Concrete compressive strength evaluation method based on multi-level Bayesian model

Abstract

The invention relates to a concrete compressive strength detection technology, in particular to a concrete compressive strength evaluation method based on a multi-level Bayesian model. A hierarchical probability structure is introduced, distribution parameters of concrete compressive strength are regarded as random variables, higher-layer prior distribution is used for constraint, and therefore a unified model capable of expressing local observation information and a global statistical rule at the same time is formed. According to the method, a hierarchical Bayesian inference mechanism is introduced, fusion of local data and group information is realized, and strength estimation under a limited sample condition is more stable; a cross-sample and cross-region information sharing mechanism is established, so that a single observation point can'borrow information 'from overall data while keeping own characteristics, and the estimation variance is remarkably reduced; the reliability and generalization ability of prediction are improved, and high estimation precision can still be kept when actually measured data are insufficient or uncertainty exists.

Description

Technical Field

[0001] This invention relates to concrete compressive strength testing technology, specifically to a method for evaluating concrete compressive strength based on a multi-level Bayesian model. Background Technology

[0002] In engineering practice, to obtain information on the compressive strength of concrete in existing structures, it is usually necessary to drill concrete core samples on-site and conduct experimental tests. However, in the testing of existing structures, due to limitations in structural integrity and construction conditions, only a limited number of core sample specimens can often be obtained. Due to the small sample size, statistical inferences based on the measured results are prone to significant errors.

[0003] Effectively supplementing and calibrating concrete compressive strength information based on limited measured data has become a pressing issue. In fact, besides the local compressive strength data obtained from field measurements, concrete also possesses multi-level probabilistic prior information that can be utilized. Organically integrating these two sets of information would help improve the accuracy and reliability of the assessment results for the compressive strength of concrete in structures. Therefore, a technical solution is urgently needed that can effectively integrate the multi-level probabilistic prior information of concrete compressive strength with field measured data, enabling robust and reliable strength estimation even under small sample or sparse data conditions, thereby significantly improving the accuracy and generalization ability of the assessment results. Summary of the Invention

[0004] To address the issues of sparse measured concrete compressive strength data and insufficient accuracy in statistical inference, this invention proposes a concrete compressive strength evaluation method based on a multi-level Bayesian model. By introducing a hierarchical probability structure, the distribution parameters of concrete compressive strength (such as mean and variance) are treated as random variables and constrained by higher-level prior distributions, thus forming a unified model that can simultaneously express local observation information and global statistical regularities. Specifically, the model establishes parameter correlations at different levels, including structural, floor, component, and measuring point levels, enabling information exchange and constraints between observation data from different locations and components through hierarchical relationships.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for evaluating the compressive strength of concrete based on a multi-level Bayesian model includes the following steps: (1) Prior information A multi-level probability model of compressive strength is used as prior information; (2) On-site measured data Local compressive strength observation data were obtained by conducting on-site measurements of the above model levels; (3) Multilevel Bayesian model Construct a multi-level Bayesian modeling structure for concrete compressive strength, including observation level, component level, floor level, and structural level; (4) Posterior distribution of unknown parameters According to Bayes' theorem, let the posterior distribution of the unknown parameters be assumed; (5) Posterior distribution sample The posterior distribution of the above multi-level Bayesian model is used to generate samples using numerical methods. Based on the posterior distribution samples and the accuracy of each level, the probability distribution of the concrete compressive strength of each level, as well as various statistics, are obtained.

[0006] Further, in step (1), the concrete compressive strength of the entire structure, the j-th layer, the k-th component, and the l-th RVE (Representative Volume Element) are respectively expressed as: (1) In the formula, μ0 is the average compressive strength of concrete of a certain strength grade, and X and Y are... j Z jk and Θ jkl Let m represent the number of floors, and p represent the random variables caused by structural, floor, component, and RVE level random factors, respectively. j q represents the number of components in floor j. jk This indicates the number of RVEs in component k of floor j.

[0007] Furthermore, in step (2), assuming an existing structure with m layers, r components are extracted from each layer, and t core samples are drilled from each component for testing, and the corresponding compressive strength observation values ​​are obtained. .

[0008] Furthermore, in step (3), it is set that Observation layer: Component hierarchy: Floor level: Structural hierarchy: Where, λ H1 , λ H2 , λ H3 and λ H4λ represents the accuracy of concrete compressive strength at the structural, floor, component, and RVE levels, respectively. N is a normal distribution, G is a Gamma distribution, and α and β are the Gamma distribution parameters of the accuracy λ.

[0009] Further, in step (4), the posterior distribution of the unknown parameter is assumed to be: (2) The full conditional posterior distributions of the unknown parameters are as follows: (3) (4) (5) Based on the conjugate property of the Normal-Gamma distribution, the full conditional posterior distribution of the unknown parameters is a Normal-Gamma distribution: (6) (7) (8) Where, m t κ is the posterior mean of the mean. t α is the number of pseudo-samples for the mean. t and β t Let λ be the Gamma distribution parameter with precision λ.

[0010] Furthermore, in step (5), the Gibbs sampling method is used to generate a Markov chain that satisfies the posterior distribution. The algorithm steps are as follows: (5.1) Given initial values ​​of parameters , , , , and ; (5.2) Perform the following iterative update for s=0,1,2,...,5000. a) From the posterior distribution of the full condition Generated in ; b) From the posterior distribution of the full condition Generated in ; c) From the posterior distribution of the full condition Generated in ; (5.3) After discarding the first 1000 “burn-in” samples, the remaining 4000 samples are retained as posterior distribution samples. , and , s=1001,1002,...,5000.

[0011] Compared with traditional evaluation methods that rely solely on on-site core sample measurement data, this invention has the following advantages: (1) The introduction of hierarchical Bayesian inference mechanism realizes the fusion of local data and group information, making the intensity estimation under limited sample conditions more robust; (2) Establish a cross-sample and cross-regional information sharing mechanism so that individual observation points can maintain their own information sharing mechanism. While highlighting features, it can also "borrow information" from the overall data, significantly reducing estimation variance; (3) It improves the reliability and generalization ability of prediction, and can maintain a high estimation accuracy even when there is insufficient measured data or uncertainty. Through the above innovative design, this invention achieves high-precision estimation of concrete compressive strength under small sample conditions, effectively overcoming the limitations of traditional methods that rely on a large amount of measured data and have large fluctuations in estimation results, and significantly improving the scientificity and reliability of existing structural strength assessment. Attached Figure Description

[0012] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings: Figure 1 This is a histogram of absolute percentage error of feature intensity in an embodiment of the present invention. Detailed Implementation

[0013] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0014] A method for evaluating the compressive strength of concrete based on a multi-level Bayesian model includes the following steps: (1) Prior information Using a multi-level probabilistic model of compressive strength as prior information, the concrete compressive strength of the entire structure, the j-th layer, the k-th component, and the l-th RVE can be expressed as follows: (1) In the formula, μ0 is the average compressive strength of concrete of a certain strength grade, and X and Y are... jZ jk and Θ jkl Let m represent the number of floors, and p represent the random variables caused by structural, floor, component, and RVE level random factors, respectively. j q represents the number of components in floor j. jk This indicates the number of RVEs in component k of floor j.

[0015] (2) On-site measured data Suppose there is an existing structure with m floors. r components are sampled from each floor, and t core samples are drilled from each component for testing. What are the corresponding observed compressive strength values? .

[0016] (3) Multilevel Bayesian model The multi-level Bayesian modeling structure for concrete compressive strength is as follows: Observation layer: Component hierarchy: Floor level: Structural hierarchy: Where, λ H1 , λ H2 , λ H3 and λ H4 α and β represent the accuracy of concrete compressive strength at the structural, floor, component, and RVE levels, respectively, with α and β being the Gamma distribution parameters of the accuracy λ.

[0017] (4) Posterior distribution of unknown parameters According to Bayes' theorem, the posterior distribution of the unknown parameters is: (2) The full conditional posterior distributions of the unknown parameters are as follows: (3) (4) (5) Based on the conjugate property of the Normal-Gamma distribution, the full conditional posterior distribution of the unknown parameters is a Normal-Gamma distribution: (6) (7) (8) Where, m t κ is the posterior mean of the mean. t α is the number of pseudo-samples for the mean. t and β t Let λ be the Gamma distribution parameter with precision λ.

[0018] (5) Posterior distribution sample Since the full conditional posterior distributions of the parameters are easy to sample, the Gibbs sampling method can be used to generate Markov chains that satisfy the posterior distribution. The algorithm steps are as follows: (5.1) Given initial values ​​of parameters , , , , and ; (5.2) Perform the following iterative update for s=0,1,2,...,5000. a) From the posterior distribution of the full condition Generated in ; b) From the posterior distribution of the full condition Generated in ; c) From the posterior distribution of the full condition Generated in ; (5.3) After discarding the first 1000 “burn-in” samples, the remaining 4000 samples are retained as posterior distribution samples. , and , s=1001,1002,...,5000.

[0019] Based on the posterior distribution samples and the precision of each level, the probability distribution of the compressive strength of concrete at each level, as well as various statistics, can be obtained.

[0020] Example: Numerical Verification To verify the effectiveness of the concrete compressive strength evaluation method proposed in this invention, a virtual structural system with multi-level variation characteristics was constructed. The model has four levels: structural level, floor level, component level, and measuring point level, with coefficients of variation of 0.113, 0.098, 0.060, and 0.060, respectively. The mean concrete compressive strength was set to 30 MPa. Based on this setting, virtual structural samples with three different variation scenarios were generated: constant coefficient of variation (Model I), coefficient of variation reduced by 50% (Model II), and coefficient of variation increased by 50% (Model III). The virtual structure contains 10 floors, each floor contains 100 components, and each component consists of 200 units.

[0021] To minimize the impact of random sampling on the results, 1000 virtual structural samples considering multi-level variability were generated for each structure. Within each virtual structure, five components were randomly selected from each level, and the compressive strength of one unit within each component was randomly selected as observation data. Based on this data, the average compressive strength of different levels of the structure and the characteristic strength of each floor level were estimated using both standard methods and the multi-level Bayesian method proposed in this invention.

[0022] Predictive performance was evaluated using absolute percentage error and mean absolute percentage error. Figure 1 The absolute percentage error distribution histogram of the floor level characteristic intensity in the virtual structure is given, and Table 1 lists the average absolute percentage error results for different models.

[0023] Table 1 Mean Absolute Percentage Error (%) for Each Model The results show that: (1) The method of the present invention significantly reduces the number of high-error samples. Specifically, the maximum error in Model I is reduced from 80% to 40%, the maximum error in Model II is reduced from 60% to 30%, and the maximum error in Model III is reduced from 100% to 60%. (2) Compared with the standard method, the method of the present invention shows a lower mean absolute percentage error in the estimation of the average compressive strength at the structural level, floor level and component level, and the prediction results are more stable. (3) The average absolute percentage error of the key indicator - floor level characteristic intensity was significantly reduced, by 53.5%, 58.0% and 50.2% in Model I, Model II and Model III respectively.

[0024] In summary, the multi-level Bayesian evaluation method proposed in this invention can achieve stable and reliable prediction of concrete compressive strength under conditions of data sparsity and parameter uncertainty, which is significantly better than traditional statistical methods, and verifies its application potential in actual structural inspection and evaluation.

[0025] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for evaluating the compressive strength of concrete based on a multi-level Bayesian model, characterized in that, Specifically, the following steps are included: (1) Prior information A multi-level probability model of compressive strength is used as prior information; (2) On-site measured data Local compressive strength observation data were obtained by conducting on-site measurements of the above model levels; (3) Multilevel Bayesian model Construct a multi-level Bayesian modeling structure for concrete compressive strength, including observation level, component level, floor level, and structural level; (4) Posterior distribution of unknown parameters According to Bayes' theorem, let the posterior distribution of the unknown parameters be assumed; (5) Posterior distribution sample The posterior distribution of the above multi-level Bayesian model is used to generate samples using numerical methods. Based on the posterior distribution samples and the accuracy of each level, the probability distribution of the concrete compressive strength of each level, as well as various statistics, are obtained.

2. The method for evaluating the compressive strength of concrete based on a multi-level Bayesian model as described in claim 1, characterized in that, In step (1), the concrete compressive strength of the entire structure, the j-th layer, the k-th component, and the l-th RVE are respectively expressed as: (1) In the formula, μ0 is the average compressive strength of concrete of a certain strength grade, and X and Y are... j Z jk and Θ jkl Let m represent the number of floors, and p represent the random variables caused by structural, floor, component, and RVE level random factors, respectively. j q represents the number of components in floor j. jk This indicates the number of RVEs in component k of floor j.

3. The method for evaluating the compressive strength of concrete based on a multi-level Bayesian model as described in claim 2, characterized in that, In step (2), assuming an existing structure with m layers, r components are extracted from each layer, and t core samples are drilled from each component for testing. The corresponding compressive strength observation values ​​are... .

4. The method for evaluating the compressive strength of concrete based on a multi-level Bayesian model as described in claim 3, characterized in that, In step (3), set Observation layer: Component hierarchy: Floor level: Structural hierarchy: Where, λ H1 , λ H2 , λ H3 and λ H4 λ represents the accuracy of concrete compressive strength at the structural, floor, component, and RVE levels, respectively. N is a normal distribution, G is a Gamma distribution, and α and β are the Gamma distribution parameters of the accuracy λ.

5. The method for evaluating the compressive strength of concrete based on a multi-level Bayesian model as described in claim 4, characterized in that, In step (4), the posterior distribution of the unknown parameter is assumed to be: (2) The full conditional posterior distributions of the unknown parameters are as follows: (3) (4) (5) Based on the conjugate property of the Normal-Gamma distribution, the full conditional posterior distribution of the unknown parameters is a Normal-Gamma distribution: (6) (7) (8) Where, m t κ is the posterior mean of the mean. t α is the number of pseudo-samples for the mean. t and β t Let λ be the Gamma distribution parameter with precision λ.

6. The method for evaluating the compressive strength of concrete based on a multi-level Bayesian model as described in claim 5, characterized in that, In step (5), the Gibbs sampling method is used to generate a Markov chain that satisfies the posterior distribution. The algorithm steps are as follows: (5.1) Given initial values ​​of parameters , , , , and ; (5.2) Perform the following iterative update for s=0,1,2,...,5000. From the posterior distribution of the full condition Generated in ； From the posterior distribution of the full condition Generated in ； From the posterior distribution of the full condition Generated in ; (5.3) After discarding the first 1000 "burn-in" samples, the remaining 4000 samples are retained as posterior distribution samples. , and , s=1001,1002,...,5000.

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