Numerical model parameter optimization method for full-curve mechanical response of concrete
By introducing a solution efficiency optimization objective into the concrete phase field model and optimizing parameters piecewise, the problems of complexity and insufficient accuracy in parameter tuning in existing technologies are solved, and efficient numerical simulation of the full-curve mechanical response of concrete is realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-22
- Publication Date
- 2026-03-24
AI Technical Summary
Existing concrete phase field models suffer from insufficient complexity and scientific rigor during parameter tuning, making it difficult to balance computational accuracy and efficiency, thus affecting the scalability and engineering applicability of numerical simulations.
Based on the fitting accuracy index, the solution efficiency is introduced as the optimization objective. A regression model is constructed by combining the piecewise model accuracy and the solution efficiency. The parameters of the concrete fracture phase field model are optimized step by step. Numerical simulation is carried out by cubic spline interpolation and orthogonal experimental design methods. The computational efficiency is improved by combining the finite element method and optimization algorithms.
It achieves improved computational efficiency within a given accuracy range, provides a systematic optimization method for the full-curve mechanical response of concrete, improves the balance between model accuracy and efficiency, and is suitable for refined analysis of concrete fracture behavior.
Smart Images
Figure CN121723554A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of phase field model solving parameter optimization calibration, more particularly to a numerical model parameter optimization method for concrete full curve mechanical response. BACKGROUND
[0002] The damage and fracture behavior of concrete structures is one of the most common and highly dangerous diseases in its whole life cycle, and deeply revealing the cross-scale damage and fracture mechanism has always been a research hotspot in the field of engineering mechanics. In recent years, various phase field models have been successfully applied to the damage and failure simulation of concrete members under static, dynamic and multi-field coupling conditions. However, there are a large number of undetermined parameters in the debugging process of the model, these model calculation parameters lack strict and objective physical meaning, and are difficult to determine through the experimental process, and are often estimated based on experience or gradually adjusted through the "trial and error method", which not only increases the complexity of parameter calibration, but also makes it difficult to ensure the scientificity and accuracy of the selection.
[0003] In order to overcome the limitations of existing models and methods in parameter debugging, more and more researches have begun to focus on introducing advanced optimization algorithms to systematically optimize the parameters in concrete physical tests, but these methods are mostly based on single indicators such as ultimate strength, and in the parameter optimization process, they generally focus on improving the calculation accuracy, but often ignore the balance and coordination between calculation efficiency and accuracy, which directly affects the scalability and engineering applicability of numerical simulation. Therefore, how to provide a numerical model parameter optimization method for concrete full curve mechanical response is a problem that needs to be solved by the person skilled in the art. SUMMARY
[0004] Therefore, the present application provides a numerical model parameter optimization method for concrete full curve mechanical response, which further introduces the solving efficiency as a new optimization target on the basis of the fitting accuracy index, determines the optimization order in combination with the stress-strain behavior full curve segmented model precision, and realizes the systematic optimization of the concrete fracture phase field model solving parameters layer by layer and target by target.
[0005] In order to achieve the above purpose, the present application provides the following technical scheme: A numerical model parameter optimization method for concrete full curve mechanical response, comprising the following steps: S1, obtaining simulation output results by a phase field model under a given phase field model solving parameter combination, and recording the corresponding solving efficiency at the same time; S2, performing curve fitting and smoothing processing on the simulation output results to obtain a Load-CMOD curve; S3. Divide the Load-CMOD curve into elastic segment, plastic segment and softening segment, and calculate the fitting degree between each group of numerical simulation results and the experimental reference model and the corresponding solution efficiency. S4. Construct a regression model with model accuracy and solution efficiency as target variables and the solution parameters of each model as explanatory variables to obtain approximate functional expressions for the fit and solution efficiency; S5. Optimize the global mechanical response curves step by step according to the size of the fit, and improve the computational efficiency within the given allowable range of model accuracy degradation.
[0006] Optionally, S1 specifically involves: conducting systematic numerical simulation experiments on the phase field model based on different combinations of solution parameters, establishing the required sample data space, obtaining the solution parameter combinations for each group of simulation experiments using orthogonal experimental design methods, constructing a three-point bending concrete phase field cohesive crack model at the microscale based on the solution parameter combinations, and simultaneously solving the three-point bending concrete phase field cohesive crack model using the finite element method.
[0007] Optionally, S2 uses cubic spline interpolation to perform curve fitting and smoothing on the simulation output results.
[0008] Optionally, in S3, the goodness of fit between the numerical simulation results and the experimental reference model is calculated as follows: ; ; In the formula, For the goodness of fit, The multiple correlation coefficient is the coefficient between the numerical simulation results and the experimental reference model. , and These represent the simulation output value, the experimental output value, and the average value, respectively.
[0009] Optionally, the solution efficiency in S3 is calculated as follows: ; In the formula, To solve for efficiency, The solution time for the simulation experiment, This is the minimum solution time for the simulation experiment. This represents the maximum solution time for the simulation experiment.
[0010] Optionally, S4 specifically involves: simultaneously constructing an ANOVA regression model using the fit and solution efficiency of each segment as target variables and the model solution parameters as explanatory variables; identifying factors and higher-order terms that contribute limitedly to the response variable; and then employing a stepwise simplification strategy, removing only the least significant term in each iteration; refitting and testing the ANOVA regression model until all retained terms reach a significant level, thereby obtaining an approximate functional relationship between the fit and solution efficiency.
[0011] Optionally, S5 specifically involves: determining the optimization solution order based on the size of the goodness of fit, and solving the problem with the goal of maximizing both the goodness of fit and solution efficiency. For each segment, the goodness of fit is first optimized. Let the optimal solution obtained by the simulation optimization algorithm be... The corresponding goodness-of-fit value is Introducing allowable reduction parameters The lower bound of the fit constraint is defined as always present in the subsequent optimization process of the corresponding segment. While ensuring the goodness of fit is not lower than Under the premise of further optimizing the search to find the parameter solution with the highest solution efficiency, the goodness of fit and solution efficiency corresponding to the end of this segment optimization are recorded.
[0012] Optional constraints for optimization include: Previous stage fit value Must be greater than or equal to the constraint value ; Discrete neighborhood constraints : ; In the formula, The neighborhood of the previous solution, the current solution The transfer can only be made to the two nearest discrete points in the previous solution set; if there is a solution in the previous solution set... At the maximum value or minimum value If a location is defined, its neighborhood contains only one adjacent discrete point.
[0013] As can be seen from the above technical solution, compared with the prior art, the present invention provides a numerical model parameter optimization method for the full-curve mechanical response of concrete, which has the following beneficial effects: 1. In the modeling process, this invention expands the optimization process from being solely focused on accuracy to emphasizing both accuracy and efficiency, thereby achieving a significant improvement in computational efficiency within the given allowable range of model accuracy degradation; 2. This invention addresses the full-curve mechanical response process of concrete and optimizes the solution parameters of the concrete fracture phase field model hierarchically and objectively based on the fitting accuracy of each stage. 3. This invention can address the multi-objective high-dimensional optimization problem caused by the reliance on empirical estimation or trial-and-error calibration of parameters in concrete fracture phase field models. It proposes a multi-objective optimization framework that balances model accuracy and computational efficiency through hierarchical segmented optimization, achieving full-curve system optimization of concrete stress-strain behavior with equal emphasis on accuracy and efficiency. This provides a theoretical basis for refined analysis and revelation of concrete fracture behavior. Attached Figure Description
[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0015] Figure 1 This is a flowchart of the numerical model parameter optimization method for the full-curve mechanical response of concrete according to the present invention. Figure 2 This is a graph of the mechanical response curve after cubic spline interpolation fitting processing according to the present invention. Figure 3 This is a comparison chart of the accuracy of each segment model under different combinations of the present invention; Figure 4 This is a flowchart of the optimization solution process of the present invention; Figure 5 The above are the global mechanical response curves of the model obtained from the optimization solutions of the genetic algorithm at each stage in this embodiment of the invention. Figure 5 (a) is the global mechanical response curve of the plastic segment model. Figure 5 (b) is the global mechanical response curve of the elastic segment model. Figure 5 (c) is the global mechanical response curve of the softened section model. Detailed Implementation
[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0017] This invention discloses a method for optimizing the parameters of a numerical model for the full-curve mechanical response of concrete, such as... Figure 1 As shown, it includes the following steps: S1. Under a given combination of phase-field model solution parameters, obtain the simulation output results through the phase-field model and record the corresponding solution efficiency at the same time; S2. Perform curve fitting and smoothing on the simulation output results to obtain the Load-CMOD curve; S3. Divide the Load-CMOD curve into elastic segment, plastic segment and softening segment, and calculate the fitting degree between each group of numerical simulation results and the experimental reference model and the corresponding solution efficiency. S4. Construct a regression model with model accuracy and solution efficiency as target variables and the solution parameters of each model as explanatory variables to obtain approximate functional expressions for the fit and solution efficiency; S5. Optimize the global mechanical response curves step by step according to the size of the fit, and improve the computational efficiency within the given allowable range of model accuracy degradation.
[0018] Furthermore, S1 specifically involves: conducting systematic numerical simulation experiments on the phase field model based on different combinations of solution parameters, establishing the required sample data space, obtaining the solution parameter combinations for each group of simulation experiments using orthogonal experimental design methods, constructing a three-point bending concrete phase field cohesive crack model at the microscale based on the solution parameter combinations, and simultaneously solving the three-point bending concrete phase field cohesive crack model using the finite element method.
[0019] Furthermore, since experimental data is typically obtained in the form of finite discrete points, and the output points of the numerical simulation results do not perfectly correspond to the experimental measurement points in terms of location, direct comparison will lead to accuracy deviations. Therefore, S2 employs cubic spline interpolation to perform curve fitting and smoothing on the simulation output results. The processed results are as follows: Figure 2 As shown.
[0020] In this embodiment, the test measurement point is set as follows: The numerical simulation results are By constructing in each adjacent interval cubic polynomial And it satisfies the following conditions for continuous function values, continuous first derivative, and continuous second derivative: ; This forms the overall cubic spline function. This allows for the acquisition of smooth and highly accurate simulated data values at the corresponding locations of the test measurement points.
[0021] The accuracy comparison results of each segment model under different combinations are as follows: Figure 3As shown, it can be clearly seen that among the three predetermined segments, the difference in model accuracy between the various combinations in the plastic segment is the greatest, followed by the elastic segment. This indicates that the model accuracy of the plastic and elastic segments depends more on the parameter settings, and their optimization has a more direct and significant effect on improving the overall accuracy. Therefore, these two segments should be prioritized in the parameter optimization process.
[0022] Furthermore, the specific steps in S3 to calculate the goodness of fit between the numerical simulation results and the experimental reference model are as follows: ; ; In the formula, For the goodness of fit, The multiple correlation coefficient is the coefficient between the numerical simulation results and the experimental reference model. , and These represent the simulation output value, the experimental output value, and the average value, respectively.
[0023] Given that the inherent material and structural parameters of the simulation model are determined, the error between the simulation model and the experimental reference model can be considered as arising solely from the solution parameters. This causes the parameter to be solved. with goodness of fit The functional relationship model is as follows: .
[0024] Furthermore, the solution efficiency is calculated in S3 as follows: ; In the formula, To solve for efficiency, The solution time for the simulation experiment, This is the minimum solution time for the simulation experiment. This represents the maximum solution time for the simulation experiment.
[0025] Furthermore, S4 specifically involves: simultaneously constructing an ANOVA regression model using the fit and solution efficiency of each segment as target variables and the model solution parameters as explanatory variables; identifying factors and higher-order terms that contribute limitedly to the response variable; and then employing a stepwise simplification strategy, removing only the least significant term in each iteration; refitting and testing the ANOVA regression model until all retained terms reach a significant level, thereby obtaining an approximate functional relationship between the fit and solution efficiency.
[0026] To fully reflect the key roles of each stage while ensuring overall consistency, a hierarchical optimization framework is constructed. Its core objective is to globally optimize the multi-stage physical fit function, while also considering computational efficiency. The framework's logical starting point is that multi-stage processes often involve coupling relationships at different levels. Without overall constraints and fine-tuning of each stage, the results may not only deviate from true physical laws but also limit the model's applicability due to excessive computational load. Therefore, a dual optimization mechanism is introduced based on a unified functional expression: on the one hand, by searching for the optimal solution, the response level of the fit function at each stage is improved, thus ensuring physical rationality; on the other hand, computational efficiency is embedded as an auxiliary objective in the optimization process to avoid over-reliance on high-cost computations. Specifically, four optimal explanatory variables need to be determined based on the aforementioned functional relationship expression. Each variable is searched within a given value space using an optimization algorithm. The direct goal of optimization is to maximize the fit value and solution efficiency, achieving a balance between accuracy and efficiency at the global level, thereby improving the reliability and generalization of the overall simulation.
[0027] Furthermore, such as Figure 4 As shown, S5 specifically involves: considering that the impact of changes in the model's explanatory variables on different stages varies in the sample data space, the optimization solution order is determined by sorting the data according to the goodness of fit. The goal is to maximize both the goodness of fit and the solution efficiency. For each segment, the goodness of fit is optimized first. Let the optimal solution obtained by the simulation optimization algorithm be... The corresponding goodness-of-fit value is Introducing allowable reduction parameters In this embodiment, The value is 5%, defined as the lower bound of the fit constraint that always exists in the subsequent optimization process of the corresponding segment. While ensuring the goodness of fit is not lower than Under the premise of further optimizing the search to find the parameter solution with the highest solution efficiency, the goodness of fit and solution efficiency corresponding to the end of this segment optimization are recorded.
[0028] Furthermore, the constraints for optimizing the solution include: Previous stage fit value Must be greater than or equal to the constraint value ; Discrete neighborhood constraints : ; In the formula, The neighborhood of the previous solution, the current solution The transfer can only be made to the two nearest discrete points in the previous solution set; if there is a solution in the previous solution set... At the maximum value or minimum value If a location is defined, its neighborhood contains only one adjacent discrete point.
[0029] In one embodiment of the present invention, the solution parameters of the three-point bending concrete phase field model are optimized, and the final output of a set of three-point bending concrete beam fracture tests with relatively small specimen sizes is selected. As a reference value for the simulation model, the final simulation output obtained based on this is: The corresponding simulation model parameters are All of them are discrete parameters, with a value range of [missing information]. The specific parameter to be solved is the time step. Tolerance Cell grid size The ratio of cell grid size to length scale parameter Therefore, it is necessary to construct an optimized solution framework based on experimental results to determine the solution parameters of the simulation model within a given range; Based on the orthogonal experimental design method, 25 representative combinations of solution parameters were obtained. A three-point bending concrete phase field cohesive crack model (PF-CZM) at the microscale was constructed according to the obtained combination of solution parameters, and the model was solved using the finite element method. The global Load-CMOD curve is divided into an elastic segment (points 1–7), a plastic segment (points 8–14), and a softening segment (points 15–28). The fit between each set of numerical simulation results and the experimental reference model, as well as the corresponding solution efficiency, are calculated. Using model accuracy and computational efficiency as target variables and the solution parameters of each model as explanatory variables, a regression model is constructed to obtain approximate functional expressions for the goodness of fit and solution efficiency: ; Based on the optimization framework proposed in this embodiment, existing optimization algorithms are used to solve the problem. The optimization results are shown in Tables 1-3 and 3-4. Figure 5 As shown, Table 1 and Figure 5 (a) shows the optimization results of the genetic algorithm, as shown in Table 2 and Figure 5 (b) shows the optimization results of the particle swarm optimization algorithm, as shown in Table 3 and Figure 5 (c) shows the optimization result of the ant colony algorithm. Table 1. Optimization results of the genetic algorithm
[0030] Table 2 Optimization results of particle swarm optimization algorithm
[0031] Table 3 Optimization results of ant colony algorithm
[0032] Combining the optimization results of genetic algorithm, particle swarm optimization and ant colony optimization shown in Table 1-3, it can be seen that although the optimization strategies are different, the optimal solutions obtained at different stages are highly consistent and the difference in their values is small. This indicates that the constructed hierarchical optimization framework exhibits good stability and robustness in the distribution of solutions and achieves the maximum improvement in computational efficiency within the given range of allowable decrease in model accuracy.
[0033] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0034] Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for optimizing parameters of a numerical model for the full-curve mechanical response of concrete, characterized in that, Includes the following steps: S1. Under a given combination of phase-field model solution parameters, obtain the simulation output results through the phase-field model and record the corresponding solution efficiency at the same time; S2. Perform curve fitting and smoothing on the simulation output results to obtain the Load-CMOD curve; S3. Divide the Load-CMOD curve into elastic segment, plastic segment and softening segment, and calculate the fitting degree between each group of numerical simulation results and the experimental reference model and the corresponding solution efficiency. S4. Construct a regression model with model accuracy and solution efficiency as target variables and the solution parameters of each model as explanatory variables to obtain approximate functional expressions for the fit and solution efficiency; S5. Optimize the global mechanical response curves step by step according to the size of the fit, and improve the computational efficiency within the given allowable range of model accuracy degradation.
2. The numerical model parameter optimization method for the full-curve mechanical response of concrete according to claim 1, characterized in that, S1 specifically involves: conducting systematic numerical simulation experiments on the phase field model based on different combinations of solution parameters, establishing the required sample data space, obtaining the solution parameter combinations for each group of simulation experiments using orthogonal experimental design methods, constructing a three-point bending concrete phase field cohesive crack model at the microscale based on the solution parameter combinations, and simultaneously solving the three-point bending concrete phase field cohesive crack model using the finite element method.
3. The numerical model parameter optimization method for the full-curve mechanical response of concrete according to claim 1, characterized in that, S2 uses cubic spline interpolation to perform curve fitting and smoothing on the simulation output results.
4. The numerical model parameter optimization method for the full-curve mechanical response of concrete according to claim 1, characterized in that, The specific steps for calculating the goodness of fit between the numerical simulation results and the experimental reference model in S3 are as follows: ； ； In the formula, For the goodness of fit, The multiple correlation coefficient is the coefficient between the numerical simulation results and the experimental reference model. , and These represent the simulation output value, the experimental output value, and the average value, respectively.
5. The numerical model parameter optimization method for the full-curve mechanical response of concrete according to claim 1, characterized in that, The specific calculation efficiency in S3 is as follows: ； In the formula, To solve for efficiency, The solution time for the simulation experiment, This is the minimum solution time for the simulation experiment. This represents the maximum solution time for the simulation experiment.
6. The numerical model parameter optimization method for the full-curve mechanical response of concrete according to claim 1, characterized in that, S4 specifically involves constructing an ANOVA regression model using the fit and solution efficiency of each segment as target variables and the model solution parameters as explanatory variables. Factors and higher-order terms that contribute limitedly to the response variable are identified. Based on this, a stepwise simplification strategy is adopted, removing only the least significant term in each iteration. The ANOVA regression model is then refitted and tested until all retained terms reach a significant level, resulting in an approximate functional relationship between the fit and solution efficiency.
7. The numerical model parameter optimization method for the full-curve mechanical response of concrete according to claim 1, characterized in that, S5 specifically involves: determining the optimization solution order based on the size of the goodness of fit, and performing the solution with the goal of maximizing both the goodness of fit and solution efficiency. For each segment, the goodness of fit is optimized first. Let the optimal solution obtained by the simulation optimization algorithm be... The corresponding goodness-of-fit value is Introducing allowable reduction parameters The lower bound of the fit constraint is defined as always present in the subsequent optimization process of the corresponding segment. While ensuring the goodness of fit is not lower than Under the premise of further optimizing the search to find the parameter solution with the highest solution efficiency, the goodness of fit and solution efficiency corresponding to the end of this segment optimization are recorded.
8. The numerical model parameter optimization method for the full-curve mechanical response of concrete according to claim 7, characterized in that, The constraints for optimization include: Previous stage fit value Must be greater than or equal to the constraint value ; Discrete neighborhood constraints : ； In the formula, The neighborhood of the previous solution, the current solution The transfer can only be made to the two nearest discrete points in the previous solution set; if there is a solution in the previous solution set... At the maximum value or minimum value If a location is defined, its neighborhood contains only one adjacent discrete point.