CN-120654408-B - Reinforced concrete beam crack optimization method and system based on Monte Carlo

CN120654408BCN 120654408 BCN120654408 BCN 120654408BCN-120654408-B

Abstract

The invention relates to the technical field of civil engineering structural design, in particular to a reinforced concrete beam crack optimization method and system based on Monte Carlo, wherein the method comprises the steps of S1, selecting relevant design parameters of a reinforced concrete beam crack, establishing a parameter set, S2, establishing a crack width model according to the parameter set established in the step S1, S3, carrying out 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 relevant design parameter and a probability value of the crack width, S4, constructing a histogram on the correlation value of the relevant design parameters, constructing a distribution map on the probability value of the crack width, S5, determining relevant design parameters to be optimized according to the histogram and the distribution map, optimizing the determined relevant design parameters, improving the sensitivity analysis on the design parameters, effectively guiding the optimization design, and carrying out quantitative analysis on the effect of optimization measures.

Inventors

JIN YANCHAO
Xu Shuizhou
MEI WEIPING
TENG LIRONG
ZHENG HAORAN
Qian Nali

Assignees

中国电建集团建筑规划设计研究院有限公司
中国电建集团北京勘测设计研究院有限公司

Dates

Publication Date: 20260505
Application Date: 20250610

Claims (6)

1. The reinforced concrete beam crack optimization method based on Monte Carlo is characterized by comprising the following steps of: S1, selecting associated design parameters of a reinforced concrete beam crack, and establishing a parameter set; S2, constructing a crack width model according to the parameter set established in the step S1, wherein the method specifically comprises the following steps: s21, constructing a reinforcing steel bar stress model according to the related design parameters, wherein the reinforcing steel bar stress model is represented by the following formula: ; ; In the above-mentioned method, the step of, Representing the stress of the reinforcing steel bar, Represents the cross-sectional area of the longitudinal reinforcing steel bar in the tension zone, Indicating the effective height of the reinforced concrete beam, Representation fetch 、 Algebraic calculated minimum values of the two; s22, constructing a crack width model according to the reinforcing steel bar stress model, wherein the crack width model is represented by the following formula: ; In the above-mentioned method, the step of, The width of the slit is indicated, 、 All represent parameters related to the strength of the concrete, Representing the elastic modulus of the steel bar The value of (2) is 2.1; S3, carrying out 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 correlation design parameter and a probability value of the crack width, wherein the correlation value of each correlation design parameter is calculated by the following formula: ; In the above-mentioned method, the step of, The correlation value representing the i-th associated design parameter, i taking 1 to 6, Representing the value of the ith associated design parameter in the kth monte carlo trial, k takes 1 to N, The crack width output value of the kth test is shown, Representing the mean of the i-th associated design parameter, Mean value of crack width; s4, constructing a histogram of the correlation value of the correlation design parameter, and constructing a distribution map of the probability value 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.
2. The method for optimizing reinforced concrete beam cracks based on Monte Carlo according to claim 1, wherein the associated design parameters in the step S1 comprise concrete strength, reinforcement strength, bending moment, protective layer thickness, section height and reinforcement ratio, N parameter sets are generated by using Latin hypercube sampling method, and each parameter set is represented by the following formula: ; In the above-mentioned method, the step of, A set of parameters is represented and, The strength of the concrete is indicated by the terms, The strength of the steel bar is represented, Indicating a bending moment, the bending moment, The thickness of the protective layer is indicated, The height of the cross-section is indicated, Representing the reinforcement ratio.
3. The reinforced concrete beam crack optimizing method based on monte carlo according to any one of claims 1 or 2, wherein the probability value of the crack width is calculated by matlab programming.
4. The method for optimizing a crack of a reinforced concrete beam based on monte carlo according to claim 1, wherein the associated design parameters to be optimized include an associated design parameter having a strongest negative correlation, an associated design parameter having a second strongest negative correlation, and an associated design parameter having a strongest positive correlation in the histogram.
5. The reinforced concrete beam crack optimization method based on Monte Carlo as claimed in claim 4, further comprising S6, optimizing the associated design parameters with the strongest negative correlation, the associated design parameters with the strongest negative correlation and the associated design parameters with the strongest positive correlation in the histogram in sequence, re-performing S1-S4 to obtain a crack width probability value range of each optimized associated design parameter, and selecting the associated design parameter with the largest peak frame number and the smallest crack width probability value corresponding to the peak as the optimized associated design parameter.
6. A reinforced concrete beam crack optimization system based on Monte Carlo, which is characterized by being performed by using the reinforced concrete beam crack optimization method based on Monte Carlo as claimed in any one of claims 1 to 5, and comprising a parameter collection module, a model generation module, a sensitivity analysis module, an optimization decision module and a visualization module; The method comprises the steps of selecting a reinforced concrete beam crack, inputting relevant design parameters of the reinforced concrete beam crack, generating a parameter set by a parameter set module, generating a crack width model by a model generation module according to the relevant design parameters, performing correlation coefficient-Monte Carlo sensitivity analysis by a sensitivity analysis module, calculating probability values of correlation coefficients of the relevant design parameters and the crack width, generating relevant design parameters to be optimized according to correlation coefficient sorting by an optimization decision module, and displaying a correlation coefficient sorting histogram and a crack width probability distribution diagram by a visualization module.

Description

Reinforced concrete beam crack optimization method and system based on Monte Carlo Technical Field The invention relates to the technical field of civil engineering structural design, in particular to a reinforced concrete beam crack optimization method and system based on Monte Carlo. Background The reinforced concrete beam is easy to generate cracks under the load effect, and the width of the cracks is an important index for evaluating the durability and the safety of the structure. The traditional crack prediction method mostly adopts a deterministic model, and is difficult to consider the randomness of material performance, geometric parameters and loads, so that the prediction result and the actual deviation are larger. The prior art CN116842620A discloses an intelligent prediction method and system for reinforced concrete bridge cracks, the method comprises the steps of modeling a first target bridge by using a construction parameter of the first target bridge by a connection simulation system, outputting a first bridge simulation model to simulate, collecting a bridge sample image set to perform model training, outputting a crack prediction double-channel model, performing image acquisition on the first target bridge according to an image acquisition device to obtain a real-time crack image set, inputting the real-time crack image set and a preset target period into the crack prediction double-channel model, and outputting a risk prediction result. However, in the crack prediction method, sensitivity analysis on design parameters is insufficient, optimization design cannot be guided effectively, and quantitative analysis on the effect of optimization measures is lacking. Therefore, compared with the prior art, the method and the system for optimizing the reinforced concrete beam cracks based on the Monte Carlo have the advantages that the sensitivity analysis on design parameters is improved, the optimization design is effectively guided, and the quantitative analysis on the effect of optimization measures is carried out. Disclosure of Invention The invention solves the technical problems in the prior art, and provides a reinforced concrete beam crack optimization method and system based on Monte Carlo. In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: A reinforced concrete beam crack optimization method based on Monte Carlo comprises the following steps: S1, selecting associated design parameters of a reinforced concrete beam crack, and establishing a parameter set; s2, constructing a crack width model according to the parameter set established in the step S1; S3, carrying out 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 correlation design parameter and a probability value of the crack width; s4, constructing a histogram of the correlation value of the correlation design parameter, and constructing a distribution map of the probability value 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. Further, the associated design parameters in the step S1 comprise concrete strength, reinforcement strength, bending moment, protective layer thickness, section height and reinforcement ratio, N parameter sets are generated by using a Latin hypercube sampling method, and each parameter set is represented by the following formula: ; In the above-mentioned method, the step of, A set of parameters is represented and,The strength of the concrete is indicated by the terms,The strength of the steel bar is represented,Indicating a bending moment, the bending moment,The thickness of the protective layer is indicated,The height of the cross-section is indicated,Representing the reinforcement ratio. Further, S2 specifically includes the following steps: S21, constructing a reinforcing steel bar stress model according to the related design parameters; s22, constructing a crack width model according to the reinforcing steel bar stress model. Further, the reinforcing steel bar stress model constructed in the step S21 is represented by the following formula: ; ; In the above-mentioned method, the step of, Representing the stress of the reinforcing steel bar,Represents the cross-sectional area of the longitudinal reinforcing steel bar in the tension zone,Indicating the effective height of the reinforced concrete beam,Representation fetch、Algebraically calculated minimum values of the two. Further, the crack width model constructed in the step S22 is represented by the following formula: ; In the above-mentioned method, the step of, The width of the slit is indicated,、All represent parameters related to the strength of the concrete,Representing the elastic modulus of the steel barThe value of (2) is 2.1. Further