.

[0033] S3. Perform a correlation coefficient-Monte Carlo sensitivity analysis on the parameter set and the crack width. Specifically, use the Monte Carlo sampling simulation technology to perform a 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 the crack width.

[0034] The relevant value of each associated design parameter is calculated by the following formula: ; In the above formula, Represents the correlation value of the i-th associated design parameter, i ranges from 1 to 6, Indicates the value of the i-th associated design parameter in the k-th Monte Carlo test, where k ranges from 1 to N. represents the crack width output value of the kth test, represents the mean value of the i-th associated design parameter, represents the mean value of the crack width, N represents the number of Monte Carlo simulations, and N is greater than or equal to 10,000.

[0035] The probability value of crack width is calculated using Matlab programming.

[0036] 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 diagram for each crack width and probability value. The histogram shows the sorting of the correlation values ​​of different associated design parameters, and the distribution diagram shows the probability of different crack width values.

[0037] S5. Optimize the values ​​of the associated design parameters according to the order of the correlation coefficients. The associated design parameters to be optimized include the associated design parameter with the strongest negative correlation in the histogram, the associated design parameter with the second strongest negative correlation, and the associated design parameter with the strongest positive correlation.

[0038] S6. Optimize the associated design parameters with the strongest negative correlation, the associated design parameters with the second strongest negative correlation, and the associated design parameters with the strongest positive correlation in the histogram in turn, and then re-perform steps S1-S4 on the optimized associated design parameters and the unoptimized associated design parameters to obtain the crack width probability value range of each optimized associated design parameter, compare multiple crack width probability value ranges, and select the associated design parameter with the largest number of peak frames and the smallest crack width probability value corresponding to the peak as the associated design parameter with the best optimization effect.

[0039] Specifically, the associated design parameter with the strongest negative correlation is optimized first, and the other associated design parameters are not optimized, and steps S1-S4 are performed to obtain a crack width probability value range; then the associated design parameter with the second strongest negative correlation is optimized, and the other associated design parameters are not optimized, and steps S1-S4 are performed to obtain another crack width probability value range; finally, the associated design parameter with the strongest positive correlation is optimized, and the other associated design parameters are not optimized to obtain a crack width probability value range; then, the peak frame numbers and the crack width probability values ​​corresponding to the peak values ​​of the three crack width probability value ranges are compared, and the associated design parameter with the largest peak frame number and the smallest crack width probability value corresponding to the peak value is selected as the associated design parameter with the best optimization effect.

[0040] Example 2 This embodiment also provides a Monte Carlo-based reinforced concrete beam crack optimization system, which 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 crack 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 and 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 diagram.

[0041] Example 3 The method in Example 1 was used for specific analysis: The values ​​of the associated design parameters are shown in the following table:

[0042] The histogram of the correlation values ​​of each associated design parameter obtained based on the data in the above table is as follows Figure 2 As shown in the figure, the distribution diagram of each crack width probability value is as follows: Figure 3 As shown, the associated design parameters to be optimized are: the associated design parameter with the strongest negative correlation is the reinforcement ratio, the associated design parameter with the second strongest negative correlation is the section height, and the associated design parameter with 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 avoid cracks exceeding the standard.

[0043] According to the method of step S6, the crack width value ranges obtained after optimizing only the reinforcement ratio, only the bending moment, and only the section height are obtained, such as Figure 4As shown in the figure, the crack width value range corresponding to increasing the reinforcement ratio, the crack width value range corresponding to reducing the bending moment, and the crack width range corresponding to increasing the section height are as follows. Among them, the peak value of the crack width value range after increasing the reinforcement ratio has the highest number of frames and the crack width value corresponding to the peak value is the smallest. Therefore, the reinforcement ratio is the associated design parameter with the best optimization effect.

[0044] The present invention takes into account the randomness of the values ​​of the associated design parameters of reinforced concrete beam cracks, and performs sensitivity analysis on the associated design parameters and crack width through correlation coefficient-Monte Carlo, which significantly improves the accuracy of crack width prediction; the present invention proposes targeted optimization measures based on the sensitivity of the associated design parameters, effectively reducing the probability of cracks exceeding the standard; the present invention is suitable for the prediction of reinforced concrete beam cracks under different specifications, materials and load conditions, and the method is transplanted to different projects, and different associated design parameters are input according to the characteristics of different projects, and the sensitivity between the associated design parameters and crack width under different project characteristics is quickly simulated, and the crack width of reinforced concrete beams is quickly and accurately simulated; the present invention can be sorted according to the correlation coefficient, and optimization measures can be provided to select economical and efficient optimization solutions, save construction costs, and improve project quality; compared with the existing technology, the present invention can improve the sensitivity analysis of design parameters, effectively guide optimization design, and quantitatively analyze the effects of optimization measures.

[0045] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions of the technical solution of the present invention by ordinary technicians in this field do not deviate from the essence and scope of the technical solution of the present invention.

Claims

1. A Monte Carlo-based crack optimization method for reinforced concrete beams, characterized in that: The following steps are involved: S1. Select the associated design parameters of reinforced concrete beam cracks and establish a parameter set; S2. constructing a crack width model based on the parameter set established in step S1; S3. performing a correlation coefficient-Monte Carlo sensitivity analysis on the parameter set and the crack width obtained by the 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 constructing a distribution diagram for the probability values ​​of the crack width; S5. Determine the associated design parameters to be optimized based on the histogram and the distribution diagram, and optimize the determined associated design parameters.

2. The Monte Carlo-based reinforced concrete beam crack optimization method according to claim 1, characterized in that: The associated design parameters in step S1 include concrete strength, steel strength, bending moment, cover thickness, section height, and reinforcement ratio. The Latin hypercube sampling method is used to generate N parameter sets, each of which is represented by the following formula: ； In the above formula, Represents a set of parameters, Indicates the strength of concrete, Indicates the strength of steel bars, represents the bending moment, Indicates the thickness of the protective layer, Indicates the section height, Indicates the reinforcement ratio.

3. The Monte Carlo-based reinforced concrete beam crack optimization method according to claim 2, characterized in that: S2 specifically includes the following steps: S21. Constructing a steel bar stress model based on associated design parameters; S22. Construct a crack width model based on the steel bar stress model.

4. The Monte Carlo-based reinforced concrete beam crack optimization method according to claim 3, characterized in that: The steel bar stress model constructed in step S21 is expressed by the following formula: ； ； In the above formula, represents the steel bar stress, represents the cross-sectional area of ​​the longitudinal reinforcement in the tension zone, represents the effective height of the reinforced concrete beam, Indicates taking 、 The minimum value of the two after algebraic calculation.

5. The Monte Carlo-based reinforced concrete beam crack optimization method according to claim 4, characterized in that: The crack width model constructed in step S22 is expressed by the following formula: ； In the above formula, represents the crack width, 、 All of them represent parameters related to concrete strength. represents the elastic modulus of steel bars. The value of is 2.

1.

6. The Monte Carlo-based reinforced concrete beam crack optimization method according to claim 5, characterized in that: The correlation value of each associated design parameter is calculated as follows: ； In the above formula, Represents the correlation value of the i-th associated design parameter, i ranges from 1 to 6, Indicates the value of the i-th associated design parameter in the k-th Monte Carlo test, where k ranges from 1 to N. represents the crack width output value of the kth test, represents the mean value of the i-th associated design parameter, represents the mean crack width.

7. A Monte Carlo-based reinforced concrete beam crack optimization method according to any one of claims 1 to 6, characterized in that: The probability value of crack width is calculated using Matlab programming.

8. The Monte Carlo-based reinforced concrete beam crack optimization method according to claim 1, characterized in that: The associated design parameters to be optimized include the associated design parameter with the strongest negative correlation in the histogram, the associated design parameter with the second strongest negative correlation, and the associated design parameter with the strongest positive correlation.

9. The Monte Carlo-based reinforced concrete beam crack optimization method according to claim 8, characterized in that: It also includes step S6, which optimizes the associated design parameters with the strongest negative correlation, the associated design parameters with the second strongest negative correlation, and the associated design parameters with the strongest positive correlation in the histogram in turn, and re-performs steps S1-S4 on the optimized associated design parameters and the unoptimized associated design parameters to obtain the crack width probability value range of each optimized associated design parameter, and selects the associated design parameter with the largest number of peak frames and the smallest crack width probability value corresponding to the peak as the associated design parameter with the best optimization effect.

10. A Monte Carlo-based reinforced concrete beam crack optimization system, characterized in that: The method is carried out using a Monte Carlo-based reinforced concrete beam crack optimization method according to any one of claims 1 to 9, 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 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 ranking; the visualization module is used to display the correlation coefficient ranking histogram and the crack width probability distribution diagram.

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