A stochastic simulation method considering dimensional deviation and variability of concrete material

Abstract

The present application relates to a kind of random simulation method considering size deviation and variability of concrete material, belong to the field of concrete structure analysis.The method is realized to the accurate simulation of the mechanical properties of concrete structure under the influence of construction error and material randomness by determining random factors, establishing random field matrix, carrying out sample transformation, batch establishing random model, batch solving and post-processing.The PRRM-EPR algorithm is used to establish machine learning prediction model by using random simulation result as output parameter and random sample as input parameter.Compared with traditional method, the present application improves the generation quality of random sample, reduces the calculation cost, and can better reflect the randomness in actual engineering.The prediction model established can directly predict the mechanical response (displacement, load, etc.) of the component by the measured random parameters.The present application is suitable for concrete structure design, evaluation and optimization, and has significant effect in improving structural safety.

Description

Technical Field

[0001] This invention belongs to the field of concrete structure analysis and relates to a stochastic simulation method that considers dimensional deviations and the variability of concrete materials. Background Technology

[0002] Concrete, as a heterogeneous material, naturally possesses numerous initial defects such as micropores and microcracks. Under external forces, these initial defects expand randomly, leading to a stochastic and nonlinear constitutive relationship. The random distribution of material defects results in the random evolution of damage, which in turn leads to random strength performance and constitutive characteristics, affecting the mechanical properties of the structural members. Furthermore, existing simulations of reinforced concrete structures assume that parameters such as cross-sectional dimensions, protective layer thickness, longitudinal reinforcement spacing, and stirrup spacing remain consistent from design to completion, rarely addressing the impact of construction on the mechanical properties of reinforced concrete structures. In reality, due to the roughness of the construction process and the existence of uncontrollable objective factors such as construction personnel, equipment, and techniques, deviations often occur. These deviations inevitably lead to variations in the mechanical properties of reinforced concrete structures, posing a significant threat to the safety of the members. In actual engineering projects, the impact of these problems is even more pronounced. Therefore, it is necessary to accurately assess the influence of these random factors on the mechanical behavior of the members in order to consider these factors from the initial design stage and avoid the aforementioned problems.

[0003] One approach is to conduct extensive experimental research to address these issues. However, this approach is time-consuming and resource-intensive. Furthermore, there is a lack of effective solutions for evaluating the mechanical properties of existing buildings by considering the impact of construction errors and material randomness. Numerical analysis, as a crucial tool in engineering, can accurately reflect the mechanical response of actual components, making numerical simulation a viable new solution. However, traditional numerical simulations employ deterministic modeling and analysis methods, failing to account for the influence of random factors. Therefore, there is an urgent need to develop new simulation methods to ensure that simulation results accurately incorporate these random factors.

[0004] Current simulations of concrete material variability and construction errors are mostly based on the Monte Carlo method, directly introducing material mechanical property parameters and component size distribution for simulation analysis, which presents three problems.

[0005] 1. Traditional simulation methods suffer from non-random patterns in their random samples. After a certain length, samples may repeat, and the sample distribution may be uneven, even leading to correlated samples, thus affecting the accuracy of the random simulation and analysis. Furthermore, this method requires a large number of random samples to approximate the solution, resulting in high computational costs.

[0006] 2. There are problems with sample selection, lacking real statistical data and material test results. Traditional simulation methods generate samples through mathematical and physical models. However, these models lack universality for different objects, and they often rely on simplifying assumptions and parameter estimates. These assumptions may ignore or simplify certain real-world correlations, leading to results that deviate from reality.

[0007] The random field model established based on this cannot accurately simulate the spatial distribution characteristics of variables in actual engineering. In addition, traditional random samples only involve low-dimensional space. Once the sample dimension is too high, the quality will decrease, causing the model to perform poorly in high-dimensional space, which further affects the accuracy of the simulation results.

[0008] 3. Existing numerical analysis platforms have a wide range of material models and element libraries, support complex geometric and multiphysics coupling analysis, perform well in handling nonlinear problems, and have good post-processing capabilities. However, when performing stochastic simulation analysis of large structures, they have low modeling efficiency, still require a lot of computational cost, and the stochastic simulation results do not have generalization ability, which has limitations.

[0009] To improve the efficiency of stochastic simulation calculations, accurately quantify the impact of the coupling effect between construction errors and the randomness of concrete materials, obtain more accurate simulation results, and advance existing research, it is urgent to develop a new stochastic simulation method for reinforced concrete structures. Summary of the Invention

[0010] In view of this, the purpose of this invention is to provide a stochastic simulation method that considers dimensional deviations and the variability of concrete materials, enabling automated modeling, solving, post-processing, and machine learning model training throughout the entire stochastic simulation process. This method, combined with existing finite element analysis software, significantly improves computational efficiency by achieving accurate results with lower computational costs. It also enhances the quality of random sample generation in high-latitude spaces, accurately simulating the real-world impact of construction errors and material randomness on reinforced concrete structures. Furthermore, by using the stochastic simulation results as output and random field samples as input, a machine learning model is trained to obtain a predictive model. This model can directly predict the stochastic mechanical response of components using measured random parameters. This method can be combined with experiments or used independently for stochastic simulation of existing buildings.

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] A stochastic simulation method considering dimensional deviations and concrete material variability, the method comprising:

[0013] S1: Random Field Sample Establishment: Before conducting random simulation, material performance tests are carried out, and the cross-sectional dimensions and steel bar spacing of the components are measured and statistically analyzed. Random factor control parameters are defined, and the dimension of the random field matrix is ​​determined. Based on the measured data, the Gaussian Mixture Model (GMM) algorithm is used to optimize the Sobol sequence point selection strategy to generate the random field matrix. The random sample covariance matrix U and the Frobenius threshold under a 95% guarantee rate are calculated to determine the random field samples.

[0014] S2: Stochastic Model Establishment: Define component modeling parameters and material modeling parameters, complete the establishment of a nonlinear material model based on the established random samples, and combine with the finite element analysis platform to realize the task of establishing a stochastic model of materials and components;

[0015] S3: Batch Solving and Post-processing: The model is solved using the finite element platform, and the results are processed. Load-displacement curves, stiffness degradation curves, cumulative hysteresis energy dissipation curves, damage morphology cloud maps, etc. are extracted in batches. Yield points, peak points, limit points, ductility are calculated and confidence intervals are given.

[0016] S4: Machine Learning Model: The S3 random simulation results are used as the output, and the S1 random field samples are used as the input. The PRRM-EPR algorithm is used to train the machine learning model and establish a prediction model. The prediction model directly predicts the mechanical response of the component, including displacement, load, stress and strain, through measured random parameters.

[0017] Furthermore, in S1, when the test is carried out, concrete test blocks are simultaneously retained for material performance testing, and the component dimensions and rebar spacing are measured; when carried out independently, the rebound test is carried out according to the "Technical Specification for Testing the Compressive Strength of Concrete by Rebound Method" to obtain the strength distribution of the research object, and the construction error is measured simultaneously; the cross-sections for measuring the construction error are no less than 5, the cross-section positions are evenly divided along the length of the component, and the measurement is carried out using a measuring instrument with a resolution of not less than 0.001 mm.

[0018] Furthermore, in S1, the number of samples for material performance testing of concrete test blocks is no less than 5.

[0019] Furthermore, the rebound test shall be conducted in no fewer than 5 sample intervals, with no fewer than 16 samples in each interval.

[0020] Furthermore, in S1, if material performance tests and construction error statistics are not conducted, the recommended values ​​in the specifications, including the limit values ​​for appearance quality and dimensional deviations specified in the "Code for Design of Concrete Structures" and the "Code for Acceptance of Construction Quality of Concrete Structures", are adopted. The design value is used as the mean and the limit error is used as the standard deviation for subsequent work.

[0021] Furthermore, in S1, based on the GMM algorithm to capture the complex structure and correlation of the data, the Sobol sequence is added as random noise to the samples generated by the GMM algorithm to establish random samples, so as to further increase the diversity and coverage of the samples.

[0022] Furthermore, in S1, a covariance matrix of cross-sectional dimension parameters and rebar spacing is established, and a covariance matrix of concrete material mechanical property parameters is established. Based on the covariance matrix, a Frobenius threshold with a 95% guarantee rate is calculated. This threshold is used as the secondary screening basis for the random sample generation by optimizing the Sobol sequence selection strategy in S1 using the GMM algorithm, so as to improve the sample quality.

[0023] Furthermore, in S2, the component model is established, the number of model sample points is defined, including the number of cross sections and the number of steel bars, and random modeling of the component cross section size and steel bar spacing is carried out.

[0024] Furthermore, in S2, a nonlinear material model is randomly established, including concrete and steel reinforcement; for the concrete plastic damage model, random modeling is performed, and the model is modeled by control parameters: elastic modulus and peak strain, axial compressive strength and descending trend.

[0025] In S2, based on the modeling methods of each finite element platform, the random samples generated in S1 are used to replace the deterministic modeling parameters of materials and components, and the tasks of model assembly, boundary condition setting and mesh generation are performed to realize the establishment of a random model.

[0026] Furthermore, in S4, the input of the machine learning model is the random sample established in S1, and the output is the mechanical response obtained in S3, that is, the random mechanical response of the component is directly predicted through the measured random parameters.

[0027] The beneficial effects of this invention are as follows:

[0028] (1) Traditional Sobol sequence (low-discrepancy sequence) samples are used to provide uniformly distributed sample points, but this sequence assumes that the variables are independent and cannot capture the correlation between data. To improve the sample generation effect, this invention proposes a method for optimizing Sobol sequence samples based on the GMM algorithm. This model combines GMM (Gaussian Mixture Model) and Sobol sequence optimization sample generation methods to enhance the correlation and diversity of generated samples. In the sample generation process, GMM is first trained using measured data to capture the complex structure and correlation of the data; subsequently, the Sobol sequence is added as random noise to the samples generated by GMM to further increase the diversity and coverage of the samples. This combined method not only considers the correlation between data but also improves the stability of the generated samples.

[0029] Compared to the GMM algorithm, this invention can introduce sample diversity, broaden the distribution range of samples, improve the uniformity of sample distribution, and reduce the local clustering effect of samples. Compared to the traditional Sobol sequence, this method can better reflect the correlation between samples, making the generated data closer to the actual distribution. Compared to the traditional Monte Carlo method, the method of this invention can achieve higher sample efficiency and quality with less sample size, and significantly reduce the model computation cost.

[0030] (2) The method of the present invention is simple to operate and easy to analyze. Combined with the optimization algorithm of the present invention, random samples are generated, which has excellent universality.

[0031] (3) By combining the existing finite element analysis platform, secondary development was carried out to realize tasks such as automatic establishment, solution, and post-processing of calculation results for stochastic models. Each step of the process implementation is controlled by Python programming, which further reduces the calculation cost and improves the calculation speed of large models.

[0032] (4) This method can be combined with existing finite element analysis platforms that support programming interfaces to achieve integrated analysis of modeling, analysis and solution, and post-processing.

[0033] (5) In addition to the analysis of concrete materials and construction errors mentioned in this invention, this method can also be used for modeling and stochastic simulation analysis of other materials.

[0034] (6) By using random simulation results and random samples to train the machine learning model, the random mechanical response of the component can be directly predicted through the measured parameters, which greatly saves computing costs and resources.

[0035] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0036] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0037] Figure 1 This represents the probability distribution of random samples of the axial compressive strength of concrete.

[0038] Figure 2 The probability distribution of random samples of component cross-sectional dimensions;

[0039] Figure 3 These are the control parameters for cross-sectional dimensions;

[0040] Figure 4 This is a flowchart of the present invention;

[0041] Figure 5 This is a sample of the axial compressive strength of concrete.

[0042] Figure 6 For component models;

[0043] Figure 7 A model for plastic damage in concrete;

[0044] Figure 8 Divide the model into meshes;

[0045] Figure 9 The results are from a random simulation of the skeleton curve.

[0046] Figure 10 The results are from a random simulation of the yield point and ductility coefficient.

[0047] Figure 11 This represents the model's damage under pressure.

[0048] Figure 12 To predict results for machine learning models. Detailed Implementation

[0049] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0050] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0051] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0052] This invention consists of three parts: S1, random field sample establishment; S2, random model establishment; and S3, batch solution and post-processing.

[0053] S1. Establishment of Random Field Samples

[0054] S1.1 Before conducting the randomized simulation, material performance tests were performed on the concrete test blocks, and the cross-sectional dimensions of the test components were measured and statistically analyzed. The relative frequency histograms for each random sample are presented, such as... Figure 1 and Figure 2 As shown in Table 1, the eccentricity ratio, obtained by dividing the sample value by the design value on the horizontal axis, reflects the degree of deviation between the actual performance of the sample and the design target. The vertical axis represents the relative proportion of data appearing in each interval, i.e., the number of data in each interval divided by the total number of data. The optimal distribution function was obtained by performing a KS test on the sample, and the optimal distribution type for each random factor was determined, as shown in Table 1.

[0055] Table 1

[0056]

[0057] If material performance tests and construction error statistics have not been conducted, the recommended values ​​from the specifications can be adopted. For example, Appendix C of the "Code for Design of Concrete Structures" (GB50010-2010) provides recommended values ​​for the coefficient of variation of concrete strength, the representative value of the specified uniaxial compressive strength of concrete, and the ultimate compressive strain ε of concrete. c,r With the shape parameter α of the concrete constitutive curve c The limits for appearance quality and dimensional deviations are specified in the "Code for Acceptance of Construction Quality of Concrete Structures" GB50204-2015.

[0058] Define the control parameters for each factor.

[0059] An example illustrates this: The concrete material utilizes a plastic damage model, which can be determined by four control parameters: elastic modulus E, axial compressive strength f, and so on. c Peak compressive strain εc descent segment parameter α c That is, to perform random modeling of concrete material using four random variables in the random field matrix.

[0060] An example illustrating the definition of component size control parameters, taking a concrete column as an example, is generated by laying out i rectangular sections. Each section's shape is determined by 4 coordinates and 8 parameters, such as... Figure 3 As shown. The number of rectangular sections, i, is determined according to the required accuracy of the simulation; the more sections, the higher the accuracy of the random simulation. That is, the dimensions of the concrete components are randomly modeled using 8i random variables in the random field matrix.

[0061] S1.2. Based on the above models, determine the required number of random variables and the dimension L of the random field, and optimize the Sobol sequence generation Mi based on the GMM algorithm:

[0062] 1) Use KL divergence as the objective function, and J is the measure of the difference between the generated random sequence and the ideal uniform distribution.

[0063]

[0064] In the formula, K is the number of components in the GMM model, and P k It is the weight of the k-th component, q k (x i ) represents the k-th component at point x. i The probability density function is given by N, where N is the number of samples.

[0065] 2) Optimize the coefficient weights pk, mean μk, and covariance matrix Σ using the Expectation-Maximization (EM) algorithm. k In the E-step, the posterior probability of each data point xi is as follows.

[0066]

[0067] Wherein, γ(z) i k) is the data point x i The posterior probability of belonging to the k-th Gaussian component, qk(xi|μ) k ,Σ k Let be the probability density function of the k-th Gaussian component at point xi, and its calculation formula is as follows:

[0068]

[0069] 3) In the M-step, the posterior probabilities calculated in the E-step are used to update the parameters of the GMM.

[0070] The updated weighted comparison is as follows:

[0071]

[0072] Update mean μ k as follows:

[0073]

[0074] The covariance matrix Σk is updated as follows:

[0075]

[0076] 4) Repeat the E-step and M-step until convergence.

[0077] 5) Update coefficient M i .

[0078]

[0079] Among them, D KL (P||Q) is the KL divergence between the distribution P of the generated random sequence and the GMM distribution Q, and α is the learning rate.

[0080] 6) Take a value less than 2 i positive odd number M i And define the direction number v i for:

[0081]

[0082] In the formula, i is the number of the pseudo-random number.

[0083] 7) Using primitive polynomials with coefficients that are only 0 or 1, the direction number v i This can be expressed by a recursive formula as follows:

[0084]

[0085] In the formula, For binary bitwise XOR, c1~c p denoted by , where is the coefficient of the primitive polynomial, and p is the number of polynomials.

[0086] 8) Based on the direction number v i Establish a pseudo-random number sequence x i for:

[0087]

[0088] In the formula, b1, b2, and b3 are integers M. i The binary representation of .

[0089] S1.3. Based on the optimal distribution type of each random factor, perform sample transformation on the numerical values ​​within the random field matrix and determine the sample conformity. For example, the axial compressive strength of concrete follows a normal distribution as follows:

[0090]

[0091] 1) A uniformly distributed Sobol sequence can be represented as U i U i ∈[0,1];

[0092] 2) The percentile function (ppf) of the normal distribution maps random field samples to normally distributed samples. Given a probability p, the ppf function Φ -1 (p) The return value x satisfies:

[0093] P(X≤x)=p (12)

[0094] Where Φ is the cumulative distribution function (CDF) of the standard normal distribution.

[0095] 3) From uniform sample U i Percentile function Φ of normal distribution -1 The matrix samples are transformed as follows:

[0096] X i =Φ -1 (U i (13)

[0097] Where X i These are the transformed normally distributed samples.

[0098] 4) For the transformed sample X i Calculate its covariance matrix U, calculate the Frobenius threshold of the covariance matrix under a 95% guarantee rate, determine the random field sample, and assign values ​​to the parameters to generate random samples.

[0099] Based on the mean and standard deviation of the statistical analysis of the axial compressive strength of concrete, values ​​are assigned to the control parameters, and a random sample f is generated. ci See below for details. Figure 5 .

[0100] f ci =μ+σ×X i (14) S2, Establishment of stochastic model

[0101] S2.1 Define modeling parameters (samples to be modeled, including but not limited to component modeling and material modeling). Based on the established random samples, complete the plastic damage model as follows.

[0102] Based on the random samples generated above, f ci E ci ε ci α ci ;

[0103] σ=(1-d c E ci ε ci (15)

[0104]

[0105] In the formula: α ci These are the parameter values ​​for the descending segment of the uniaxial compressive stress-strain curve of concrete;

[0106] f ci,r This represents the uniaxial compressive strength of concrete.

[0107] ε ci,r To compare with the representative value of uniaxial compressive strength f ci,r The corresponding peak compressive strain;

[0108] d c These are the parameters for the evolution of uniaxial compressive damage in concrete.

[0109] Using the above formula, the uniaxial compressive stress-strain curve of concrete is calculated, and a stochastic plastic damage model is established.

[0110] 2) Define the number of model sample points

[0111] In one embodiment of the present invention, random modeling of the component cross-sectional dimensions was carried out, by... Figure 6 As can be seen, the model is controlled by six cross-sections, resulting in higher sample quality and a better reflection of the random characteristics of the component cross-sectional dimensions. For example... Figure 7 As shown, a stochastic model of concrete plastic damage was developed. This model consists of four control parameters: elastic modulus E, peak strain ε (log-normal distribution), axial compressive strength f, and peak strain ε. c Modeling with a normal distribution and a descending trend α (translated Gamma distribution) results in a more uniform distribution, allowing for the representation of the variability of concrete materials with fewer samples. The material is then assigned to a stochastic model for calculation.

[0112] S2.2, complete the assembly of each model, define material properties, set boundaries, mesh generation, interactions, etc., such as Figure 8 As shown (this is based on finite element analysis software, and the definitions are based on the characteristics of each platform), taking the Abaqus platform as an example, the above work is automatically completed by compiling a Python program. The process is as follows:

[0113] 1) Based on the random samples corresponding to the component size control parameters, establish control sections, and then establish concrete column components by laying out the control sections;

[0114] 2) Model assembly

[0115] 3) Cutting of concrete protective layer

[0116] 4) Define the material properties of the cross section

[0117] 5) Mesh generation

[0118] 6) Define interactions

[0119] 7) Set boundary conditions

[0120] Model checks (including model integrity and correctness checks, calculation input file checks, and estimated calculation resource checks) are performed. Based on the above, random batch modeling of material models and component models is completed, including modeling of the randomness of concrete materials and their coupling with construction errors. At the same time, modeling of other non-homogeneous materials and influencing factors can also be performed.

[0121] S3, Batch Solving and Post-processing

[0122] In one embodiment of this invention, the model is solved using the Abaqus platform, and the results are extracted in batches. Yield point calculation is taken as an example.

[0123] 1) After the model is solved, extract the skeleton curves in batches;

[0124] 2) Calculate the total energy, taking the energy equivalence method as an example;

[0125]

[0126] Where δ is the displacement and P(δ) is the corresponding load.

[0127] 3) Determine the equivalent energy point, assumed to be δ. y P y Then we have:

[0128]

[0129] Through iteration, E total =E ideal δ can then be obtained y P y .

[0130] 4) For δ y P y Calculate the sample mean and standard deviation;

[0131] Sample mean

[0132]

[0133] Sample standard deviation S:

[0134]

[0135] 5) Determine the confidence level and obtain the quantiles;

[0136] With a 95% guarantee rate of α = 0.05, the critical value of the standard normal distribution with 0.5α is 0.5α = 0.025, corresponding to Z0. 0.025 ≈1.96.

[0137] 6) The confidence interval is calculated as follows:

[0138]

[0139] The confidence intervals for the randomly simulated feature points are shown in Table 2. Figure 9 and Figure 10 The results of some random simulation analysis are presented and automatically analyzed. The confidence intervals of random simulation feature points are evaluated with a 95% guarantee rate, and the correspondence between each feature point is given. This method more accurately shows the stochastic mechanical characteristics of the model.

[0140] Table 2

[0141] Yield displacement (0.84，1.09) (0.75，1.48) Yield load (0.82，1.12) (0.78，1.23) Peak displacement (0.47，1.15) (0.66，1.58) Peak load (0.81，1.09) (0.83，1.11) Limit Displacement (0.66，1.18) (0.63，1.19) Ultimate load (0.80，1.09) (0.82，1.11) Ductility (0.72，1.20) (0.52，1.15)

[0142] In one example of the present invention, such as Figure 11 As shown, this demonstrates the characteristics of the random development of compressive damage in concrete materials, and the results can be used to better track the development path of major damage.

[0143] S4, Machine Learning Model

[0144] In one example of this invention, the machine learning model is established as follows. Using the random samples established in S1 as input and the random simulation results obtained in S3 as output, a data-driven prediction model is established based on the PRRM-EPR (Polynomial Ridge Regularized Model with Engineering Parameter Regression) algorithm to effectively handle the nonlinear relationship between input features and response variables. Furthermore, regularization is used to control the complexity of the model and avoid overfitting. Specifically, as follows.

[0145] 1) Polynomial feature extension

[0146] The input features of the quadratic transform are X = [X1, X2, ..., X...] n ] is the characteristic matrix

[0147]

[0148] 2) Standardization

[0149] For the expanded characteristic matrix Standardized processing.

[0150] 3) Regression Analysis

[0151] By constraining the regression coefficients using L2 regularization, the objective function J(β) is:

[0152]

[0153] In the formula, m is the sample size, and y i and For the true value and the predicted value, β j Let be the regression coefficient of the j-th feature, and α be the regularization parameter.

[0154] 4) Prediction Model

[0155]

[0156] In one example of the present invention, such as Figure 12 As shown, this paper presents an example of using random structural samples as input and employing the prediction model provided in this invention to predict the stochastic mechanical response of a structure, providing guidance for the probabilistic seismic design of structures.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A stochastic simulation method considering dimensional deviations and the variability of concrete materials, characterized in that: The method includes: S1: Random Field Sample Establishment: Before conducting random simulation, material performance tests are carried out, and the cross-sectional dimensions and steel bar spacing of the components are measured and statistically analyzed. Random factor control parameters are defined, and the dimension of the random field matrix is ​​determined. Based on the measured data, the Gaussian Mixture Model (GMM) algorithm is used to optimize the Sobol sequence point selection strategy to generate the random field matrix. The random sample covariance matrix U and the Frobenius threshold under a 95% guarantee rate are calculated to determine the random field samples. S2: Stochastic Model Establishment: Define component modeling parameters and material modeling parameters, complete the establishment of a nonlinear material model based on the established random samples, and combine with the finite element analysis platform to realize the task of establishing a stochastic model of materials and components; S3: Batch Solving and Post-processing: The model is solved using the finite element platform, and the results are processed. Load-displacement curves, stiffness degradation curves, cumulative hysteresis energy dissipation curves and damage morphology cloud maps are extracted in batches. Yield points, peak points, limit points, ductility are calculated and confidence intervals are given. S4: Machine Learning Model: The S3 random simulation results are used as the output, and the S1 random field samples are used as the input. The PRRM-EPR algorithm is used to train the machine learning model and establish a prediction model. The prediction model directly predicts the mechanical response of the component, including displacement, load, stress and strain, through measured random parameters.

2. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 1, characterized in that: In S1, when the test is carried out in conjunction with the test, concrete test blocks are simultaneously retained for material performance testing, and the dimensions of the component and the spacing of the reinforcing bars are measured. When the test is carried out independently, the rebound test is carried out in accordance with the "Technical Specification for Testing the Compressive Strength of Concrete by Rebound Method" to obtain the strength distribution of the research object, and the construction error is measured simultaneously. The cross-sections for measuring the construction error shall be no less than 5, the cross-sections shall be evenly divided along the length of the component, and the measurement shall be carried out using a measuring instrument with a resolution of not less than 0.001 mm.

3. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 1, characterized in that: In S1, the number of samples for material performance testing of concrete test blocks shall not be less than 5.

4. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 2, characterized in that: The rebound test shall be conducted in no less than 5 sample intervals, with no less than 16 samples in each group.

5. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 1, characterized in that: In S1, based on the GMM algorithm to capture the complex structure and correlation of the data, the Sobol sequence is added as random noise to the samples generated by the GMM algorithm to establish random samples, so as to further increase the diversity and coverage of the samples.

6. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 1, characterized in that: In step S1, a covariance matrix of cross-sectional dimension parameters and rebar spacing is established, and a covariance matrix of concrete material mechanical performance parameters is established. Based on the covariance matrix, the Frobenius threshold with a 95% guarantee rate is calculated. This threshold is used as the secondary screening basis for the random sample generation by optimizing the Sobol sequence selection strategy in the GMM algorithm in step S1, so as to improve the sample quality.

7. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 1, characterized in that: In step S2, component model establishment is carried out, the number of model sample points is defined, including the number of cross sections and the number of steel bars, and random modeling of component cross section dimensions and steel bar spacing is carried out.

8. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 1, characterized in that: In S2, a nonlinear material model is randomly established, including concrete and steel reinforcement; for the concrete plastic damage model, random modeling is performed, and the model is modeled by control parameters: elastic modulus and peak strain, axial compressive strength and descending trend. In S2, based on the modeling methods of each finite element platform, the random samples generated in S1 are used to replace the deterministic modeling parameters of materials and components, and the tasks of model assembly, boundary condition setting and mesh generation are performed to realize the establishment of a random model.

9. The stochastic simulation method considering dimensional deviations and concrete material variability according to claim 1, characterized in that: In S4, the input of the machine learning model is the random sample established in S1, and the output is the mechanical response obtained in S3, that is, the random mechanical response of the component is directly predicted through the measured random parameters.

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