An analysis system and method for the shear bearing capacity of reinforced concrete members subjected to bending.

Abstract

This invention discloses a system and method for analyzing the shear capacity of reinforced concrete members subjected to deep bending, belonging to the field of civil engineering structural safety assessment technology. In the system, a data acquisition module collects and preprocesses experimental data of reinforced concrete members subjected to deep bending; a Bayesian-MCMC calculation engine is used to estimate the posterior distribution of model parameters; a probabilistic model generation module is used to generate a probabilistic calculation model of shear capacity based on the posterior distribution data, and simplifies the probabilistic calculation model of shear capacity through parameter elimination; a reliability analysis module is used to calculate the reliability index of the member under the ultimate limit state of bearing capacity by combining the statistical characteristics of load and resistance; and a visualization and output module displays the output. This invention achieves systematic quantification of multi-source uncertainties, automates data processing and analysis from data to reliability indexes, and improves the objectivity and accuracy of the assessment.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering structural safety assessment technology, specifically relating to an analysis system and method for the shear bearing capacity of reinforced concrete members subjected to bending. Background Technology

[0002] Reinforced concrete members with high flexural strength (span-to-depth ratio l0 / h ≤ 5) are widely found in critical components such as transfer floors of high-rise buildings, bridge cap beams, and foundation beams. Their shear capacity is the core factor controlling design safety. Currently, engineering practice mainly relies on semi-empirical and semi-theoretical formulas provided by design codes for deterministic calculations. Although these formulas have been calibrated through extensive testing, they are difficult to quantify the discreteness of material properties, geometric deviations, and uncertainties in the calculation models themselves, leading to potentially overly conservative evaluation results or unforeseen risks.

[0003] As an improvement, probabilistic and statistical methods have been introduced to account for uncertainty. Bayesian methods can integrate historical prior information with current experimental data to update our understanding of model parameters, making them an effective tool for probabilistic modeling. However, for complex engineering models, the Bayesian posterior distribution is often high-dimensional and non-standard, making it difficult to solve using traditional methods. The Markov Chain Monte Carlo (MCMC) method provides an efficient approach to solving complex Bayesian integrals by constructing a stationary distribution as the posterior distribution of a Markov chain for sampling.

[0004] Existing research has attempted to apply the Bayesian-MCMC method to the performance analysis of concrete members, such as modifying the shear resistance formulas for beams and columns. However, these works have largely focused on the algorithmic implementation and theoretical verification of specific models, and have not yet formed a complete system integrating data management, multi-model compatibility, automated analysis, and reliability assessment. For D-zone members, which are subjected to complex stresses, particularly those in bending, the lack of systematic engineering-based probabilistic analysis tools has become a bottleneck restricting their accurate design and safety assessment. Therefore, in summary, when applying the Bayesian-MCMC method to the performance analysis of concrete members, the focus is mainly on the algorithmic implementation and theoretical verification of specific models, making it difficult to accurately quantify systems with multi-source uncertainties. The objectivity and accuracy of reliability index analysis need further optimization. Summary of the Invention

[0005] This invention provides an analysis system and method for the shear bearing capacity of reinforced concrete members subjected to bending. The purpose is to address the shortcomings of existing technologies, where the Bayesian-MCMC method, when applied to the performance analysis of concrete members, mainly focuses on the algorithm implementation and theoretical verification of specific models. It is difficult to accurately quantify systems with multiple sources of uncertainty, and the objectivity and accuracy of reliability index analysis need further optimization.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: This invention discloses an analysis system for the shear bearing capacity of reinforced concrete members subjected to deep bending, comprising a data acquisition module, a prior model library module, a Bayesian-MCMC calculation engine, a probability model generation module, a reliability analysis module, and a visualization and output module; wherein: The data acquisition module is used to collect and preprocess the material parameters, geometric parameters, and shear test data of reinforced concrete members subjected to bending, and transmit the data to the Bayesian-MCMC calculation engine; the prior model library module is used to transmit the information of the target prior model to the Bayesian-MCMC calculation engine; the Bayesian-MCMC calculation engine is used to construct a Bayesian probability model and perform Markov chain Monte Carlo sampling to estimate the posterior distribution of the model parameters, and transmit the posterior distribution data to the probability model generation module; The probabilistic model generation module generates a probabilistic calculation model of shear capacity based on posterior distribution data and simplifies the model using parameter elimination. This simplified model is then transferred to the reliability analysis module. The reliability analysis module calculates the reliability index under the ultimate limit state of the component's bearing capacity by combining the statistical characteristics of load and resistance, and transmits the reliability index to the visualization and output module. The visualization and output module receives the analyzed data and displays it.

[0007] In some implementations, the Bayesian-MCMC computation engine includes a Bayesian probability model building unit, an MCMC sampling unit, and a parameter estimation unit; the Bayesian probability model building unit is used to establish a correlation model between shear bearing capacity and the prior model and deviation correction term; the MCMC sampling unit is used to perform sampling operations on the model parameters and the model standard deviation respectively; the parameter estimation unit is used to calculate the statistical characteristic values ​​of the posterior distribution of the model parameters based on the iterative sampling results.

[0008] Furthermore, the Bayesian probability model constructed by the Bayesian probability model building unit satisfies the following formula: ; in, The vector form represents the factors affecting the shear capacity of reinforced concrete members subjected to bending, where Θ=(θ, σ) represents the model parameters corrected for fitting experimental data. For shear bearing capacity, Existing prior models of members subjected to shear under bending are available. This is a deviation correction term. For a standard normal variable, Indicates to X The correction coefficient, σ, is the variance produced by the posterior distribution; The This is a function term constructed based on concrete strength, reinforcement ratio, and geometric parameters. The function term is used to correct the deviation between the calculated values ​​of the prior model and the actual shear bearing capacity.

[0009] Furthermore, the MCMC sampling unit uses the Gibbs sampling method to sample the model parameters and the Metropolis-Hastings algorithm to sample the model standard deviation; the parameter estimation unit performs statistics on the sampled samples after combustion period treatment and outputs the statistical characteristic values ​​of the posterior distribution of the model parameters.

[0010] In some implementations, the parameter elimination method in the probabilistic model generation module is to calculate the coefficient of variation of the posterior distribution of each model parameter and remove parameter terms with coefficients of variation below a set threshold from the shear bearing capacity probabilistic calculation model.

[0011] In some implementations, the prior model library module stores various standard shear capacity calculation models and tension / compression bar models, and uses standardized interfaces to enable the expansion and calling of these models.

[0012] In some implementations, the data acquisition module includes a built-in data cleaning and standardization submodule, which is used to standardize the acquired concrete strength, cross-sectional dimensions, shear span ratio, span-to-depth ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, and shear test values.

[0013] In some implementations, the reliability analysis module establishes the limit state equation as follows: ; in, For resistance based on probabilistic models, For load effect, This represents the importance coefficient of the structure.

[0014] In some implementations, the visualization and output module outputs content including MCMC sampling trajectory, posterior distribution density, model comparison scatter plot, reliability index analysis chart, and structured analysis report.

[0015] This invention also provides a method for analyzing the shear capacity of reinforced concrete members subjected to deep bending, which is based on the aforementioned system for analyzing the shear capacity of reinforced concrete members subjected to deep bending, and includes the following steps: The material parameters, geometric parameters, and shear test data of reinforced concrete members subjected to bending are collected and preprocessed by the data acquisition module to obtain preprocessed test data. The prior model library module transmits the information of the target prior model to the Bayesian-MCMC computing engine. The Bayesian-MCMC computing engine receives preprocessed experimental data and information from the target prior model, constructs a Bayesian probability model, performs Markov chain Monte Carlo sampling, estimates the posterior distribution of the model parameters, and obtains the posterior distribution data. The probability model generation module receives the posterior distribution data, generates a shear bearing capacity probability calculation model based on the posterior distribution data, and simplifies the shear bearing capacity probability calculation model by using a parameter elimination method to obtain a simplified shear bearing capacity probability calculation model. The simplified shear bearing capacity probability calculation model is received by the reliability analysis module. Combined with the statistical characteristics of load and resistance, the reliability index of the component under the ultimate limit state of bearing capacity is calculated to obtain the reliability index data. The visualization and output module receives reliability index data and analysis process data, and displays and outputs the data.

[0016] Compared with the prior art, the present invention provides an analysis system and method for the shear bearing capacity of reinforced concrete members subjected to bending, which has the following advantages: This invention provides an analysis system for the shear bearing capacity of reinforced concrete members subjected to bending. It effectively avoids operational errors, data loss, and workflow inconsistencies caused by manual processing, thus improving the reliability of the analysis process. The data acquisition module collects and preprocesses relevant parameters of the member and transmits data in a targeted manner, ensuring the basic quality and transmission directionality of the input data. The prior model library module accurately provides target prior model information, providing stable and reliable basic model support for subsequent analysis. The Bayesian-MCMC calculation engine, relying on Bayesian probability models and Markov chain Monte Carlo sampling, effectively estimates the posterior distribution of model parameters, overcoming the shortcomings of current deterministic analysis methods that cannot quantify the uncertainties of materials, geometry, and computational models. The probabilistic model generation module generates and simplifies the probabilistic calculation model of shear bearing capacity based on posterior distribution data. The reliability analysis module combines the statistical characteristics of load and resistance to calculate the reliability index under the ultimate limit state of the member's bearing capacity, providing a quantitative basis for structural safety assessment. This invention achieves systematic quantification of multi-source uncertainties, automating data processing and analysis from data to reliability indices, improving the objectivity and accuracy of the assessment to a certain extent, and possessing engineering applicability. Attached Figure Description

[0017] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0018] Figure 1This is a schematic diagram of the architecture of an analysis system for the shear bearing capacity of reinforced concrete members subjected to bending according to the present invention. Figure 2 This is a flowchart of the Bayesian-MCMC method in the analysis method of shear bearing capacity of reinforced concrete members subjected to bending according to the present invention. Figure 3 This is a simulation trajectory diagram of the parameters to be estimated in a Markov chain formed by iteration based on the A-code in an analysis system for the shear bearing capacity of reinforced concrete members subjected to bending according to the present invention. Figure 4 This invention provides a posterior density function graph of parameters generated iteratively based on the A-code in an analysis system for the shear bearing capacity of reinforced concrete members subjected to bending. Figure 5 This is a posterior frequency histogram generated by sampling model parameters in an analysis system for the shear bearing capacity of reinforced concrete members subjected to bending according to the present invention. Figure 6 This is a comparison chart showing the deviation of the shear force calculation results from standard A and the shear force calculation results from the probability model relative to the concrete strength in the analysis system of shear bearing capacity of reinforced concrete members subjected to bending according to the present invention. Figure 7 This is a sample distribution diagram of the calculated values ​​of the shear bearing capacity based on the A-code, the four national codes, and the test results in the analysis system of shear bearing capacity of reinforced concrete members subjected to bending according to the present invention. Figure 8 This is the reliability index calculation result of the shear bearing capacity probability model obtained from the B code in the analysis system of shear bearing capacity of reinforced concrete members subjected to bending according to the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0020] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0021] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0022] It should be noted that the apparatus and methods disclosed in the embodiments herein can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings show the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments herein. In this regard, each block in a flowchart or block diagram may represent a module, program, or part of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system to perform the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions.

[0023] In addition, the functional modules in the various embodiments of this article can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0024] How to provide an analysis system for the shear bearing capacity of reinforced concrete members subjected to bending, which can achieve coordinated monitoring of UPS operating status and grid voltage status, and assist wind turbines in completing low-voltage ride-through by dynamically adjusting the UPS output mode, thereby improving the success rate of ride-through and the grid connection stability of wind farms.

[0025] like Figure 1 As shown, this invention provides an analysis system for the shear bearing capacity of reinforced concrete members subjected to deep bending, comprising a data acquisition module, a prior model library module, a Bayesian-MCMC calculation engine, a probabilistic model generation module, a reliability analysis module, and a visualization and output module; wherein: The data acquisition module is used to collect and preprocess the material parameters, geometric parameters, and shear test data of reinforced concrete members subjected to bending, and transmit the data to the Bayesian-MCMC calculation engine; the prior model library module is used to transmit the information of the target prior model to the Bayesian-MCMC calculation engine; the Bayesian-MCMC calculation engine is used to construct a Bayesian probability model and perform Markov chain Monte Carlo sampling to estimate the posterior distribution of the model parameters, and transmit the posterior distribution data to the probability model generation module; The probabilistic model generation module generates a probabilistic calculation model of shear capacity based on posterior distribution data and simplifies the model using parameter elimination. This simplified model is then transferred to the reliability analysis module. The reliability analysis module calculates the reliability index under the ultimate limit state of the component's bearing capacity by combining the statistical characteristics of load and resistance, and transmits the reliability index to the visualization and output module. The visualization and output module receives the analyzed data and displays it.

[0026] This invention organically integrates prior knowledge and experimental information through Bayesian updates, establishing a probabilistic model whose predictions more closely approximate experimental values, thus improving computational accuracy and reducing dispersion. MCMC sampling provides the posterior distribution of parameters, giving characteristic values ​​of bearing capacity at different confidence levels (e.g., 95%), achieving a quantitative description of uncertainty. This invention encapsulates complex probabilistic statistical processes into a standardized workflow, lowering the barrier to entry and improving analytical efficiency. The generated simplified probabilistic model is concise in form and has clearly defined parameters, making it suitable for design verification or evaluation of existing structures. The reliability index output by this invention provides relatively objective and accurate data for performance-based design and risk management.

[0027] Specifically, this invention is an integrated hardware and software analysis platform, comprising a data acquisition module, a priori model library module, a Bayesian-MCMC calculation engine, a probabilistic model generation module, a reliability analysis module, and a visualization and output module. The data acquisition module is responsible for input and preprocessing, receiving key parameters such as concrete strength (fc), cross-sectional dimensions (b, h), shear span ratio (a / h0), span-to-depth ratio (l0 / h), longitudinal and stirrup reinforcement ratios (ρ, ρv), and shear test values ​​(Vtest). It includes a built-in data cleaning and standardization submodule to ensure data quality. The priori model library module, as the system's knowledge core, integrates currently standardized calculation models and classical mechanical models such as tension / compression bar models. The module uses standardized interfaces, supporting flexible expansion and invocation. The priori model library module meets the analysis needs of various engineering scenarios and supports flexible model expansion and invocation, improving the system's adaptability. Specialized processing of core parameters removes abnormal data and unifies data formats, ensuring the quality of input data.

[0028] The Bayesian-MCMC calculation engine is the core of the system's algorithm. It includes a Bayesian probability model building unit, an MCMC sampling unit, and a parameter estimation unit. The Bayesian probability model building unit establishes a correlation model between the shear bearing capacity and the prior model and deviation correction terms. The MCMC sampling unit performs sampling operations on the model parameters and model standard deviations. The parameter estimation unit calculates the statistical characteristic values ​​of the posterior distribution of the model parameters based on the iterative sampling results. Through the collaboration of these units, the complex Bayesian-MCMC calculation process becomes clearer, runs more stably, and improves the reliability of the posterior distribution calculation.

[0029] The Bayesian-MCMC computation engine includes Bayesian probability model building blocks: The building format is as follows: ; in, The vector form represents the factors affecting the shear capacity of reinforced concrete members subjected to bending, where Θ=(θ, σ) represents the model parameters corrected for fitting experimental data. For shear bearing capacity, The existing prior model calculations for shear stress in members subjected to bending are... This is a deviation correction term. For a standard normal variable, Indicates to X The correction coefficient, σ, is the variance produced by the posterior distribution; Among them, the deviation correction term The function can be represented as: ; in, Indicates to X Correction factor, This is a functional expression for the factors affecting shear bearing capacity. This represents the vector form of the factors affecting the shear capacity of reinforced concrete members subjected to bending. Factors affecting shear bearing capacity P The number of factors affecting shear bearing capacity; This allows for relatively accurate correction of the discrepancy between the calculated values ​​of the prior model and the actual shear capacity, making the probabilistic model more closely match the actual stress state of the component.

[0030] The MCMC sampling unit integrates Gibbs sampling (for parameter θ) and Metropolis-Hastings sampling (for parameter σ) algorithms to efficiently generate sample chains from complex posterior distributions. The parameter estimation unit statistically analyzes the sample chains after combustion period processing, outputting characteristic values ​​such as the mean, variance, and confidence interval of the parameter posterior distribution. By using Gibbs sampling and the Metropolis-Hastings algorithm to sample model parameters and standard deviations respectively, combined with combustion period sample removal processing, invalid sample interference can be eliminated, ensuring the validity of the sampling results.

[0031] Furthermore, the probability model generation module of the present invention receives the output of the calculation engine and automatically assembles it into a complete probability calculation formula as follows: ; in, V MCMC For the simplified Bayesian probabilistic calculation model of shear capacity, To calculate values ​​based on a priori models of the specification, Indicates to X Correction factor, This represents the vector form of the factors affecting the shear capacity of reinforced concrete members subjected to bending. This is a functional expression for the factors affecting shear bearing capacity. Factors affecting shear bearing capacity P The number of factors affecting shear bearing capacity. Furthermore, it applies a parameter significance judgment method based on the coefficient of variation (standard deviation / mean) to automatically eliminate parameter terms with weak influence, generating a concise and practical simplified model. This method can filter out parameter terms with weak influence on the model, simplifying the model structure and reducing computational complexity without reducing the accuracy of the analysis.

[0032] The reliability analysis module uses the probabilistic model as the resistance model and combines it with load statistics to construct the limit state equation. ; in, For resistance based on probabilistic models, For load effect, The importance coefficient of the structure is used. The Monte Carlo importance sampling method is employed to efficiently calculate the failure probability and reliability index β of the components. The limit state equation of the reliability analysis module incorporates the structural importance coefficient, which aligns with the actual code requirements for engineering structural design and reflects the safety margin of components at different importance levels.

[0033] This invention also provides a method for analyzing the shear capacity of reinforced concrete members subjected to deep bending, comprising the following steps: The material parameters, geometric parameters, and shear test data of reinforced concrete members subjected to bending are collected and preprocessed by the data acquisition module to obtain preprocessed test data. The prior model library module transmits the information of the target prior model to the Bayesian-MCMC computing engine. The Bayesian-MCMC computing engine receives preprocessed experimental data and information from the target prior model, constructs a Bayesian probability model, performs Markov chain Monte Carlo sampling, estimates the posterior distribution of the model parameters, and obtains the posterior distribution data. The probability model generation module receives the posterior distribution data, generates a shear bearing capacity probability calculation model based on the posterior distribution data, and simplifies the shear bearing capacity probability calculation model by using a parameter elimination method to obtain a simplified shear bearing capacity probability calculation model. The simplified shear bearing capacity probability calculation model is received by the reliability analysis module. Combined with the statistical characteristics of load and resistance, the reliability index of the component under the ultimate limit state of bearing capacity is calculated to obtain the reliability index data. The visualization and output module receives reliability index data and analysis process data, and displays and outputs the data.

[0034] The following detailed description of the analysis system for the shear bearing capacity of reinforced concrete members subjected to bending according to the present invention will be provided through specific embodiments.

[0035] Example 1 A probabilistic model of shear bearing capacity of members subjected to deep bending is established based on the standard GB50010.

[0036] This embodiment demonstrates the entire process of establishing a high-precision probabilistic model using the analysis system for the shear bearing capacity of reinforced concrete members subjected to bending according to the present invention, based on the specifications.

[0037] The system data acquisition module is invoked to load a pre-organized database containing 645 sets of shear test data for deeply bent members.

[0038] Select the shear capacity calculation formula for heavily flexural members from the A concrete structure design code as the prior model V from the prior model library. GB .

[0039] The Bayesian-MCMC calculation engine automatically constructs a Bayesian probability model, with bias correction terms including logarithmic terms of eight influencing factors such as concrete strength, reinforcement ratio, and geometric parameters. The MCMC sampling iteration is set to 50,000 times, and the combustion period to 2,000 times.

[0040] Sampling process as follows Figure 3 As shown, Figure 3This is a simulated trajectory diagram of the parameters to be estimated for the Markov chain formed by the A-standard iteration of this invention. The horizontal axis represents the number of iterations, which is 50,000 in this paper, and the vertical axis represents the parameters to be estimated. The estimated value is obtained by arbitrarily choosing an initial value at the beginning of the iteration. After 50,000 iterations, the parameter... The value of will tend to a fixed value, indicating that the Markov chain eventually converges; Sampling results as follows Figure 4 As shown, Figure 4 This invention is based on the A-standard iterative parameter generation. The posterior density function plot; the horizontal axis represents the estimated value. The range of values, the simulation environment is a posterior sample of N=5000, and the estimated value The frequency width is 0.01962, and the vertical axis represents its cumulative probability. As can be seen from the figure, the posterior distribution density function curve is close to the normal distribution function curve, and the parameter estimate will take its fixed value at the maximum probability.

[0041] Sampling results as follows Figure 5 As shown, Figure 5 This is a histogram of posterior frequencies generated by sampling the model parameters of this invention; the horizontal axis represents the range of values ​​of the parameter to be estimated with a certain class interval, and the vertical axis represents the number of samples; as can be seen from the figure, after 50,000 iterations of analysis, the posterior frequencies of the estimated values ​​of the model parameters are mostly concentrated in the region near the simulation result values, which is basically consistent with the values ​​of the model parameter θ in the simulation trajectory diagram and the posterior density function diagram. This indicates that the Markov chain Monte Carlo method has high reliability when sampling, simulating and iteratively analyzing parameters, and effectively solves the systematic error problem that exists when using general mathematical statistics methods to estimate model parameters.

[0042] After sampling, parameter estimates and models are generated, and the mean of the posterior distribution of the parameters is obtained: θ1=0.704, θ2=0.094, θ3=-0.344, θ4=0.122, θ5=0.131, θ6=-0.015, θ7=-0.194, θ8=0.330.

[0043] Based on the coefficient of variation, terms θ3, θ5, and θ8 are removed to generate a simplified probability model: .

[0044] Model validation: The model was used to calculate 645 sets of data to obtain experimental values. V test Compared with the predicted value V MCMCThe ratios have a mean of 1.038 and a standard deviation of 0.289. Compared to the original canonical model (mean 1.401, standard deviation 0.342), this improves accuracy and stability.

[0045] Model validation results are as follows Figure 6 As shown, Figure 6 This is a comparison chart showing the deviation between the shear force calculation results from Standard A and the shear force calculation results from the probabilistic model relative to the concrete strength. As can be seen from the chart, the calculation results of the probabilistic calculation model for the shear capacity of deeply flexural members based on Standard A... V MCMC Comparison with shear capacity calculation results of Code A V GB The distribution of values ​​is generally consistent, but the calculated values ​​of the shear bearing capacity probability model are closer to the experimental failure values ​​and the distribution is more concentrated with less dispersion. V test / V GB It is mainly distributed between 1.060 and 1.743. V test / V MCMC The values ​​are mainly distributed between 0.739 and 1.337, indicating that the model simulated by the MCMC method significantly reduces the bias caused by influencing factors, further proving the effectiveness of the MCMC method. The discreteness and randomness of the shear bearing capacity probability model based on the A code are significantly reduced.

[0046] Based on shear test data from 645 sets of members subjected to deep bending, the Bayesian-MCMC method was introduced into the solution of the reliability of members subjected to deep bending. Using the probabilistic calculation model of shear capacity obtained based on the Bayesian-MCMC method, the reliability of the probabilistic calculation model of shear capacity obtained based on the A code under the ultimate limit state was analyzed using the Monte Carlo importance sampling method. Furthermore, the load effect ratio was investigated. q Impact on reliability metrics.

[0047] The reliability index calculation results are as follows Figure 8 As shown, Figure 8 This is a schematic diagram of the reliability index calculation results of the shear bearing capacity probability model obtained by this invention based on the A standard; the horizontal axis represents the load effect ratio. q The vertical axis represents the reliability index of the shear bearing capacity of the member subjected to bending. Reliability index With load effect ratio The reliability index increases with the increase of the load, and the calculated reliability index is greater than the target reliability index under the ultimate limit state of bearing capacity in the code. This indicates that the probabilistic calculation model of shear bearing capacity of deeply bent members obtained based on the Bayesian-MCMC method has a certain reliability and meets the reliability index required by the code under the ultimate limit state of bearing capacity.

[0048] Example 2 This embodiment demonstrates the application of the probabilistic model generated by the present invention for structural reliability assessment.

[0049] Repeat the steps of Example 1, but select the tension / compression bar model in specification B as the prior, and obtain the corresponding simplified probability model V through system analysis. MCMC-ACI .

[0050] Evaluate a deep bending member with a safety level of 2 (γ0=1.0). Its span-to-depth ratio l0 / h=3.0, shear span ratio a / h0=1.0, and common load effect ratio q=1.0 are known.

[0051] Input the above parameters and load statistics (dead load follows a normal distribution, live load follows an extreme value type I distribution) into the system reliability analysis module. The module is based on V MCMC-ACI The model uses Monte Carlo importance sampling (sample size 10). 5 Calculate the reliability index. The results of the reliability index calculation are as follows: Figure 8 As shown.

[0052] The system outputs a reliability index β=4.72. This value is greater than the requirements for ductile failure (β=3.7) and brittle failure (β=4.2) in the "Unified Standard for Reliability Design of Building Structures" (GB50068), indicating that the component has sufficient safety margin under current conditions.

[0053] Example 3 This embodiment demonstrates the value of the system of the present invention in resolving practical engineering disputes.

[0054] The project background is as follows: A dispute arose regarding the shear capacity assessment of a transfer beam (l0 / h=3.5, C40 concrete, ρ=1.8%) in a certain project. The calculated value V according to standard A is... GB =1850kN, lower than the design load V design =1950kN, deemed unsafe, reinforcement may be necessary.

[0055] Using the shear bearing capacity analysis system for reinforced concrete members subjected to bending according to this invention, Bayesian-MCMC analysis was performed based on four prior models (ABCD) from the code, resulting in four probabilistic models. Eigenvalues ​​at the 95% confidence level were then compared.

[0056] System calculations show that the predicted value of the probabilistic model updated based on specification A is V. MCMC =2150kN (95% confidence level). This value is higher than the design load, and the assessment result is safe. Subsequent long-term monitoring showed that the beam was in good working condition, verifying the accuracy of the assessment results of this invention, avoiding unnecessary reinforcement, and saving engineering costs.

[0057] In summary, this invention provides an analysis system for the shear capacity of reinforced concrete members subjected to deep bending, comprising a data acquisition module, a prior model library module, a Bayesian-MCMC calculation engine, a probabilistic model generation module, a reliability analysis module, and a visualization output module. This invention constructs an experimental database and selects prior models from the model library; using the Bayesian-MCMC calculation engine, it establishes a probabilistic model of shear capacity by sampling and estimating the posterior distribution through Gibbs and Metropolis-Hastings algorithms; based on the probabilistic model, it employs Monte Carlo importance sampling for reliability assessment. This invention, by integrating Bayesian statistics, MCMC sampling, and structural reliability theory, achieves probabilistic analysis and automated assessment of the shear capacity of members subjected to deep bending, thereby improving assessment accuracy and engineering practicality to a certain extent.

[0058] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Anyone skilled in the art can readily implement the present invention according to the description and above. Any modifications, alterations, or equivalent variations made using the technical content disclosed above are equivalent embodiments of the present invention. Furthermore, any modifications, alterations, or variations made to the above embodiments based on the essential technology of the present invention are still within the protection scope of the present invention.

Claims

1. A system for analyzing the shear bearing capacity of reinforced concrete members subjected to bending, characterized in that, It includes a data acquisition module, a prior model library module, a Bayesian-MCMC calculation engine, a probability model generation module, a reliability analysis module, and a visualization and output module; among which: The data acquisition module is used to collect and preprocess the material parameters, geometric parameters, and shear test data of reinforced concrete members subjected to bending, and transmit the data to the Bayesian-MCMC calculation engine; the prior model library module is used to transmit the information of the target prior model to the Bayesian-MCMC calculation engine; the Bayesian-MCMC calculation engine is used to construct a Bayesian probability model and perform Markov chain Monte Carlo sampling to estimate the posterior distribution of the model parameters, and transmit the posterior distribution data to the probability model generation module; The probability model generation module generates a probabilistic calculation model of shear capacity based on posterior distribution data and simplifies the model using a parameter elimination method. The simplified shear capacity probabilistic calculation model is then transmitted to the reliability analysis module. The reliability analysis module calculates the reliability index of the component under the ultimate limit state of its bearing capacity by combining the statistical characteristics of load and resistance, and transmits the reliability index to the visualization and output module. The visualization and output module receives the analyzed data and displays it.

2. The analysis system for the shear bearing capacity of reinforced concrete members subjected to bending as described in claim 1, characterized in that, The Bayesian-MCMC calculation engine includes a Bayesian probability model building unit, an MCMC sampling unit, and a parameter estimation unit. The Bayesian probability model building unit is used to establish a correlation model between shear bearing capacity and the prior model and the deviation correction term. The MCMC sampling unit is used to perform sampling operations on the model parameters and the model standard deviation, respectively. The parameter estimation unit is used to calculate the statistical characteristic values ​​of the posterior distribution of the model parameters based on the iterative sampling results.

3. The analysis system for the shear bearing capacity of reinforced concrete members subjected to deep bending as described in claim 2, characterized in that, The Bayesian probability model constructed by the Bayesian probability model construction unit satisfies the following formula: ； in, The vector form represents the factors affecting the shear capacity of reinforced concrete members subjected to bending, where Θ=(θ, σ) represents the model parameters corrected for fitting experimental data. For shear bearing capacity, Existing prior models of bending members subjected to shear are... This is a deviation correction term. For a standard normal variable, Indicates to X The correction coefficient, σ, is the variance produced by the posterior distribution; The This is a function term constructed based on concrete strength, reinforcement ratio, and geometric parameters. The function term is used to correct the deviation between the calculated values ​​of the prior model and the actual shear bearing capacity.

4. The analysis system for the shear bearing capacity of reinforced concrete members subjected to bending as described in claim 2, characterized in that, The MCMC sampling unit uses the Gibbs sampling method to sample the model parameters and the Metropolis-Hastings algorithm to sample the model standard deviation; the parameter estimation unit performs statistics on the sampled samples after combustion period treatment and outputs the statistical characteristic values ​​of the posterior distribution of the model parameters.

5. The analysis system for the shear bearing capacity of reinforced concrete members subjected to bending as described in claim 1, characterized in that, The parameter elimination method in the probability model generation module is as follows: calculate the coefficient of variation of the posterior distribution of each model parameter, and remove the parameter items with the coefficient of variation below a set threshold from the shear bearing capacity probability calculation model.

6. The analysis system for the shear bearing capacity of reinforced concrete members subjected to bending as described in claim 1, characterized in that, The prior model library module stores various standard shear capacity calculation models and tension / compression bar models, and uses standardized interfaces to enable the expansion and calling of these models.

7. The analysis system for the shear bearing capacity of reinforced concrete members subjected to bending as described in claim 1, characterized in that, The data acquisition module has a built-in data cleaning and standardization submodule, which is used to standardize the acquired concrete strength, cross-sectional dimensions, shear span ratio, span-to-depth ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, and shear test values.

8. The analysis system for the shear bearing capacity of reinforced concrete members subjected to bending as described in claim 1, characterized in that, The reliability analysis module establishes the limit state equation as follows: ； in, For resistance based on probabilistic models, For load effect, This represents the importance coefficient of the structure.

9. The analysis system for the shear bearing capacity of reinforced concrete members subjected to deep bending as described in claim 1, characterized in that, The visualization and output module outputs MCMC sampling trajectory, posterior distribution density, model comparison scatter plot, reliability index analysis chart, and structured analysis report.

10. A method for analyzing the shear capacity of reinforced concrete members subjected to deep bending, based on the analysis system for the shear capacity of reinforced concrete members subjected to deep bending as described in any one of claims 1-9, characterized in that, Includes the following steps: The material parameters, geometric parameters, and shear test data of reinforced concrete members subjected to bending are collected and preprocessed by the data acquisition module to obtain preprocessed test data. The prior model library module transmits the information of the target prior model to the Bayesian-MCMC computing engine. The Bayesian-MCMC computing engine receives preprocessed experimental data and information from the target prior model, constructs a Bayesian probability model, performs Markov chain Monte Carlo sampling, estimates the posterior distribution of the model parameters, and obtains the posterior distribution data. The probability model generation module receives the posterior distribution data, generates a shear bearing capacity probability calculation model based on the posterior distribution data, and simplifies the shear bearing capacity probability calculation model by using a parameter elimination method to obtain a simplified shear bearing capacity probability calculation model. The simplified shear bearing capacity probability calculation model is received by the reliability analysis module. Combined with the statistical characteristics of load and resistance, the reliability index of the component under the ultimate limit state of bearing capacity is calculated to obtain the reliability index data. The visualization and output module receives reliability index data and analysis process data, and displays and outputs the data.

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