Method for determining compressive strength representative value of coarse aggregate high-performance concrete

Abstract

The invention provides a method for determining a compressive strength representative value of coarse aggregate high-performance concrete. The method is characterized by comprising the following steps: 1) establishing a compressive strength probability prediction model according to a method I; 2) processing the main characteristic parameter group of the mix proportion of the coarse aggregate high-performance concrete according to a method 6 by utilizing a compressive strength probability prediction model to obtain a compressive strength representative value of the coarse aggregate high-performance concrete; the first method comprises the steps of obtaining a training data set, determining a main characteristic parameter set, establishing a deterministic prediction model and establishing a compressive strength probability prediction model. According to the method, the mix proportion of the coarse aggregate high-performance concrete is designed, and the representative value of compressive strength is checked, so that the design efficiency can be greatly improved, and the design cost is reduced.

Description

Technical Field

[0001] This invention relates to the field of building materials technology, and in particular to a method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate. Background Technology

[0002] Ultra-High-Performance Concrete (UHPC) has gained widespread attention and application in bridge engineering, marine structures, and high-rise buildings due to its high strength, good ductility, strong resistance to freeze-thaw cycles, corrosion, and carbonation, as well as its self-healing capabilities. However, traditional UHPC generally uses fine aggregate as the main component, with little or no coarse aggregate, which not only leads to excessively high material costs but also limits its application in large-volume components. To improve economic efficiency and applicability, researchers have introduced coarse aggregate into the UHPC system, developing Ultra-High-Performance Concrete with Coarse Aggregate (UHPC-CA). This significantly reduces material costs without drastically reducing mechanical properties and durability, showing promising prospects for engineering application.

[0003] In practical engineering applications, mix design is a crucial factor in determining concrete performance. Considering that: ① the introduction of coarse aggregate enhances the interfacial transition zone (ITZ) effect in high-performance concrete, thus affecting its compressive strength; and ② compressive strength is the most representative parameter of the mechanical properties of concrete materials, and this is no exception for high-performance concrete with coarse aggregate. Therefore, mix design under compressive strength control is particularly important for high-performance concrete with coarse aggregate.

[0004] Currently, the mix design of coarse aggregate high-performance concrete relies heavily on experimental methods, which are closer to an "enumeration method." This involves first finding a mix proportion that meets the compressive strength requirements through continuous experimentation, then conducting numerous tests on a large number of specimens based on the determined mix proportion, and finally processing the test results using statistical methods to obtain a representative value of the compressive strength of the coarse aggregate high-performance concrete for that mix proportion. This representative value is then used to assess the safety of the coarse aggregate high-performance concrete. However, this method suffers from drawbacks such as long development cycles, high costs, unsuitability for rapid design, and difficulty in adapting to fluctuations in raw material prices and complex working conditions. Therefore, verifying whether the mix design meets the compressive strength requirements after completion is crucial.

[0005] In the existing technology, machine learning seems to provide a new approach for the mix design of high-performance coarse aggregate concrete under compressive strength control, taking into account the combined effects of multiple factors. However, due to the significant "black box" characteristics of machine learning, the models it trains often lack interpretability, which affects the relevant decision-making in engineering applications. Summary of the Invention

[0006] To address the problems in the prior art, this invention provides a method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate, thereby solving the problems of long design cycle, low efficiency, and high cost in the mix design of high-performance concrete with coarse aggregate in the prior art.

[0007] To achieve the objective of this invention, a method for determining the representative value of compressive strength in high-performance coarse aggregate concrete is provided. The mix proportion characteristics of the high-performance coarse aggregate concrete include coarse aggregate strength (X1), minimum coarse aggregate particle size (X2), maximum coarse aggregate particle size (X3), coarse aggregate content (X4), steel fiber volume fraction (X5), fly ash content (X6), silica fume content (X7), and water-reducing agent content (X8). The values ​​of each mix proportion characteristic parameter of the high-performance coarse aggregate concrete whose representative compressive strength is to be determined are known. The method comprises: 1) Establish a probabilistic prediction model for compressive strength according to Method 1; (ii) Using the compressive strength probability prediction model, the main characteristic parameter group of the mix proportion of coarse aggregate high-performance concrete is processed according to method six to obtain the representative value of the compressive strength of coarse aggregate high-performance concrete. The first method includes: 1) Obtain the training dataset using Method 2; 2) Determine the main characteristic parameter set according to Method 3; 3) Establish a deterministic prediction model according to Method 4; 4) Establish a probabilistic prediction model for compressive strength according to Method 5; The second method includes: X1, X2, X3, X4, X5, X6, X7, and X8 are denoted as characteristic parameter groups. Each proportion characteristic parameter under the characteristic parameter group takes a value within its own value range. By combining different values ​​of each proportion characteristic parameter under the characteristic parameter group, multiple characteristic parameter groups are obtained. Multiple compression specimens are prefabricated based on multiple sets of feature parameters, and the compression strength of each specimen is obtained by testing the multiple compression specimens. The combination of the feature parameter set and the corresponding compression strength is recorded as a training data, and multiple training data are combined to form a training dataset. The third method includes: 2-1) Randomly divide the training data in the training dataset into two groups: one group forms the training set, and the other group forms the initial test set. Both the training set and the initial test set include multiple training data sets. The ratio of the number of training data sets in the training set to the number of training data sets in the initial test set is g:k. Let p be the combination of compressive strengths corresponding to the multiple training data sets in the initial test set. Randomly swap the X1 of the feature parameter groups of the multiple training data sets in the initial test set to obtain the first test set. Randomly swap the X2 of the feature parameter groups of the multiple training data sets in the initial test set to obtain the second test set. Then, the initial test set... The X3 feature parameter groups of the multiple training data under the jurisdiction are randomly swapped to obtain the 3rd test set. The X4 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 4th test set. The X5 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 5th test set. The X6 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 6th test set. The X7 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 7th test set. The X8 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 8th test set. 2-2) Train a BP neural network using the training set to obtain a predictive machine model, where the feature parameter set is used as input and the compressive strength is used as output; 2-3) Process the initial test set and the data from test set 1 to test set 8 as follows: For a single test set: each feature parameter group under the test set is used as the input of the prediction machine model. Each input feature parameter group is processed by the prediction machine model and outputs a predicted compressive strength. Multiple feature parameter groups result in multiple corresponding predicted compressive strengths. Let p' be the combination of multiple predicted compressive strengths obtained from the initial test set; let p' be the combination of multiple predicted compressive strengths obtained from the i-th test set. Xi ', where i is an integer from 1 to 8, thus obtaining p X1 'to p X8 '; Repeat steps 2-1) to 2-3) above N times, combining the N obtained p into vector P, combining the N obtained p' into vector P', and combining the N obtained p... Xi 'Combined into vector P' Xi ', thus obtaining P X1 'To P X8 '; Then calculate the regression fit metric r0 between vector P and vector P'; and calculate the regression fit metric r0 between vector P and P' respectively. X1 'To P X8The regression fitting measures of these 8 vectors are r1 to r8; then the differences between r0 and each of the 8 regression fitting measures r1 to r8 are calculated to obtain Δr1 to Δr8. Δr1 to Δr8 are sorted in descending order of value, and the first 4 are taken as the principal differences. The 4 matching ratio characteristic parameters corresponding to the 4 principal differences are denoted as principal characteristic parameters x1, x2, x3 and x4. The combination of the 4 principal characteristic parameters is denoted as the principal characteristic parameter group. The fourth method includes: The four matching ratio feature parameters other than the main feature parameters in the training dataset are deleted to obtain a usable training dataset. Then, using the genetic programming symbolic regression method, with the available training dataset as samples, an elementary function equation, i.e., a deterministic prediction model, is established with the four main feature parameters x1, x2, x3, and x4 as independent variables and compressive strength Y as the dependent variable: Y = f (x1,x2,x3,x4,a,b,…) Where a, b, ... are deterministic parameters obtained by the symbolic regression method; Method five includes: The available training dataset is randomly divided into three available sub-training datasets; Replace the deterministic parameters a, b, ... in the deterministic prediction model with random variables α, β, ... represented by a normal distribution, and add a random normal error term γσ. 2 This yields the following formula: Y'= f (x1,x2,x3,x4, α,β,…)+γσ 2 Then, using the Markov Monte Carlo method based on Bayesian theory, the parameters α, β, ..., γσ in Equation 1 are processed three times using three available sub-training datasets. 2 The formula obtained after updating the parameters is the compressive strength probability prediction model. Method six includes: The random variables α, β, ..., and γ in the probabilistic prediction model of compressive strength are denoted as normal distribution parameters; A) The Monte Carlo method is used to sample the normal distribution parameters to obtain t normal distribution parameter sample groups; the t normal distribution parameter sample groups are combined with the main characteristic parameter group of coarse aggregate high-performance concrete to be determined to obtain t prediction parameter groups; B) The compressive strength probability prediction model is used to process the data of t prediction parameter groups respectively to obtain t Y' values; C) The KS test method is used to process the t Y' values ​​to obtain the mean μ and standard deviation s of their distribution; D) Determine the representative value of compressive strength Y" of high-performance concrete with coarse aggregate according to the following formula: Y"=μ-1.96s.

[0008] Furthermore, in method two, the combination ratio characteristic parameter of the characteristic parameter group is valued in the following manner: X1, X2, and X3 are designated as the first parameter group, and X4, X5, X6, X7, and X8 are designated as the second parameter group. The characteristic parameters of the mix proportions under the first parameter group are taken as follows: For a single mix proportion characteristic parameter under the first parameter group: its value range is divided into 3 equal-width intervals, and the midpoint value of any equal-width interval is taken as the value of the mix proportion characteristic parameter. The characteristic parameters of the mix proportions under the second parameter group are taken as follows: For a single mix proportion characteristic parameter under the second parameter group: its value range is divided into 6 equal-width intervals, and the midpoint value of any equal-width interval is taken as the value of the mix proportion characteristic parameter. Based on the above method, the Latin hypercube sampling method is used to obtain multiple feature parameter sets.

[0009] Furthermore, the feature parameter set obtained in method two consists of 100 parameters.

[0010] Furthermore, in Method 2, the Max-Min normalization method is used to process and scale the various mix proportion feature parameters and compressive strength data in each training data to the range of [0.2, 0.8].

[0011] Furthermore, in step 2-1), the ratio of g:k is 4:1.

[0012] Furthermore, in method three, N is 20.

[0013] Furthermore, in step 2-2), the number of hidden layer neurons in the BP neural network is 9, and the maximum number of training iterations is 10. 6 The target error is 10. -3 The learning rate is 10. -2 .

[0014] Furthermore, the parameters of the genetic programming symbolic regression method are set as follows: population size 10000; crossover probability 80%; subtree mutation probability 10%; boost mutation probability 5%; node mutation probability 5%; tournament size 20; parsimony coefficient 0.005; function set +, -, ×, ÷, exp, log, sin, and cos; selection strategy is tournament selection; crossover method is subtree swapping; mutation method is subtree mutation, boost mutation, or node mutation, or a combination of the above three mutations; fitness evaluation index is mean squared error.

[0015] Furthermore, in method six, t is 10000.

[0016] The principle of this invention is as follows: The compressive strength of high-performance concrete with coarse aggregate is influenced by multiple material parameters (mix design control parameters), and also contains uncertainties due to raw material fluctuations and process differences. In traditional engineering practice, the strength prediction formulas or models guiding concrete mix design always use mix design control parameters as independent variables and compressive strength as the dependent variable. They are expressed in elementary function form and output specific values ​​as predictive results, representing deterministic models. The inherent defects of these models and their formation process include: ① The establishment of deterministic models relies on a large number of experimental samples. For high-performance concrete systems, the high experimental costs and wide mix design range amplify the economic problems caused by this defect; ② The specific values ​​output by deterministic models represent the predicted compressive strength results, which are close to the statistical average rather than the widely accepted representative value (lower confidence limit) in engineering. The average value cannot describe the uncertainties that may exist due to raw material fluctuations and process differences, nor can it guarantee the safety of the mix design of high-performance concrete with coarse aggregate. Only when the representative value of the compressive strength of the high-performance concrete with coarse aggregate is greater than the specification requirements can the safety of its mix design be guaranteed. In existing technologies, after completing the mix design using a deterministic model, determining the representative value of the structural compressive strength requires conducting compressive strength tests on a large number of physical engineering specimens controlled by the mix design. The representative compressive strength value corresponding to the mix design can only be determined by statistically analyzing the compressive strength of this series of specimens. This process is not only inefficient but also very costly.

[0017] To overcome the above-mentioned difficulties, this invention fundamentally changes the traditional approach to constructing compressive strength prediction models. It proposes a methodological system that integrates feature engineering, genetic programming, and Bayesian principles, so that the final compressive strength prediction model has explicit formula expression, high interpretability, and uncertainty disclosure capabilities.

[0018] First, this invention utilizes feature engineering principles combined with a backpropagation (BP) neural network to rank the matching ratio feature parameters X1~X8 in the original dataset according to their importance, and selects the four matching ratio feature parameters with the highest contribution for subsequent model training, thus obtaining a simplified training dataset. The inventors recognized that by controlling the input feature dimensions in a reasonable manner, the complexity of the compressive strength prediction model obtained by the genetic programming method, expressed as an elementary function, can be significantly improved. This feature engineering work not only effectively avoids the interference of redundant features on the formula structure, allowing genetic programming to operate in a smaller search space and improving the simplicity and readability of the formula, but also makes the resulting model more suitable for engineering interpretation and design applications. Furthermore, since subsequent steps involve converting the above prediction model from a deterministic model to a non-deterministic model, the impact of eliminating non-essential parameters on the accuracy of the prediction results can be included in the non-deterministic description.

[0019] Next, this invention performs symbolic regression on a simplified training dataset using genetic programming to obtain an explicit calculation formula for the compressive strength of high-performance coarse aggregate concrete, i.e., a deterministic prediction model composed of elementary functions. This step overcomes the inherent "black box" defect of traditional machine learning models. The resulting explicit calculation formula for compressive strength helps designers intuitively understand the influence of different mix proportion design control parameters on compressive strength. This deterministic prediction model can be used to complete the mix proportion trial work of high-performance coarse aggregate concrete.

[0020] However, the inventors further discovered that even with an explicit calculation formula composed of elementary functions, the formula remains a deterministic model, and its output cannot describe uncertainty. When the number of samples in the original training dataset is limited, the model's prediction accuracy is extremely limited, failing to effectively support the design of high-performance concrete with coarse aggregate. Therefore, this invention introduces a Bayesian method, using the explicit calculation formula as prior knowledge, and simplifies the training dataset by fusing posterior information to obtain a probabilistic prediction model for compressive strength. The output of the probabilistic prediction model for compressive strength is the distribution law of compressive strength. Based on this distribution law combined with mathematical statistics, the representative value (lower confidence limit) prediction result can be directly obtained. The probabilistic model can not only describe the objective uncertainty in the process of obtaining the original training dataset, but also quantify the subjective uncertainty in the process of generating the explicit calculation formula. Moreover, it does not require the production of a large number of specimens for experimentation and statistical analysis to directly obtain the representative value of compressive strength. This greatly improves design efficiency and reduces design costs.

[0021] This invention achieves several key technological breakthroughs. First, in the construction stage of the probabilistic prediction model for compressive strength, efficient experimental design methods such as super-Latin sampling are employed, significantly reducing the number of test samples while maintaining model accuracy, overcoming the limitation of traditional deterministic formulas requiring a large number of test points. Second, in the application stage of the probabilistic prediction model for compressive strength, based on the probability prediction results, this invention can directly calculate the representative value of compressive strength, no longer relying on further actual experiments after design, thus advancing statistical inference to the model prediction stage. Third, the prediction model constructed by this invention combines interpretable explicit calculation formulas (i.e., deterministic prediction models) with probabilistic outputs (i.e., probabilistic prediction models for compressive strength), enabling engineers to understand the logical relationship of material strength formation and directly obtain representative values ​​of compressive strength during the design stage. This achieves a shift from the traditional "experiment-design-re-experiment" process to "prediction-evaluation-one-time design," greatly improving the efficiency of mix design and reducing design costs.

[0022] In summary, this invention establishes an innovative strength prediction system that combines interpretability and accuracy by constraining the input dimension through feature engineering, constructing interpretable formulas through genetic programming, and endowing the formulas with probabilistic meaning through Bayesian principles. This system not only overcomes the core shortcomings of existing deterministic models, such as their reliance on large amounts of experimental data and inability to express uncertainty, but also achieves for the first time the model-based inference of representative values ​​of compressive strength, demonstrating significant engineering application value and scientific innovation significance.

[0023] Therefore, the present invention has the following beneficial effects: the method of the present invention for determining the representative value of compressive strength of high-performance concrete with coarse aggregate greatly improves the efficiency of mix design of high-performance concrete with coarse aggregate and reduces the design cost. Detailed Implementation

[0024] The present invention will be further described below with reference to the embodiments.

[0025] This invention provides a method for determining the representative value of compressive strength of high-performance coarse aggregate concrete. The mix proportion characteristics of the high-performance coarse aggregate concrete include coarse aggregate strength (X1), minimum coarse aggregate particle size (X2), maximum coarse aggregate particle size (X3), coarse aggregate content (X4), steel fiber volume fraction (X5), fly ash content (X6), silica fume content (X7), and water-reducing agent content (X8). The values ​​of each mix proportion characteristic parameter of the high-performance coarse aggregate concrete whose compressive strength representative value is to be determined are known. The method comprises: 1) Establish a probabilistic prediction model for compressive strength according to Method 1; (ii) Using the compressive strength probability prediction model, the main characteristic parameter group of the mix proportion of coarse aggregate high-performance concrete is processed according to method six to obtain the representative value of the compressive strength of coarse aggregate high-performance concrete. The first method includes: 1) Obtain the training dataset using Method 2; 2) Determine the main characteristic parameter set according to Method 3; 3) Establish a deterministic prediction model according to Method 4; 4) Establish a probabilistic prediction model for compressive strength according to Method 5; The second method includes: X1, X2, X3, X4, X5, X6, X7, and X8 are denoted as characteristic parameter groups. Each proportion characteristic parameter within a characteristic parameter group is valued within its own value range (the value range specified in the technical specifications of the prior art). By combining different values ​​of the proportion characteristic parameters within each characteristic parameter group, multiple characteristic parameter groups are obtained. In this embodiment, the proportion characteristic parameters of the characteristic parameter groups are valued in the following manner: X1, X2, and X3 are designated as the first parameter group, and X4, X5, X6, X7, and X8 are designated as the second parameter group. The characteristic parameters of the mix proportions under the first parameter group are taken as follows: For a single mix proportion characteristic parameter under the first parameter group: its value range is divided into 3 equal-width intervals, and the midpoint value of any equal-width interval is taken as the value of the mix proportion characteristic parameter. The characteristic parameters of the mix proportions under the second parameter group are taken as follows: For a single mix proportion characteristic parameter under the second parameter group: its value range is divided into 6 equal-width intervals, and the midpoint value of any equal-width interval is taken as the value of the mix proportion characteristic parameter. Based on the above method, 100 feature parameter sets were obtained using the Latin hypercube sampling (LHS) method.

[0026] One hundred compressive strength specimens were prefabricated based on multiple sets of characteristic parameters. Tests were conducted on these specimens to obtain the compressive strength of each specimen. The combination of the characteristic parameter set and its corresponding compressive strength was recorded as a training dataset. Multiple training datasets constituted a training dataset. The specimen size and curing methods followed the relevant requirements of the "Standard for Testing and Evaluation of Concrete Strength" (GB50107-2022), and the test methods also followed the requirements of the same standard. This resulted in dataset X, which contains 100 examples. Each example is described by eight attributes X1~X8 and also includes a labeled compressive strength Y, obtained from the previous tests. The independent variables X1~X8 and the dependent variable Y are scaled to the interval [0.2, 0.8] using the Max-Min normalization method to obtain the dataset X'. The dataset X' is now a matrix of 100 rows × 9 columns, where: each row corresponds to an example; columns 1~8 correspond to attributes X1~X8; and column 9 corresponds to the label Y.

[0027] The third method includes: 2-1) Randomly divide the training data in the training dataset into two groups: one group forms the training set, and the other group forms the initial test set. Both the training set and the initial test set contain multiple training data sets. The ratio of the number of training data sets in the training set to the number of training data sets in the initial test set is 4:1. Let p be the combination of compressive strengths corresponding to the multiple training data sets in the initial test set. Randomly swap the X1 feature parameter groups of the multiple training data sets in the initial test set to obtain the first test set. Randomly swap the X2 feature parameter groups of the multiple training data sets in the initial test set to obtain the second test set. Then, the initial test set... The X3 feature parameter groups of the multiple training data under the jurisdiction are randomly swapped to obtain the 3rd test set. The X4 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 4th test set. The X5 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 5th test set. The X6 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 6th test set. The X7 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 7th test set. The X8 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 8th test set. 2-2) Train a BP neural network using the training set to obtain a predictive machine model, where the feature parameter set is used as input and the compressive strength is used as output; 2-3) Process the initial test set and the data from test set 1 to test set 8 as follows: For a single test set: each feature parameter group under the test set is used as the input of the prediction machine model. Each input feature parameter group is processed by the prediction machine model and outputs a predicted compressive strength. Multiple feature parameter groups result in multiple corresponding predicted compressive strengths. Let p' be the combination of multiple predicted compressive strengths obtained from the initial test set; let p' be the combination of multiple predicted compressive strengths obtained from the i-th test set. Xi ', where i is an integer from 1 to 8, thus obtaining p X1 'to p X8 '; Repeat steps 2-1) to 2-3) above N times, combining the N obtained p into vector P, combining the N obtained p' into vector P', and combining the N obtained p... Xi 'Combined into vector P' Xi ', thus obtaining P X1 'To P X8 '; Specific examples are as follows: a. Randomly divide the dataset X' into training set X' and training set X' in a 4:1 ratio. t1 (80×9) and test set X p1 (20×9), using X t1 Train a backpropagation (BP) neural network. Define the number of hidden layer neurons as 9; the maximum number of training iterations as 10. 6 Target error 10 -3 Learning rate 10 -2 The trained model is denoted as M1; b. Test set X p1 The original dependent variable vector in (20×9) is denoted as p1(20×1). The test set X... p1 The independent variable matrix (20×8) is input into model M1 to obtain the prediction result vector p1' (20×1); c. Randomly shuffle the trial set X p1 The data in the first column (corresponding to feature X1) of the independent variable matrix (20×8) are shuffled and then input into model M1 to obtain the prediction result vector p. 1X1 '(20×1) d. Repeat step c to obtain vector p. 1X2 '~ p 1X8 '(20×1) e. Repeat steps a, b, c, and d for a total of 20 rounds (including round 1). Set the training set X during the process. t2 X t3 ... X ti ... X t20 (All are 80×9); Set the test set X p2 X p3 ... X pi ... X p20 (All are 20×9). Training models M2, M3, ..., M i M 20 Based on this, we obtain vectors p2, p3, ..., p i ... p 20 (All are 20×1); p2', p3', ..., p i '、…、p 20 '(All are 20×1); p 2X1 '、p 3X1 '、…、p iX1 '、…、p 20X1 ' (both are 20×1); p 2X2 '、p 3X2 '、…、p iX2 '、…、p 20X2 ' (both are 20×1); p 2X3 '、p3X3 '、…、p iX3 '、…、p 20X3 ' (both are 20×1); p 2X4 '、p 3X4 '、…、p iX4 '、…、p 20X4 ' (both are 20×1); p 2X5 '、p 3X5 '、…、p iX5 '、…、p 20X5 ' (all 20×1); p 2X6 '、p 3X6 '、…、p iX6 '、…、p 20X6 ' (all 20×1); p 2X7 '、p 3X7 '、…、p iX7 '、…、p 20X7 ' (all 20×1); p 2X8 '、p 3X8 '、…、p iX8 '、…、p 20X8 (All are 20×1); where 1≤i≤20; f. Combining vectors p1, p2, ..., p i ... p 20 (All are 20×1) to obtain vector P (400×1). Combine vectors p1', p2', ..., p i '、…、p 20 ' (both 20×1) yields vector P' (400×1). Combine vector p 1X1 '、 p 2X1 '、…、p iX1 '、…、p 20X1 (Both are 20×1) to obtain vector P X1 (400×1). And so on, to obtain vector P. X2 '、 P X3 '、P X4 '、P X5 '、P X6 '、P X7 '、P X8 (All are 400×1); Then calculate the regression fit metric r0 between vector P and vector P'; and calculate the regression fit metric r0 between vector P and P' respectively. X1 'To P X8The regression fitting measures of these 8 vectors are r1 to r8; then the differences between r0 and each of the 8 regression fitting measures r1 to r8 are calculated to obtain Δr1 to Δr8. Δr1 to Δr8 are sorted in descending order of value, and the first 4 are taken as the principal differences. The 4 matching ratio characteristic parameters corresponding to the 4 principal differences are denoted as principal characteristic parameters x1, x2, x3 and x4. The combination of the 4 principal characteristic parameters is denoted as the principal characteristic parameter group. The fourth method includes: Delete the other four matching ratio feature parameters besides the main feature parameters in the training dataset X' to obtain the usable training dataset X" (100×5). Then, using the genetic programming symbolic regression method, with the available training dataset as samples, an elementary function equation, i.e., a deterministic prediction model, is established with the four main feature parameters x1, x2, x3, and x4 as independent variables and compressive strength Y as the dependent variable: Y = f (x1,x2,x3,x4,a,b,…) Where a, b, ... are deterministic parameters obtained by the symbolic regression method; The genetic programming symbolic regression method is briefly introduced below: The parameters of the genetic programming symbolic regression method are set as follows: population size 10000; crossover probability 80%; subtree mutation probability 10%; boost mutation probability 5%; node mutation probability 5%; tournament size 20; parsimony coefficient 0.005; function set +, -, ×, ÷, exp, log, sin, and cos; selection strategy is tournament selection; crossover method is subtree swapping; mutation method is subtree mutation, boost mutation, or node mutation, or any two or three combinations of the above three mutations; fitness evaluation index is mean squared error.

[0028] 3-1) A set of formula trees is randomly generated (a set of formula trees contains formulas expressing multiple independent functions); 3-2) Subsequently, it will produce offspring through a pattern of reproduction, mutation, and evolution (offspring also contain formulas expressed by multiple independent functions). 3-3) At this point, the initial formula tree group will be compared with the child generation with X" as the validation set (each independent function calculates the root mean square error for the X" validation set and takes the average). 3-4) After the comparison, the generation that is more "suitable" to describe the relationship between input and output is retained; 3-5) After the new generation of population is obtained through evolution, determine whether the new population meets the preset termination conditions, such as reaching the maximum number of iterations or the average root mean square error of each tree in the new population being less than a certain specified value. 3-6) Repeat the above steps iteratively until the final formula tree group is obtained; 3-7) Calculate the root mean square error of each independent function in the termination formula tree group for the validation set X". The function with the smallest error is the most "suitable" function expression.

[0029] Method five includes: The available training dataset is randomly divided into three available sub-training datasets, denoted as X1", X2", and X3". Replace the deterministic parameters a, b, ... in the deterministic prediction model with random variables α, β, ... represented by a normal distribution, and add a random normal error term γσ. 2 This yields the following formula: Y'= f (x1,x2,x3,x4, α,β,…)+γσ 2 Then, using the Markov Monte Carlo method based on Bayesian theory, the parameters α, β, ..., γσ in Equation 1 are processed three times using three available sub-training datasets. 2 The formula obtained after updating the parameters is the compressive strength probability prediction model; specifically: 4-1) With Y' = f (x1,x2,x3,x4, α,β,…)+γσ 2 As the prior equation, X1" is used as the posterior sample, and the information of α, β, ... and γ is updated using the Markov Monte Carlo method based on Bayesian theory. 4-2) With the updated Y'= f (x1,x2,x3,x4, α,β,…)+γσ 2 Using X2" as the prior and X2" as the posterior sample, the information of α, β, ... and γ is updated using the Markov Monte Carlo method based on Bayesian theory. 4-3) With the updated Y'= f (x1,x2,x3,x4, α,β,…)+γσ 2 Using X3" as the prior and X3" as the posterior sample, the Markov Monte Carlo method based on Bayesian theory is used to update the information of α, β, ..., γ, resulting in the probabilistic prediction model Y'= for the compressive strength of high-performance coarse aggregate concrete. f (x1,x2,x3,x4, α,β,…)+γσ 2 .

[0030] Method six includes: The random variables α, β, ..., and γ in the probabilistic prediction model of compressive strength are denoted as normal distribution parameters; A) The Monte Carlo method is used to sample the normal distribution parameters to obtain t normal distribution parameter sample groups; the t normal distribution parameter sample groups are combined with the main characteristic parameter group of coarse aggregate high-performance concrete to be determined to obtain t prediction parameter groups; B) The compressive strength probability prediction model is used to process the data of t prediction parameter groups respectively to obtain t Y' values; C) The Kolmogorov-Smirnov (KS) test was used to process the t Y' values ​​to obtain the mean μ and standard deviation s of their distribution; D) Determine the representative value of compressive strength Y" of high-performance concrete with coarse aggregate according to the following formula: Y"=μ-1.96s.

[0031] In actual design or verification process, as long as the representative value Y" is greater than the requirements of the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG 3362-2018), the mix proportion of the coarse aggregate high-performance concrete to be determined is qualified and safe and reliable in terms of compressive strength index.

[0032] The Latin hypercube sampling (LHS) method, Max-Min normalization method, BP neural network, genetic programming symbolic regression, Markov Monte Carlo method based on Bayesian theory, Monte Carlo method and KS test and other related theories used in this invention are all common processing methods or calculation methods in the prior art. The relevant content can be obtained by those skilled in the art from the relevant literature of the prior art.

Claims

1. A method for determining the representative value of compressive strength of high-performance coarse aggregate concrete, wherein the mix proportion characteristic parameters of the high-performance coarse aggregate concrete include coarse aggregate strength X1, minimum coarse aggregate particle size X2, maximum coarse aggregate particle size X3, coarse aggregate content X4, steel fiber volume fraction X5, fly ash content X6, silica fume content X7, and water-reducing agent content X8, wherein the values ​​of each mix proportion characteristic parameter of the high-performance coarse aggregate concrete whose compressive strength representative value is to be determined are known, characterized in that: The method includes: 1) Establish a probabilistic prediction model for compressive strength according to Method 1; (ii) Using the compressive strength probability prediction model, the main characteristic parameter group of the mix proportion of coarse aggregate high-performance concrete is processed according to method six to obtain the representative value of the compressive strength of coarse aggregate high-performance concrete. The first method includes: 1) Obtain the training dataset using Method 2; 2) Determine the main characteristic parameter set according to Method 3; 3) Establish a deterministic prediction model according to Method 4; 4) Establish a probabilistic prediction model for compressive strength according to Method 5; The second method includes: X1, X2, X3, X4, X5, X6, X7, and X8 are denoted as characteristic parameter groups. Each proportion characteristic parameter under the characteristic parameter group takes a value within its own value range. By combining different values ​​of each proportion characteristic parameter under the characteristic parameter group, multiple characteristic parameter groups are obtained. Multiple compression specimens are prefabricated based on multiple sets of feature parameters, and the compression strength of each specimen is obtained by testing the multiple compression specimens. The combination of the feature parameter set and the corresponding compression strength is recorded as a training data, and multiple training data are combined to form a training dataset. The third method includes: 2-1) Randomly divide the training data in the training dataset into two groups: one group forms the training set, and the other group forms the initial test set. Both the training set and the initial test set include multiple training data sets. The ratio of the number of training data sets in the training set to the number of training data sets in the initial test set is g:k. Let p be the combination of compressive strengths corresponding to the multiple training data sets in the initial test set. Randomly swap the X1 of the feature parameter groups of the multiple training data sets in the initial test set to obtain the first test set. Randomly swap the X2 of the feature parameter groups of the multiple training data sets in the initial test set to obtain the second test set. Then, the initial test set... The X3 feature parameter groups of the multiple training data under the jurisdiction are randomly swapped to obtain the 3rd test set. The X4 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 4th test set. The X5 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 5th test set. The X6 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 6th test set. The X7 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 7th test set. The X8 feature parameter groups of the multiple training data under the jurisdiction of the initial test set are randomly swapped to obtain the 8th test set. 2-2) Train a BP neural network using the training set to obtain a predictive machine model, where the feature parameter set is used as input and the compressive strength is used as output; 2-3) Process the initial test set and the data from test set 1 to test set 8 as follows: For a single test set: each feature parameter group under the test set is used as the input of the prediction machine model. Each input feature parameter group is processed by the prediction machine model and outputs a predicted compressive strength. Multiple feature parameter groups result in multiple corresponding predicted compressive strengths. Let p' be the combination of multiple predicted compressive strengths obtained from the initial test set; let p' be the combination of multiple predicted compressive strengths obtained from the i-th test set. Xi ', where i is an integer from 1 to 8, thus obtaining p X1 'to p X8 '; Repeat steps 2-1) to 2-3) above N times, combining the N obtained p into vector P, combining the N obtained p' into vector P', and combining the N obtained p... Xi 'Combined into vector P' Xi ', thus obtaining P X1 'To P X8 '; Then calculate the regression fit metric r0 between vector P and vector P'; and calculate the regression fit metric r0 between vector P and P' respectively. X1 'To P X8 The regression fitting measures of these 8 vectors are r1 to r8; then the differences between r0 and each of the 8 regression fitting measures r1 to r8 are calculated to obtain Δr1 to Δr8. Δr1 to Δr8 are sorted in descending order of value, and the first 4 are taken as the principal differences. The 4 matching ratio characteristic parameters corresponding to the 4 principal differences are denoted as principal characteristic parameters x1, x2, x3 and x4. The combination of the 4 principal characteristic parameters is denoted as the principal characteristic parameter group. The fourth method includes: The four matching ratio feature parameters other than the main feature parameters in the training dataset are deleted to obtain a usable training dataset. Then, using the genetic programming symbolic regression method, with the available training dataset as samples, an elementary function equation, i.e., a deterministic prediction model, is established with the four main feature parameters x1, x2, x3, and x4 as independent variables and compressive strength Y as the dependent variable: Y = f (x1,x2,x3,x4,a,b,…) Where a, b, ... are deterministic parameters obtained by the symbolic regression method; Method five includes: The available training dataset is randomly divided into three available sub-training datasets; Replace the deterministic parameters a, b, ... in the deterministic prediction model with random variables α, β, ... represented by a normal distribution, and add a random normal error term γσ. 2 This yields the following formula: = f (x1,x2,x3,x4, a,b,…)+γσ 2 Then, using the Markov Monte Carlo method based on Bayesian theory, the parameters α, β, ..., γσ in Equation 1 are processed three times using three available sub-training datasets. 2 The formula obtained after updating the parameters is the compressive strength probability prediction model. Method six includes: The random variables α, β, ..., and γ in the probabilistic prediction model of compressive strength are denoted as normal distribution parameters; A) The Monte Carlo method is used to sample the normal distribution parameters to obtain t normal distribution parameter sample groups; the t normal distribution parameter sample groups are combined with the main characteristic parameter group of coarse aggregate high-performance concrete to be determined to obtain t prediction parameter groups; B) The compressive strength probability prediction model is used to process the data of t prediction parameter groups respectively to obtain t prediction parameters. value; C) Use the KS test method to examine the t items. The values ​​are processed to obtain the mean μ and standard deviation s of their distribution; D) Determine the representative value of compressive strength of high-performance concrete with coarse aggregate according to the following formula. : 。 2. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1, characterized in that: In Method Two, the combination ratio characteristic parameters of the characteristic parameter group are taken in the following manner: X1, X2, and X3 are designated as the first parameter group, and X4, X5, X6, X7, and X8 are designated as the second parameter group. The characteristic parameters of the mix proportions under the first parameter group are taken as follows: For a single mix proportion characteristic parameter under the first parameter group: its value range is divided into 3 equal-width intervals, and the midpoint value of any equal-width interval is taken as the value of the mix proportion characteristic parameter. The characteristic parameters of the mix proportions under the second parameter group are taken as follows: For a single mix proportion characteristic parameter under the second parameter group: its value range is divided into 6 equal-width intervals, and the midpoint value of any equal-width interval is taken as the value of the mix proportion characteristic parameter. Based on the above method, the Latin hypercube sampling method is used to obtain multiple feature parameter sets.

3. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1 or 2, characterized in that: The feature parameter set obtained in Method 2 consists of 100 parameters.

4. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1, characterized in that: In Method 2, the Max-Min normalization method is used to process and scale the various mix proportion feature parameters and compressive strength data in each training data to the range of [0.2, 0.8].

5. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1, characterized in that: In step 2-1), the ratio of g:k is 4:

1.

6. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1, characterized in that: In method three, N is 20.

7. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1, characterized in that: In step 2-2), the number of hidden layer neurons in the BP neural network is 9, and the maximum number of training iterations is 10. 6 The target error is 10. -3 The learning rate is 10. -2 .

8. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1, characterized in that: The parameters of the genetic programming symbolic regression method are set as follows: population size 10000; crossover probability 80%; subtree mutation probability 10%; boost mutation probability 5%; node mutation probability 5%; tournament size 20; parsimony coefficient 0.005; function set +, -, ×, ÷, exp, log, sin, and cos; selection strategy is tournament selection; crossover method is subtree swapping; mutation method is subtree mutation, boost mutation, or node mutation, or a combination of the above three mutations; fitness evaluation index is mean squared error.

9. The method for determining the representative value of compressive strength of high-performance concrete with coarse aggregate as described in claim 1, characterized in that: In Method Six, t is 10000.

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