A Concrete Performance Prediction Method Based on Multivariate Nonlinear Regression Analysis

Abstract

This invention discloses a method for predicting concrete performance based on multivariate nonlinear regression analysis, comprising the following steps: obtaining a real-valued dataset of concrete performance under different combinations of conditional parameters using an orthogonal strategy; defining the type of regression equation and solving the parameters in the regression model using the least squares method based on the aforementioned dataset; verifying the accuracy of the regression model using the aforementioned dataset and additional datasets; and predicting the concrete performance of different parameters using the validated regression model. The results show that this performance prediction method can establish an excellent regression prediction model based on a small amount of real data and achieve rapid and accurate prediction of concrete performance with different parameters.

Description

Technical Field

[0001] This invention relates to a method for predicting concrete performance based on multivariate nonlinear regression analysis, belonging to the field of concrete performance evaluation technology. Background Technology

[0002] As a multiphase heterogeneous material, concrete's properties are closely related to the microstructure of each phase. However, traditional experimental studies struggle to establish the correlation between the properties of each phase's microstructure and concrete performance. This is primarily because related research indicates that the interfacial transition zone between aggregates and mortar is typically a region of uneven thickness (20-100 μm), and its properties differ significantly from those of the mortar matrix. Therefore, it is difficult to quantify the mapping relationship between ITZ parameters and concrete performance through experimental methods. In recent years, with the rapid development of computer technology, numerical simulation has been widely used to investigate the static and dynamic mechanical properties, ion diffusion properties, and thermal conductivity of concrete under load, elucidating the influence of ITZ and aggregate properties on concrete performance. Simultaneously, multiple regression analysis has been widely used across various disciplines to establish quantitative relationships between independent and dependent variables. Therefore, there is an urgent need to propose a concrete performance prediction method based on multiple nonlinear regression analysis. Summary of the Invention

[0003] Purpose of the invention: In view of the shortcomings of the prior art, the purpose of this invention is to provide a concrete performance prediction method based on multivariate nonlinear regression analysis, which solves the problem that existing experimental studies are unable to establish a quantitative relationship between the microstructure of each phase of concrete and its properties.

[0004] Technical solution: The present invention provides a method for predicting concrete performance based on multivariate nonlinear regression analysis, characterized by comprising the following steps:

[0005] (1) Based on the concrete performance to be predicted, set the ITZ and aggregate parameters and their boundary threshold parameters, select parameter set I from them based on orthogonal experiments, and form a randomly selected parameter set II;

[0006] (2) Using numerical simulation, the ITZ and aggregate parameters in parameter set I and parameter set II are used as input parameters, and concrete performance is used as output parameter to obtain concrete performance dataset I and dataset II under different combinations of ITZ and aggregate parameters.

[0007] (3) Confirm the type of regression model, and solve for each parameter in the regression model using the least squares method based on dataset I;

[0008] (4) Use dataset I and dataset II to test the accuracy of the regression model. If the accuracy does not meet the requirements, reconfirm the type of regression model until an accurate regression model is obtained.

[0009] (5) Based on the accurate regression model, input the ITZ and aggregate parameters of the concrete performance to be predicted, draw the concrete performance cloud map, and realize the prediction of concrete performance with any combination of parameters within the boundary threshold range.

[0010] In step (1), the concrete properties are one or more of the following: concrete compressive strength, tensile strength, thermal conductivity, moisture transport coefficient, and ion diffusion coefficient.

[0011] In step (1), the ITZ parameters are one or more of the following: ITZ thickness, ITZ strength, ITZ thermal conductivity, and ITZ moisture / ion diffusion coefficient.

[0012] In step (1), the aggregate parameters are one or more of aggregate gradation, shape, and volume fraction.

[0013] In step (1), setting the ITZ and aggregate parameters and their boundary threshold parameters refers to setting the interval and boundary of the ITZ and aggregate parameters, for example, the aggregate volume fraction is 0~60%, with an interval of 5%.

[0014] In step (1), selecting parameter I based on orthogonal experiments refers to forming an orthogonal parameter set with boundary thresholds. For example, when predicting the compressive strength of concrete, the aggregate volume fraction is set to 0-60%, with 5% intervals; the ITZ thickness is set to 0-500μm, with 50μm intervals; and when the ITZ strength is 50-100% of the mortar strength, with 5% intervals. The selected orthogonal parameter set with boundary thresholds (parameter set I) is as follows: Figure 1 As shown, parameter set I must account for more than 60% of the entire parameter set.

[0015] In step (1), forming a randomly selected parameter set II means that ITZ and aggregate parameters are randomly combined to form a parameter set other than the parameter set I described in step (1).

[0016] In step (2), the numerical simulation is performed using ABAQUS and / or COMSOL numerical simulation software. Data set I and data set II are respectively composed of parameter set I, parameter set II, and concrete performance values ​​generated based on parameter set I and parameter set II.

[0017] In step (3), the regression model is of type Y= β 0+ β 1X1+ β 2X2+ β 3X3+ β 4X1X2+ β 5X1X3+ β 6 x 2 x 3 + ... + βn-2 X1 n + β n-1 X2 n + β n X3 n The terms included in the document are linear terms, quadratic terms, and / or cross-variable terms; among which, β 0~ β n All are constants, X1~X n For ITZ and / or aggregate parameters, including one or more of ITZ thickness, ITZ strength, ITZ thermal conductivity, ITZ moisture / ion diffusion coefficient, aggregate gradation, aggregate shape, and aggregate volume fraction.

[0018] In step (3), solving for the parameters in the regression model using the least squares method means using MATLAB software to solve for the constants in the regression model.

[0019] In step (4), the average relative error is used to measure the accuracy of the regression model. When the average relative error is less than 10%, the accuracy of the regression model is determined to meet the requirements.

[0020] In step (5), concrete performance cloud maps are drawn using Origin and MATLAB software.

[0021] Invention principle: This invention is based on multivariate nonlinear regression analysis and uses an orthogonal dataset with parameter boundary thresholds to obtain a regression model that can accurately predict concrete performance under different parameter combinations.

[0022] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0023] This invention uses orthogonal datasets, which ensures the accuracy of the prediction model even with a small amount of data. At the same time, the influence of parameter boundary thresholds is considered in the regression model, which further ensures the accuracy of the model. Attached Figure Description

[0024] Figure 1 A diagram showing the boundary threshold parameters and orthogonal parameters (parameter set 1) for predicting the compressive strength of concrete;

[0025] Figure 2 This is a surface diagram showing the predicted compressive strength of concrete. Detailed Implementation

[0026] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0027] Example 1: Prediction of Concrete Compressive Strength

[0028] Since the compressive strength of concrete is mainly related to the ITZ thickness, ITZ strength, and aggregate volume fraction, a regression prediction model for concrete compressive strength is proposed based on these three parameters. Literature review shows that the ITZ thickness is typically 0-500 μm in 50 μm intervals; the ITZ strength is typically 50-100% of the mortar strength in 5% intervals; and the aggregate volume fraction is typically 0-60% in 5% intervals. Based on orthogonal experimental design, Table 1 and... Figure 1 The boundary threshold parameters and orthogonal parameters shown in Table 1 (parameter set I) and the random parameter set shown in Table 2 (parameter set II).

[0029] Table 1 Parameter Set I (94 points in total)

[0030] ITZ thickness ITZ strength (ITZ / mortar) aggregate volume fraction 0-500μm (50μm intervals) 75% 45% 250μm 50%-100% (5% intervals) 45% 250μm 75% 0-60% (5% intervals) 0μm 50%-100% (5% intervals) 45% 0-500μm (50μm intervals) 100% 45%

[0031] Table 2 Parameter Set II (50 points in total)

[0032] ITZ thickness ITZ strength (ITZ / mortar) aggregate volume fraction 250μm 50% 5%-60% (5% is an interval, no 45%) 250μm 90% 5%-60% (5% is an interval, no 45%) 250 60 0-60 (5% interval) 100-500 (100μm interval) 50 50 450 95 45 50 95 45 50 95 60 50 50 60 30 50 60 450 95 45 50 95 45 200 50 10 300 50 35 400 50 35 300 50 55 350 50 55

[0033] (2) Based on the damage-plasticity model in the ABAQUS finite element analysis software, the failure criterion is the maximum tensile strain criterion. Data sets I and II are obtained, consisting of parameter set I, parameter set II, and concrete compressive strength values ​​generated based on parameter sets I and II. The specific parameter settings in the simulation process are shown in Table 3.

[0034] Table 3 Mechanical parameters of various microstructure components of concrete

[0035] parameter <![CDATA[ ρ (kg / m 3 )]]> (MPa) <![CDATA[ f c (MPa)]]> <![CDATA[ f t (MPa)]]> aggregate 2600 65000 0.15 / / mortar 2300 30000 0.22 32.4 2.64 ITZ 2100 15000-30000 0.20 16.2-32.4 1.32-2.64

[0036] Note: In the table ρ Density; E It is the elastic modulus; μ Poisson's ratio; f c Compressive strength; f t This represents the tensile strength.

[0037] (3) Determine the type of regression model, and then use the least squares method to determine the parameters in the regression equation based on dataset I.

[0038] The steps to determine the type of regression model are as follows:

[0039] ①Since the compressive strength of concrete is a constant regardless of the thickness of the ITZ when the aggregate volume fraction is constant and the ITZ strength is 100%, or a constant regardless of the ITZ strength when the ITZ thickness is 0, the influence of ITZ on the compressive strength of concrete can be expressed by equation (1):

[0040] (1)

[0041] in, A This represents the thickness of the ITZ. B Represents the strength of ITZ. The values ​​represent the compressive strength of concrete considering the influence of ITZ thickness and ITZ strength, where a, b, c, and d are all constants.

[0042] ②Since the compressive strength of concrete remains constant regardless of the thickness and strength of the ITZ when the aggregate volume fraction is 0, the effect of aggregate volume fraction on the compressive strength of concrete can be expressed by equation (2):

[0043] (2)

[0044] in, C Represents aggregate volume fraction. F This represents the compressive strength value of concrete considering the thickness and strength of the ITZ (Intense Iron Zone). The value represents the compressive strength of concrete considering the effects of ITZ thickness, ITZ strength, and aggregate volume fraction. e, f, and g are all constants.

[0045] ③ Combining equations (1) and (2) (i.e., equation (1) multiplied by equation (2)), the effects of ITZ thickness, ITZ strength, and aggregate volume fraction on the compressive strength of concrete can be expressed by equation (3):

[0046] (3)

[0047] in, To determine the compressive strength of concrete considering the effects of ITZ thickness, ITZ strength, and aggregate volume fraction; h, i, j, k, and l are all constants, which need to be solved using the least squares method. h =-19.3477; i =39.6185; j =2.4719e-4; k =0.2523; l =-0.3751; A , B , C These represent the thickness of the ITZ, the strength of the ITZ, and the aggregate volume fraction, respectively.

[0048] (4) Based on the average relative error, the accuracy of the regression model was tested using dataset I and dataset II. The average relative errors of datasets I and II were 1.53% and 5.60%, respectively, and the regression model (3) met the accuracy requirements.

[0049] (5) Using the validated regression model (3), the compressive strength of concrete with different parameters to be predicted is predicted, and the final result is as follows: Figure 2 The values ​​of concrete compressive strength are shown for different ITZ thicknesses (0-500 μm, in 5 μm intervals), ITZ strengths (50-100%, in 0.5% intervals), and aggregate volume fractions (0-60%, in 0.5% intervals).

Claims

1. A method for predicting concrete performance based on multivariate nonlinear regression analysis, characterized in that, Includes the following steps: (1) Based on the concrete performance to be predicted, set ITZ and aggregate parameters and their boundary threshold parameters, select parameter set I from them based on orthogonal experiments, and form a randomly selected parameter set II; wherein, concrete performance is one or more of concrete compressive strength, tensile strength, thermal conductivity, moisture transport coefficient, and ion diffusion coefficient; setting ITZ and aggregate parameters and their boundary threshold parameters refers to setting the interval and boundary of ITZ parameters and aggregate parameters; ITZ parameters are one or more of ITZ thickness, ITZ strength, ITZ thermal conductivity, and ITZ moisture / ion diffusion coefficient; aggregate parameters are one or more of aggregate gradation, shape, and volume fraction; selecting parameter I from them based on orthogonal experiments refers to forming an orthogonal parameter set with boundary thresholds; (2) Using numerical simulation, the ITZ and aggregate parameters in parameter set I and parameter set II are used as input parameters, and concrete performance is used as output parameter to obtain concrete performance dataset I and dataset II under different combinations of ITZ and aggregate parameters. (3) Confirm the type of regression model, and based on dataset I, solve for each parameter in the regression model using the least squares method; the type of the regression model is Y= β 0+ β 1X1+ β 2X2+ β 3X3+ β 4X1X2+ β 5X1X3+ β 6 x 2 x 3 + ... + β n-2 X1 n + β n-1 X2 n + β n X3 n ;in, β 0~ β n All are constants, X1~X n For ITZ and / or aggregate parameters; (4) Use dataset I and dataset II to test the accuracy of the regression model. If the accuracy does not meet the requirements, reconfirm the type of regression model until an accurate regression model is obtained. (5) Based on the accurate regression model input of the ITZ and aggregate parameters of the concrete performance to be predicted, draw the concrete performance cloud map and realize the prediction of concrete performance with any combination of parameters within the boundary threshold range.

2. The method for predicting concrete performance based on multivariate nonlinear regression analysis according to claim 1, characterized in that, In step (1), forming a randomly selected parameter set II means that ITZ and aggregate parameters are randomly combined to form a parameter set other than the parameter set I described in step (1).

3. The method for predicting concrete performance based on multivariate nonlinear regression analysis according to claim 1, characterized in that, In step (2), the numerical simulation is performed using ABAQUS and / or COMSOL numerical simulation software. The dataset I and dataset II are respectively composed of parameter sets I and II and concrete performance values ​​generated based on parameter sets I and II.

4. The method for predicting concrete performance based on multivariate nonlinear regression analysis according to claim 1, characterized in that, In step (3), the use of least squares to solve for each parameter in the regression model refers to using MATLAB software to solve for the constants in the regression model.

5. The method for predicting concrete performance based on multivariate nonlinear regression analysis according to claim 1, characterized in that, In step (4), the average relative error is used to measure the accuracy of the regression model. When the average relative error is less than 10%, the accuracy of the regression model is determined to meet the requirements.

6. The method for predicting concrete performance based on multivariate nonlinear regression analysis according to claim 1, characterized in that, In step (5), concrete performance cloud maps are drawn using Origin and MATLAB software.

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