A method and system for multiphase composition isothermal curve parameter calibration of a cement-based material

Abstract

The present application relates to the technical field of cement-based materials, and discloses a method and system for calibrating isothermal line parameters of a cement-based material, which constructs a phase superposition isothermal line model according to experimental data and hydration product phase data of various modified cements, wherein the isothermal line model parameters of each hydration product phase are taken as to-be-optimized parameters; based on the phase superposition isothermal line model, the fitting goodness of each modified cement is calculated according to the experimental data of each modified cement; a multi-objective optimization problem is established according to the fitting goodness of each modified cement, and the adaptive weight of each modified cement is calculated; based on a preset multi-objective optimization solving algorithm, a solving operation corresponding to the multi-objective optimization problem is performed to generate a Pareto optimal solution set; and the optimal trade-off solution is determined from the Pareto optimal solution set through the adaptive weight, so as to calibrate the isothermal line model parameters of each hydration product phase, which can improve the parameter fitting precision and parameter stability, thereby improving the parameter calibration accuracy.

Description

Technical Field

[0001] This invention relates to the field of cement-based materials technology, and in particular to a method and system for calibrating the parameters of multiphase combined isotherms of cement-based materials. Background Technology

[0002] Currently, the service life assessment of cement-based materials under chloride salt corrosion environments mainly relies on accurate chloride ion binding isotherm models. In practice, due to the diverse nature of cement hydration products (which mainly include Calcium Silicate Hydrate gel, monosulfate phase, and Hydrotalcite, i.e., CSH phase, AFm phase, and HT phase, where CSH phase can also be written as CSH phase), these products have different chloride ion binding mechanisms. The CSH phase is mainly physically adsorbed, while the AFm and HT phases are mainly chemically bound. Furthermore, the HT phase has different adsorption forms due to the diversity of adsorption sites. Therefore, when establishing a total binding isotherm model, it is necessary to distinguish the contribution of each hydration product phase and assign different isotherm model forms to them. Moreover, the existing multiphase isotherm model parameter calibration methods for various modified cement-based materials (such as pure cement PC, FA with fly ash, SL with slag, etc.) usually adopt the global least squares regression method (which can be simply referred to as the global regression method).

[0003] However, practice has shown that existing model parameter calibration methods based on global regression often only pursue the minimum total error across all data points when fitting parameters, neglecting the differences between different modified cements in terms of data volume, noise characteristics, and model fit. This results in the following technical drawbacks: First, when the data volume for one modified cement is much larger than that for other modified cements (research data for pure cement PC is usually much larger than that for other modified cements), the final calibration parameters will be biased towards the modified cement with the larger data volume, easily leading to lower prediction accuracy for other modified cements, i.e., "fitting imbalance"; Second, the global regression method... In terms of noise characteristics and model fit, simply reducing the sum of squared residuals is often insufficient. Low-noise modified cement, due to its small residual fluctuations, easily achieves a low RMSE (root mean square error). However, high-noise modified cement or modified cement with poor model fit suffers from higher RMSE because the sum of squared residuals is easily masked during fitting, resulting in ineffective control of single-point residuals, uneven fitting accuracy, and poor parameter stability. This forces parameter optimization to shift towards low-noise modified cement, leading to a lower fitting quality score for high-noise modified cement, making it difficult to form effective constraints, and ultimately resulting in lower accuracy of model parameter calibration. Therefore, proposing a technical solution that can improve parameter fitting accuracy and parameter stability, thereby improving parameter calibration accuracy, is particularly important for multiphase combined isotherm models with various modified cements. Summary of the Invention This invention provides a method and system for calibrating the parameters of multiphase combined isotherms of cement-based materials, which can improve the parameter fitting accuracy and parameter stability, thereby improving the accuracy of parameter calibration.

[0004] To address the aforementioned technical problems, the first aspect of this invention discloses a method for calibrating the parameters of multiphase combined isotherms of cement-based materials, the method comprising: Experimental data and hydration product phase data for each of the various modified cements were obtained. The experimental data included the concentration of free chloride ions and the measured amount of bound chloride ions. The hydration product phase data included the mass fraction of various hydration product phases, all of which included CSH phase, AFm phase and HT phase. Based on the experimental data and the hydration product phase data, a phase-separated superimposed isotherm model is constructed, wherein the isotherm model parameters of each hydration product phase included in the phase-separated superimposed isotherm model are used as parameters to be optimized. Based on the phase-separated superimposed isotherm model, the goodness of fit of each modified cement under the parameters to be optimized is calculated according to the experimental data of each modified cement; and a multi-objective optimization problem is established according to the goodness of fit of each modified cement; and the adaptive weight of each modified cement in the multi-objective optimization problem is calculated according to the goodness of fit of each modified cement. Based on the adaptive weights and the preset multi-objective optimization algorithm, the solution operation corresponding to the multi-objective optimization problem is executed to obtain the optimal trade-off solution. Based on the optimal trade-off solution, the isothermal model parameters of each hydration product phase are calibrated.

[0005] As an optional implementation, in a second aspect of the invention, the Pareto optimal solution set includes one or more Pareto optimal solutions; Furthermore, the specific method by which the parameter calibration module determines the optimal trade-off solution from the Pareto optimal solution set through the adaptive weights includes: For each Pareto optimal solution, calculate the weighted Euclidean distance between the Pareto optimal solution and the preset ideal goodness of fit; and select the Pareto optimal solution with the smallest weighted Euclidean distance from all Pareto optimal solutions as the optimal trade-off solution; or... The Pareto optimal solution set is calculated using the entropy weight method to obtain the target objective weight of each Pareto optimal solution. Based on the target objective weight of each Pareto optimal solution, the relative closeness between each Pareto optimal solution and the preset ideal goodness of fit is calculated. The Pareto optimal solution with the largest relative closeness is selected from all Pareto optimal solutions as the optimal trade-off solution.

[0006] A third aspect of this invention discloses another system for calibrating the multiphase combined isotherm parameters of cement-based materials, the system comprising: Memory containing executable program code; A processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the multiphase combination isotherm parameter calibration method for cement-based materials disclosed in the first aspect of the present invention.

[0007] The fourth aspect of the present invention discloses a computer storage medium storing computer instructions, which, when invoked, are used to execute the method for calibrating the multiphase combination isotherm parameters of cement-based materials disclosed in the first aspect of the present invention.

[0008] Compared with the prior art, the embodiments of the present invention have the following beneficial effects: Implementing this invention enables the acquisition of experimental data and hydration product phase data for various modified cements; based on the experimental data and hydration product phase data, a phase-separated superimposed isotherm model is accurately constructed, with the isotherm model parameters serving as the parameters to be optimized; based on the phase-separated superimposed isotherm model, the goodness of fit of each modified cement under the parameters to be optimized is calculated according to the experimental data of each modified cement; and based on the goodness of fit of each modified cement, a multi-objective optimization problem is established; and the adaptive weight of each modified cement in the multi-objective optimization problem is calculated; subsequently, based on the adaptive weight and the preset multi-objective optimization solution algorithm, the solution operation corresponding to the multi-objective optimization problem is executed to obtain the optimal trade-off solution; and based on the optimal trade-off solution, the isotherm model parameters of each hydration product phase are calibrated. Compared with the limitations of existing technologies where the model still uses single-objective global fitting and only performs parameter inversion for a single cement-based material, this invention... This approach models the isotherm calibration problem of multiple modified cements as a multi-objective optimization problem, using the goodness of fit of each modified cement as an independent optimization objective. By combining a multi-objective optimization algorithm and adaptive weights, it overcomes the limitations of single-objective global regression in existing technologies. This not only improves the parameter fitting accuracy and stability of the obtained parameters but also enhances the balance of fitting accuracy among different modified cements, thereby improving the accuracy of parameter calibration. This, in turn, improves the accuracy of the calibrated isotherm model in predicting the amount of bound chloride ions, providing an accurate assessment basis for the service life of modified cements under chloride erosion environments. Furthermore, by constructing a phase-separated superimposed isotherm model, it facilitates the establishment of a shared parameter collaborative identification framework for multiple modified cements, ensuring that the final calibrated parameters are applicable to all types of cements, rather than being optimal only for a single dominant modified cement. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating a method for calibrating the multiphase combined isotherm parameters of a cement-based material, as disclosed in an embodiment of the present invention. Figure 2 This is a flowchart illustrating another method for calibrating the multiphase combination isotherm parameters of cement-based materials disclosed in an embodiment of the present invention. Figure 3 This is a schematic diagram of the structure of a multiphase combined isotherm parameter calibration system for cement-based materials disclosed in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of another cement-based material multiphase combination isotherm parameter calibration system disclosed in an embodiment of the present invention. Detailed Implementation

[0011] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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.

[0012] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this invention are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or end that includes a series of steps or modules is not limited to the listed steps or modules, but may optionally include steps or modules not listed, or may optionally include other steps or modules inherent to these processes, methods, products, or ends.

[0013] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0014] This invention discloses a method and system for calibrating multiphase combined isotherm parameters of cement-based materials. It overcomes the limitations of existing single-objective global regression methods, improving not only the model's parameter fitting accuracy and the stability of the obtained parameters, but also the balance of fitting accuracy among different modified cements. This enhances the accuracy of parameter calibration, thereby improving the accuracy of the calibrated isotherm model in predicting the amount of bound chloride ions. This provides an accurate assessment basis for the service life of modified cements under chloride erosion environments. Furthermore, by constructing a phase-separated superimposed isotherm model, it facilitates the establishment of a shared parameter collaborative identification framework for multiple modified cements, ensuring that the final calibrated parameters are applicable to all types of cements, rather than being optimal only for a single dominant modified cement. Detailed explanations follow.

[0015] Example 1 Please see Figure 1 , Figure 1 This is a schematic flowchart illustrating a method for calibrating multiphase combined isotherm parameters of cement-based materials, as disclosed in an embodiment of the present invention. Figure 1 The described method for calibrating the multiphase combined isotherm parameters of cement-based materials can be applied to a calibration system for multiphase combined isotherm parameters of cement-based materials. This system may include calibration equipment or a calibration server, which may include a cloud server or a local server; this embodiment of the invention does not impose limitations. Figure 1 As shown, the method for calibrating the multiphase combined isotherm parameters of this cement-based material may include the following operations: 101. Obtain experimental data and hydration product phase data for each type of modified cement.

[0016] In this embodiment of the invention, the experimental data includes the free chloride ion concentration and the measured bound chloride ion amount. The hydration product phase data includes the mass fraction of multiple hydration product phases. All hydration product phases include the CSH phase, AFm phase, and HT phase. The measured bound chloride ion amount of each modified cement may further include the measured bound chloride ion amounts of sub-types of the CSH phase, sub-types of the AFm phase, and sub-types of the HT phase within that modified cement. Specifically, experimental data for each modified cement in the multiple modified cements are obtained, including the free chloride ion concentration and the measured bound chloride ion amount; and the mass fractions of the CSH phase, AFm phase, and HT phase in each modified cement are obtained through thermodynamic calculations.

[0017] 102. Based on experimental data and hydration product phase data, construct a phase-separated superimposed isotherm model.

[0018] In this model, the isotherm model parameters of each hydration product phase included in the phase-separated superimposed isotherm model are used as parameters to be optimized. Specifically, these parameters serve as decision variables, which are adjustable variables controlled by the decision-maker or algorithm in optimization problems or mathematical modeling, used to find the optimal solution. The free chloride ion concentration is used as input, the measured bound chloride ion amount as output, and the parameters to be optimized as training targets. Model training is then performed on the phase-separated superimposed isotherm model. The trained model is used to predict the bound chloride ion amount based on the input free chloride ion concentration.

[0019] In this embodiment of the invention, the phase-separated superimposed isotherm model is formed by combining a first isothermal adsorption model for the CSH phase, a second isothermal adsorption model for the AFm phase, and a third isothermal adsorption model for the HT phase. Specifically, a phase-separated superimposed isotherm model is constructed using the mass fraction of each hydration product phase as a weight. This includes the first isothermal adsorption model for the CSH phase, the second isothermal adsorption model for the AFm phase, and the third isothermal adsorption model for the HT phase. For example, a phase-separated superimposed isotherm model is constructed that includes the Langmuir model for the CSH phase, the Freundlich model for the AFm phase, and the two-site Langmuir-Freundlich model for the HT phase (wherein the Langmuir-Freundlich model can be simply referred to as the LF model). Compared to existing technologies that fail to quantify the chloride ion binding capacity of the HT phase and whose simplified formulas assume HT adsorption at a single site and thus cannot adequately describe its true adsorption state, this approach constructs a phase-separated superimposed isotherm model that includes the CSH phase (Langmuir model), AFm phase (Freundlich model), and HT phase (two-site Langmuir-Freundlich model). The introduced two-site Langmuir-Freundlich model more fully characterizes the nonlinear adsorption behavior of multiple modified cement sites on the HT surface through multiple parameters, which is beneficial to improving the goodness of fit of each modified cement.

[0020] 103. Based on the phase-separated superimposed isotherm model, calculate the goodness of fit of each modified cement under the parameters to be optimized based on the experimental data of each modified cement.

[0021] 104. Based on the goodness of fit of each modified cement, establish a multi-objective optimization problem, and calculate the adaptive weight of each modified cement in the multi-objective optimization problem based on the goodness of fit of each modified cement.

[0022] In this embodiment of the invention, the goodness of fit of each modified cement is used as an independent optimization objective to establish a multi-objective optimization problem; single-objective pre-optimization is performed on each modified cement to obtain the maximum goodness of fit of each modified cement, and the adaptive weight of each modified cement in the multi-objective optimization problem is calculated based on the maximum goodness of fit.

[0023] 105. Based on the adaptive weights and the preset multi-objective optimization algorithm, perform the solution operation corresponding to the multi-objective optimization problem to obtain the optimal trade-off solution.

[0024] In this embodiment of the invention, the number of times the solution operation is run is greater than or equal to a preset number. For example, the number of times the solution is run independently is not less than 10. Furthermore, each independent run can use a different random seed or initial population to ensure the independence between each run.

[0025] 106. Based on the optimal trade-off solution, calibrate the isothermal model parameters for each hydration product phase.

[0026] It is evident that implementation Figure 1 The described method for calibrating the multiphase combined isotherm parameters of cement-based materials can acquire experimental data and hydration product phase data of various modified cements. Based on the experimental data and hydration product phase data, a phase-separated superimposed isotherm model is accurately constructed, and the isotherm model parameters are used as the parameters to be optimized. Based on the phase-separated superimposed isotherm model, the goodness of fit of each modified cement under the parameters to be optimized is calculated according to the experimental data of each modified cement. A multi-objective optimization problem is established based on the goodness of fit of each modified cement, and the adaptive weight of each modified cement in the multi-objective optimization problem is calculated. Subsequently, according to the adaptive weight and the preset multi-objective optimization solution algorithm, the solution operation corresponding to the multi-objective optimization problem is executed to obtain the optimal trade-off solution. Then, based on the optimal trade-off solution, the isotherm model parameters of each hydration product phase are calibrated. Compared with the existing technology, which still uses single-objective global fitting and only performs parameter calibration for a single cement-based material, this method offers a superior solution. Overcoming the limitations of numerical inversion, this scheme models the isotherm calibration problem of multiple modified cements as a multi-objective optimization problem, using the goodness of fit of each modified cement as an independent optimization objective. By combining a multi-objective optimization algorithm and adaptive weights, it overcomes the limitations of single-objective global regression in existing technologies. This not only improves the parameter fitting accuracy and stability of the obtained parameters but also enhances the balance of fitting accuracy among different modified cements, thereby improving the accuracy of parameter calibration. This, in turn, improves the accuracy of the calibrated isotherm model in predicting the amount of bound chloride ions, providing an accurate assessment basis for the service life of modified cements under chloride erosion environments. Furthermore, by constructing a phase-separated superimposed isotherm model, it facilitates the establishment of a shared parameter collaborative identification framework for multiple modified cements, ensuring that the final calibrated parameters are applicable to all types of cements, rather than being optimal only for a single dominant modified cement.

[0027] In an optional embodiment, the phase-separated superimposed isotherm model includes: ; The first isothermal adsorption model includes: ; The second isothermal adsorption model includes: ; The third isothermal adsorption model includes: ; in, To predict the amount of bound chloride ions, The concentration of free chloride ions. The type of hydration product phase, For the first Mass fraction of the hydration product phase. For the first Predicting the amount of bound chloride ions by subclasses of hydrochemical product phases. , , , , , , , , , These are the parameters to be optimized. Predict the amount of bound chloride ions for subclasses of the CSH phase. Predict the amount of bound chloride ions for subclasses of the AFm phase. Predict the amount of bound chloride ions for subclasses of the HT phase. , For the isotherm model parameters of the CSH phase, , The isotherm model parameters for the AFm phase are... , , , , , The isotherm model parameters for the HT phase are shown in Table 1. Each isotherm model parameter, its associated hydration product phase, its corresponding model, and its physical meaning are also shown in Table 1.

[0028] In this invention, all parameters of the isotherm model are non-negative real numbers. Compared to the shortcomings of traditional word regression parameters which lack clear physical meaning, this invention ensures the physical rationality of the calibration results from multiple levels: the mass fraction of each hydration product phase is calculated using GEMS thermodynamic software (GEMS is short for CemGEMS, a professional thermodynamic simulation tool focused on the cement field), ensuring that the contribution ratio of each phase in the total binding amount conforms to the actual distribution of hydration products; parameter boundary constraints restrict the optimization search to a physically meaningful parameter subspace; and the mechanistic correspondence of the HT dual-site model (site 1 corresponds to interlayer chemical bonding, site 2 corresponds to surface physical adsorption) gives the parameters clear physicochemical connotations, which is conducive to providing a systematic solution for the calibration of chloride ion curing model parameters of cement-based materials that combines accuracy, fairness, verifiability, and physical rationality.

[0029] As can be seen, this optional embodiment can more accurately quantitatively characterize the chloride ion binding capacity of each hydration product phase by constructing a phase-separated superimposed isotherm model including the CSH phase (Langmuir model), AFm phase (Freundlich model), and HT phase (two-site Langmuir-Freundlich model). This is beneficial for distinguishing the contribution of each hydration product phase and assigning corresponding isotherm model parameters to them, thereby improving the accuracy of establishing the phase-separated superimposed isotherm model. In turn, it is beneficial for improving the accuracy of subsequent prediction of the amount of bound chloride ions through an accurate isotherm model.

[0030] In another optional embodiment, step 103 above, based on the phase-separated superimposed isotherm model, calculates the goodness of fit of each modified cement under the parameters to be optimized based on the experimental data of each modified cement, including: For each type of modified cement, the free chloride ion concentration of the modified cement is input into the phase-separated superimposed isotherm model for prediction, and the predicted bound chloride ion content of the modified cement under the parameters to be optimized is obtained. Based on the predicted bound chloride ion content of the modified cement and the measured bound chloride ion content of the modified cement, calculate the sum of squared residuals of the modified cement under the parameters to be optimized. Based on the measured bound chloride ion content of the modified cement and the calculated measured average value, the total sum of squares of deviations of the modified cement under the parameters to be optimized is calculated. The measured average value is the average of the measured bound chloride ion content of all modified cements. The goodness of fit of the modified cement under the parameters to be optimized is calculated based on the sum of squared residuals of the modified cement under the parameters to be optimized and the sum of squared total deviations of the modified cement under the parameters to be optimized.

[0031] In this embodiment of the invention, specifically, for each type of modified cement, the difference between the predicted bound chloride ion content and the measured bound chloride ion content of the modified cement is calculated to obtain the residual sum of squares of the modified cement, denoted as SS. res Calculate the dispersion of the measured bound chloride ion content of the modified cement relative to the measured average value, and obtain the total sum of squares of deviations of the modified cement, denoted as SS. tot Then, based on the residual sum of squares and the total sum of squares of deviations of the modified cement, the goodness of fit of the modified cement is calculated. The formula for calculating the goodness of fit is as follows: R 2 =1-SS res / SS tot .

[0032] In this embodiment of the invention, optionally, a NaN (Not a Number) defense mechanism is added during the optimization process. This NaN defense mechanism utilizes the characteristic that NaN is not equal to itself and a dedicated detection function to construct a numerical security defense line from input verification and calculation monitoring to anomaly blocking, preventing the silent propagation of invalid values ​​that could lead to system crashes or logical errors. Specifically, it detects whether the predicted bound chloride ion content of each modified cement obtained through the phase-separated superposition isotherm model contains a NaN value. If a NaN value is detected, the goodness of fit of the modified cement is assigned a very small value, equivalent to assigning a penalty value much larger than the normal range to the corresponding objective function value, to prevent illegal solutions from entering the non-dominated solution set. If no NaN value is detected in the predicted bound chloride ion content of the modified cement, the above-mentioned process of calculating the residual sum of squares, total deviation sum of squares, and goodness of fit is triggered.

[0033] This invention provides Example 1, which specifically includes: selecting chloride ion binding experimental data of three different modified cements (e.g., PC, FA, SL), using the method of this invention to calibrate multiphase isotherm parameters, and verifying the convergence consistency of the solutions obtained by three different paradigm multi-objective algorithms in terms of fitting effect. Example 1 includes steps S1-S4, as follows: S1: Collect chloride ion binding data for various cements, including free chloride ion concentration and measured bound chloride ion amount, with 20 data points for each sample; and obtain the mass fractions of CSH phase, AFm phase and HT phase in each cement sample by calculation using GEMS thermodynamic software (e.g., PC based on the embedded MPK model, FA and SL based on the embedded 5PL model). S2: Construct phase-separated superimposed isotherm models. The CSH phase adopts the Langmuir model, the AFm phase adopts the Freundlich model, and the HT phase adopts the two-site Langmuir-Freundlich model. There are a total of 10 decision variables, all of which have values ​​≥0. S3: Perform single-objective pre-optimization for each modified cement. A genetic algorithm (population 300, iterations 400) is used to maximize the R-value of each modified cement. 2 To achieve the goal, obtain the upper limit of independent fitting R. 2 max Based on this, the adaptive weights of each modified cement in multi-objective decision-making are calculated; S4: The same multi-objective problem is solved independently by three different paradigms of multi-objective evolutionary algorithms: G-MOGA-WI, MOPSO, and MOEA / D. The three algorithms represent dominant, swarm intelligence, and decomposition search mechanisms, respectively. Each algorithm runs independently to obtain the Pareto optimal set, and the optimal solution is selected by weighted ideal point distance.

[0034] The traditional single-objective global regression method, denoted as the comparative example, uses the same cement data and phase-separated superimposed isotherm model as in Example 1 above. However, it uses the traditional single-objective global regression method to aggregate all modified cement data into the same residual sum of squares function for single-objective minimization. To conduct a fair and robust comparison, the single-objective global regression method in the comparative example is also run independently 10 times, and the average value of each indicator is calculated. The comparison with Example 1 of this invention is shown in Table 2.

[0035] Among them, R 2 The larger the better, the smaller the RMSE the better.

[0036] Furthermore, this embodiment of the invention provides Example 2 to verify the improvement effect of using the two-site Langmuir-Freundlich model for the HT phase compared with the traditional simplified model. Example 2 specifically includes: replacing the HT model in Example 1 with the common single-site Langmuir model and single-site Freundlich model, respectively, while keeping the conditions of the CSH model and AFm model unchanged, and using G-MOGA-WI for solving. The comparison results between Example 2 and Example 1 are shown in Table 3:

[0037] Among them, R 2 MIN The minimum goodness of fit is 1.

[0038] As can be seen, this optional embodiment can input the free chloride ion concentration of each modified cement into the phase-separated superimposed isotherm model for prediction, obtaining the predicted bound chloride ion content of the modified cement under the parameters to be optimized; and calculate the residual sum of squares of the modified cement under the parameters to be optimized based on the predicted bound chloride ion content and the measured bound chloride ion content of the modified cement; calculate the total deviation sum of squares of the modified cement under the parameters to be optimized based on the measured bound chloride ion content and the calculated measured average value, where the measured average value is the average of the measured bound chloride ion content of all modified cements; and calculate the goodness of fit of the modified cement under the parameters to be optimized based on the residual sum of squares and the total deviation sum of squares of the modified cement under the parameters to be optimized. This can improve the accuracy and reliability of calculating the residual sum of squares and the total deviation sum of squares of each modified cement, thereby improving the accuracy and reliability of calculating the goodness of fit of each modified cement, which is beneficial to improving the accuracy and reliability of subsequently establishing a multi-objective optimization problem and calculating adaptive weights.

[0039] In another optional embodiment, step 104 above, calculating the adaptive weight of each modified cement in the multi-objective optimization problem based on the goodness of fit of each modified cement, includes: For each type of modified cement, the goal is to maximize the goodness of fit of the modified cement. This is achieved by performing single-objective pre-optimization on the parameters to be optimized, thus obtaining the maximum goodness of fit of the modified cement. Based on the maximum goodness of fit of the modified cement, calculate the adaptive weight of the modified cement in the multi-objective optimization problem; The formula for calculating the adaptive weights is as follows: ; in, For the first Adaptive weights for modified cement, For the first The maximum goodness of fit of the modified cement. This represents the total amount of modified cement. less than or equal to Positive integers.

[0040] In this embodiment of the invention, the core of the adaptive weighting mechanism lies in the maximum goodness of fit, also known as the upper limit of independent fit, which reflects the fit potential and noise level of each modified cement data. The weights constructed using this value can automatically suppress the excessive influence of high-noise modified cement on the final solution, while amplifying the influence of high-quality modified cement. Thus, by using the adaptive weighting mechanism based on the upper limit of independent fit of each modified cement, the influence weight of high-quality, high-model-fit modified cement in decision-making is automatically increased, while the interference of high-noise, low-fit modified cement on the final solution is reduced. Furthermore, the adaptive weights enable modified cement with high fit potential to have a greater influence in subsequent Pareto (i.e., Pareto optimal solution set) frontier decisions, ensuring that the final parameters prioritize the fitting accuracy of high-quality modified cement. Through the weighting mechanism of the adaptive weights, when the amount of data for a certain modified cement is much greater than that of other modified cements, the excessive influence of this dominant modified cement can be automatically suppressed, thereby improving the fit of the worst modified cement from an extremely low level in traditional methods to an acceptable range close to that of the best modified cement, achieving a balance in fitting accuracy among modified cements.

[0041] This invention provides Example 3, which quantifies the contribution of the adaptive weighting mechanism for the upper limit of independent fitting to the fitting balance. Example 3 specifically includes: using the data from Example 1, two weighting schemes are set for comparison: Scheme A is the adaptive weighting scheme of this invention, and Scheme B is the scheme with equal weights. Both schemes use G-MOGA-WI for multi-objective optimization, and the results are shown in Table 4.

[0042] In Scheme A, the adaptive weights of each modified cement (PC, FA, SL) are 0.3034, 0.3643, and 0.3323, respectively; in Scheme B, the weight of each modified cement is 0.3333. As shown in Table 4, the goodness of fit obtained by Scheme A is greater than that obtained by Scheme B, and the minimum goodness of fit obtained by Scheme A is greater than that obtained by Scheme B. Therefore, the scheme with adaptive weights in this invention is superior to the existing scheme with equal weights.

[0043] As can be seen, this optional embodiment aims to maximize the goodness of fit of each modified cement. By performing single-objective pre-optimization on the parameters to be optimized, the maximum goodness of fit of the modified cement is obtained. Based on the maximum goodness of fit of the modified cement, the adaptive weight of the modified cement in the multi-objective optimization problem is calculated. Compared with the shortcomings of the prior art, which suffers from "fit imbalance" due to ignoring the differences in data volume, noise characteristics and model adaptability among modified cements, this scheme is based on the adaptive weighting mechanism of the independent fitting upper limit (i.e., the maximum goodness of fit). By independently pre-optimizing each modified cement to obtain its achievable maximum goodness of fit, the weight of each modified cement in the multi-objective optimization problem is constructed. This makes the voice of each modified cement in the final decision dynamically determined by its own fitting potential, rather than by the amount of data or subjective preference.

[0044] Example 2 Please see Figure 2 , Figure 2 This is a schematic flowchart illustrating a method for calibrating multiphase combined isotherm parameters of cement-based materials, as disclosed in an embodiment of the present invention. Figure 2 The described method for calibrating the multiphase combined isotherm parameters of cement-based materials can be applied to a calibration system for multiphase combined isotherm parameters of cement-based materials. This system may include calibration equipment or a calibration server, where the calibration server may be a cloud server or a local server; this embodiment of the invention does not impose limitations. Figure 2 As shown, the method for calibrating the multiphase combined isotherm parameters of this cement-based material may include the following operations: 201. Obtain experimental data and hydration product phase data for each type of modified cement.

[0045] 202. Based on experimental data and hydration product phase data, construct a phase-separated superimposed isotherm model.

[0046] 203. Based on the phase-separated superimposed isotherm model, calculate the goodness of fit of each modified cement under the parameters to be optimized based on the experimental data of each modified cement.

[0047] 204. Based on the goodness of fit of each modified cement, establish a multi-objective optimization problem, and calculate the adaptive weight of each modified cement in the multi-objective optimization problem based on the goodness of fit of each modified cement.

[0048] 205. Solve the multi-objective optimization problem according to the preset multi-objective optimization algorithm to generate a Pareto optimal solution set.

[0049] In this embodiment of the invention, the Pareto optimal solution set includes one or more Pareto optimal solutions.

[0050] 206. Based on the adaptive weights, determine the optimal trade-off solution from the Pareto optimal solution set.

[0051] 207. Based on the optimal trade-off solution, calibrate the isothermal model parameters for each hydration product phase.

[0052] In this embodiment of the invention, specifically, each independent run solves the above-mentioned multi-objective optimization problem to obtain a recommended combination of parameter values ​​(i.e., Pareto optimal solution) for the parameters to be optimized. Each recommended combination of parameter values ​​includes recommended values ​​for the isotherm model parameters of each hydration product phase. For the recommended combination of parameter values ​​obtained from each independent run, a final recommended parameter combination and its confidence interval are obtained through statistical central trend extraction, which serves as the optimal trade-off solution. Based on the final recommended parameter combination and confidence interval, the isotherm model parameters of each hydration product phase are calibrated. Statistical central trend extraction may include: calculating the median, kernel density estimation peak (i.e., KDE peak), first quantile, and second quantile of each recommended parameter combination, and using the median or kernel density estimation peak as the final recommended parameter combination, and the numerical range between the first quantile and the second quantile as the confidence interval of the final recommended parameter combination. Optionally, the first quantile can be the 25th quantile, and the second quantile can be the 75th quantile, in which case the 25%~75% quantile is used as the confidence interval.

[0053] It should be noted that, due to the randomness of multi-objective optimization algorithms, the optimal solution obtained in a single run may drift along the isosurface in the parameter space. To address this issue of parameter non-uniqueness, this embodiment of the invention obtains a robust final recommended parameter combination by running the algorithm independently multiple times and using statistical central trend extraction.

[0054] This invention provides Example 4, which demonstrates the process of overcoming parameter non-uniqueness and obtaining a high-probability stable recommended value through multiple independent repeated runs and statistical central trend extraction. Example 4 specifically includes: using the G-MOGA-WI algorithm from Example 1, running it independently 10 times; wherein, in each run, the pre-optimization step and the multi-objective optimization step use different random initializations to ensure complete independence between runs; and recording the 10 parameter vectors corresponding to the optimal solution obtained in each run; it can be seen that the probability density distribution of each parameter exhibits a clear unimodal shape, indicating that the algorithm can stably converge to a high-probability parameter region in the search space; then, the median, KDE peak, 25th percentile, and 75th percentile are calculated for all 10 parameters, and the results are shown in Table 5.

[0055] Among them, the medians of each parameter are very close to the peak values ​​of the KDE, indicating good symmetry in parameter distribution; the 25% to 75% quantile interval provides the confidence range of the parameters, and the width of this interval is very narrow compared to the parameter value range, indicating that the optimal solutions from multiple runs are clustered in a compact region; using the median of this set as the final recommended parameter, the corresponding R values ​​for various modified cements such as PC, FA, and SL are... 2 The values ​​were 0.95, 0.84, and 0.90 respectively, with an average R0. 2 The result is 0.90, which is highly consistent with the results of each run. As shown in Example 4, by repeatedly running the algorithm independently and combining it with statistical central trend extraction, this invention can stably output the parameter combination with the highest probability and the most representative characteristics, thus overcoming the problem of parameter non-uniqueness in traditional single regression or single optimization. The extracted median model parameter can be used as a standard recommended value for engineering applications, while the quantile interval provides a direct basis for quantifying the uncertainty of the model parameter. Compared with the shortcomings of the existing global least squares regression method, which directly solves for a unique solution to the model parameter, this invention can solve for multiple sets of recommended values, which is beneficial to improving the stability of the obtained model parameter.

[0056] It should be noted that the above Examples 1 to 4 and comparative examples are only used to illustrate the design concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly, and are not intended to limit the scope of protection of the present invention.

[0057] In this embodiment of the invention, for other descriptions of steps 201-207, please refer to the detailed description of steps 101-106 in Embodiment 1. These descriptions will not be repeated in this embodiment of the invention.

[0058] It is evident that implementation Figure 2The described method for calibrating the multiphase combined isotherm parameters of cement-based materials can acquire experimental data and hydration product phase data of various modified cements. Based on the experimental data and hydration product phase data, a phase-separated superimposed isotherm model is accurately constructed, and the isotherm model parameters are used as the parameters to be optimized. Based on the phase-separated superimposed isotherm model, the goodness of fit of each modified cement under the parameters to be optimized is calculated according to the experimental data of each modified cement. A multi-objective optimization problem is established based on the goodness of fit of each modified cement, and the adaptive weight of each modified cement in the multi-objective optimization problem is calculated. Subsequently, according to the adaptive weight and the preset multi-objective optimization solution algorithm, the solution operation corresponding to the multi-objective optimization problem is executed to obtain the optimal trade-off solution. Then, based on the optimal trade-off solution, the isotherm model parameters of each hydration product phase are calibrated. Compared with the existing technology, which still uses single-objective global fitting and only performs parameter calibration for a single cement-based material, this method offers a superior solution. Overcoming the limitations of numerical inversion, this scheme models the isotherm calibration problem of multiple modified cements as a multi-objective optimization problem, using the goodness of fit of each modified cement as an independent optimization objective. By combining a multi-objective optimization algorithm and adaptive weights, it overcomes the limitations of single-objective global regression in existing technologies. This not only improves the parameter fitting accuracy and stability of the obtained parameters but also enhances the balance of fitting accuracy among different modified cements, thereby improving the accuracy of parameter calibration. This, in turn, improves the accuracy of the calibrated isotherm model in predicting the amount of bound chloride ions, providing an accurate assessment basis for the service life of modified cements under chloride erosion environments. Furthermore, by constructing a phase-separated superimposed isotherm model, it facilitates the establishment of a shared parameter collaborative identification framework for multiple modified cements, ensuring that the final calibrated parameters are applicable to all types of cements, rather than being optimal only for a single dominant modified cement. Furthermore, it can solve multi-objective optimization problems according to a preset multi-objective optimization algorithm to generate a Pareto optimal solution set; and determine the optimal trade-off solution from the Pareto optimal solution set according to adaptive weights. Solving multi-objective optimization problems through a multi-objective optimization algorithm can improve the accuracy of obtaining the Pareto optimal solution set, thereby improving the accuracy of determining the optimal trade-off solution, and further improving the accuracy of calibrating the parameters of the isotherm model.

[0059] In an optional embodiment, the multi-objective optimization solution algorithm includes at least two of the following: a guided multi-objective genetic algorithm based on dominance relations (wherein the guided multi-objective genetic algorithm includes a prior guided multi-objective genetic algorithm and a weighted ideal point decision algorithm, i.e., Guided Multi-Objective Genetic Algorithm with Weighted Ideal Point Decision, abbreviated as G-MOGA-WI), a multi-objective particle swarm optimization algorithm based on swarm intelligence (abbreviated as MOPSO), and a multi-objective evolutionary algorithm based on decomposition (abbreviated as MOEA / D). The present invention does not limit the examples.

[0060] In this optional embodiment, optionally, the multi-objective optimization problem is solved according to a preset multi-objective optimization algorithm to generate a Pareto optimal solution set, including: When the multi-objective optimization solution algorithm includes a guided multi-objective genetic algorithm, the initial parameter solution is obtained by pre-optimizing the parameters to be optimized by calculating the average goodness of fit of all modified cements; based on the initial parameter solution, a guided initial population is generated, and the guided initial population is used as the initial candidate solution set of the multi-objective optimization problem. The initial candidate solution set is optimized to obtain the Pareto candidate solution set of the guided multi-objective genetic algorithm. When the multi-objective optimization algorithm includes a multi-objective particle swarm optimization algorithm, the particle swarm is initialized, and an external archive is established to store non-dominated solutions. Each particle in the swarm has an initial velocity and position, and the position of each particle represents a candidate parameter solution for the multi-objective optimization problem. The external archive is updated based on the objective function vector corresponding to each particle in the multi-objective optimization problem. The objective function vector includes the goodness-of-fit of each modified cement. After each iteration of the multi-objective optimization problem, the congestion distance of the non-dominated solutions stored in the external archive is calculated. The congestion distance is then cleaned to obtain a cleaned congestion distance. The cleaning process can involve setting the distance value to less than a preset threshold. Crowding distance is removed based on a threshold to eliminate non-dominated solutions with small crowding distances. Based on the cleaned crowding distances, a global leader is selected from the external archive to guide the next solution of the multi-objective optimization problem. The current velocity and position of the particles are updated according to the global leader and the historical best position of each particle. The objective function vector corresponding to the multi-objective optimization problem is recalculated according to the updated current position of the particles to update the historical best position and the external archive, thus obtaining the Pareto candidate solution set of the multi-objective particle swarm optimization algorithm. In the first iteration, the historical best position is the initial position of each particle, and in subsequent iterations, the historical best position is the best position experienced by each particle up to the current iteration. When the multi-objective optimization algorithm includes a multi-objective evolutionary algorithm, multiple weight vectors are generated for the multi-objective optimization problem, and neighbor relationships are established based on the distance between each weight vector. Based on the weight vectors, the multi-objective optimization problem is decomposed into multiple sub-problems, and offspring individuals corresponding to the neighbor solutions of each sub-problem are generated. Based on the goodness of fit of each modified cement corresponding to the offspring individuals under the multi-objective optimization problem, the ideal point and neighbor solutions are updated to obtain the Pareto candidate solution set of the multi-objective optimization algorithm. By integrating all Pareto candidate solution sets, we obtain the Pareto optimal solution set.

[0061] In this embodiment of the invention, the specific implementation of G-MOGA-WI is as follows: First, with the average goodness of fit of all modified cements as the objective, a genetic algorithm is used for pre-optimization to obtain a high-quality initial parameter solution; then, a guided initial population is generated with the initial parameter solution as the center, and subsequently injected into the gamultiobj solver (Genetic Algorithm Multiobjective, which is defined as "a solver that uses a genetic algorithm to find the Pareto front of multiple fitness functions") for multi-objective optimization; The specific implementation of MOPSO is as follows: Initialize the particle swarm and establish an external archive; calculate the crowding distance of archive members in the external archive in each generation. Specifically, after each iteration, recalculate the crowding distance of all non-dominated solutions in the archive to prioritize solutions in sparsely distributed regions during the next generation's global leader selection, thereby maintaining the uniformity of the Pareto front; then, based on the cleaned crowding distance, select the global leader using a proportional selection strategy in a custom genetic algorithm; update particle velocities and positions; and update individual optimum and the external archive. By integrating a NaN defense mechanism and a proportional selection strategy in a custom genetic algorithm, this effectively avoids algorithm crashes or search misdirection caused by illegal values ​​in model predictions, thus improving stability and robustness when handling real data.

[0062] The specific implementation of MOEA / D is as follows: generate a uniformly distributed weight vector and establish neighbor relationships; decompose the multi-objective problem into multiple single-objective sub-problems using Chebyshev scalarization; generate offspring through SBX crossover (Simulated Binary Crossover) and polynomial mutation; update the ideal point and neighbor solutions. After calculating the Pareto candidate solution sets for various algorithms, the Pareto candidate solution sets are merged, and the merged candidate solutions are filtered based on non-dominated sorting to generate the Pareto optimal solution set.

[0063] In this embodiment of the invention, in addition to the goodness of fit of each modified cement, the RMSE calculated simultaneously can also be used as an evaluation index during the optimization process. The balancing mechanism of multi-objective optimization can make the RMSE of each modified cement be controlled within an acceptable range at the same time, which is beneficial to reduce the occurrence of extremely uneven fitting accuracy caused by some modified cements having extremely high RMSE (e.g., RMSE>0.05 mmol / g) in the prior art.

[0064] As can be seen, this optional embodiment can solve multi-objective optimization problems using various solution algorithms, obtain Pareto candidate solution sets for each algorithm, and integrate these Pareto candidate solution sets to obtain the Pareto optimal solution set. This diversified solution algorithm improves the accuracy and flexibility of solving multi-objective optimization problems, thereby enhancing the accuracy and flexibility of obtaining Pareto candidate solution sets for various algorithms, and ultimately improving the accuracy of obtaining the Pareto optimal solution set. Furthermore, compared to traditional single-regression methods that cannot assess the reliability of calibration results (e.g., whether the obtained parameters fluctuate significantly due to initial value selection or algorithm randomness, whether the parameters are consistent across different algorithm systems, and the inability to quantify the root mean square error of each modified cement), this approach offers a more comprehensive solution. To address the shortcomings of RMSE (Resolution for Evolutionary Models) such as its balance, this scheme integrates three different paradigms (dominant G-MOGA-WI, swarm intelligence MOPSO, and decompositional MOEA / D) for collaborative solution and cross-validation. The consistency of Pareto solutions obtained from different paradigms helps provide objective criteria for the reliability of subsequent calibration results. Furthermore, by repeatedly running the algorithm independently and extracting statistical central trends (median, kernel density estimation peak, quantiles), the scheme effectively solves the problem of parameter non-uniqueness caused by model parameter compensation effects. This ensures that the output median parameter has the highest probability of occurrence in all independent runs, and provides a quantifiable indicator of parameter reliability through quantile intervals, which helps improve the reproducibility of calibration results.

[0065] In another optional embodiment, step 206 above, which involves determining the optimal trade-off solution from the Pareto optimal solution set using adaptive weights, includes: For each Pareto optimal solution, calculate the weighted Euclidean distance between the Pareto optimal solution and the preset ideal goodness of fit; and select the Pareto optimal solution with the smallest weighted Euclidean distance from all Pareto optimal solutions as the optimal trade-off solution; or... The Pareto optimal solution set is calculated using the entropy weight method to obtain the objective weight of each Pareto optimal solution. Based on the objective weight of each Pareto optimal solution, the relative closeness between each Pareto optimal solution and the preset ideal goodness of fit is calculated. The Pareto optimal solution with the largest relative closeness is selected from all Pareto optimal solutions as the optimal trade-off solution.

[0066] In this embodiment of the invention, the method for selecting the optimal trade-off solution in each independent run is as follows: calculate the solution in the Pareto optimal set to the ideal point (the ideal point is the point where the goodness of fit of each modified cement is 1, i.e., R). 2 The solution with the smallest weighted Euclidean distance (=1) is selected; or, after determining the objective weights of each objective using the entropy weight method on the Pareto optimal set, the solution with the largest relative proximity is selected using the TOPSIS method. The formula for calculating the weighted Euclidean distance is as follows: ; in, For weighted Euclidean distance, For the first The goodness of fit of the modified cement, For the first Adaptive weights for modified cement.

[0067] As can be seen, this optional embodiment can calculate the weighted Euclidean distance between each Pareto optimal solution and a preset ideal goodness of fit; and select the Pareto optimal solution with the smallest weighted Euclidean distance from all Pareto optimal solutions as the optimal trade-off solution, which can improve the accuracy of the weighted Euclidean distance calculation and thus improve the accuracy of the optimal trade-off solution selection; or, the Pareto optimal solution set can be calculated using the entropy weight method to obtain the target objective weight of each Pareto optimal solution, and the relative closeness between each Pareto optimal solution and the preset ideal goodness of fit can be calculated based on the target objective weight of each Pareto optimal solution; and select the Pareto optimal solution with the largest relative closeness from all Pareto optimal solutions as the optimal trade-off solution, which can improve the accuracy of the relative closeness calculation between each Pareto optimal solution and the ideal goodness of fit and thus improve the accuracy of the optimal trade-off solution selection, and the selection of the optimal solution by using weighted Euclidean distance or relative closeness can improve the flexibility and efficiency of the optimal trade-off solution selection.

[0068] Example 3 Please see Figure 3 , Figure 3 This is a schematic diagram of the structure of a multiphase combined isotherm parameter calibration system for cement-based materials disclosed in an embodiment of the present invention. Figure 3 The described calibration system for multiphase combined isotherm parameters of cement-based materials may include calibration equipment or a calibration server, wherein the calibration server may include a cloud server or a local server, and this embodiment of the invention is not limited thereto. Figure 3 As shown, the multiphase combined isotherm parameter calibration system for this cement-based material may include: The data acquisition module 301 is used to acquire experimental data and hydration product phase data for each type of modified cement in various modified cements. The experimental data includes the concentration of free chloride ions and the measured amount of bound chloride ions. The hydration product phase data includes the mass fraction of various hydration product phases, including CSH phase, AFm phase and HT phase.

[0069] The model building module 302 is used to construct a phase-separated superimposed isotherm model based on experimental data and hydration product phase data. The isotherm model parameters of each hydration product phase included in the phase-separated superimposed isotherm model are used as parameters to be optimized.

[0070] The objective optimization module 303 is used to calculate the goodness of fit of each modified cement under the parameters to be optimized based on the experimental data of each modified cement according to the phase-separated superimposed isotherm model; and to establish a multi-objective optimization problem based on the goodness of fit of each modified cement; and to calculate the adaptive weight of each modified cement in the multi-objective optimization problem based on the goodness of fit of each modified cement.

[0071] The parameter calibration module 304 is used to perform the solution operation corresponding to the multi-objective optimization problem according to the adaptive weight and the preset multi-objective optimization solution algorithm, obtain the optimal trade-off solution, and calibrate the isothermal model parameters of each hydration product phase according to the optimal trade-off solution.

[0072] It is evident that implementation Figure 3 The described multiphase combined isotherm parameter calibration system for cement-based materials can acquire experimental data and hydration product phase data of various modified cements. Based on the experimental data and hydration product phase data, it accurately constructs a phase-separated superimposed isotherm model, with the isotherm model parameters serving as the parameters to be optimized. Based on the phase-separated superimposed isotherm model, it calculates the goodness of fit of each modified cement under the parameters to be optimized, using experimental data for each type of modified cement. Then, based on the goodness of fit of each modified cement, it establishes a multi-objective optimization problem and calculates the adaptive weight of each modified cement in the multi-objective optimization problem. Subsequently, based on the adaptive weight and a preset multi-objective optimization solution algorithm, it executes the solution operation corresponding to the multi-objective optimization problem to obtain the optimal trade-off solution. Finally, based on the optimal trade-off solution, it calibrates the isotherm model parameters for each hydration product phase. Compared to existing technologies where the model still uses a single-objective global fitting and only performs parameter calibration for a single cement-based material, this system offers a more comprehensive solution. Overcoming the limitations of numerical inversion, this scheme models the isotherm calibration problem of multiple modified cements as a multi-objective optimization problem, using the goodness of fit of each modified cement as an independent optimization objective. By combining a multi-objective optimization algorithm and adaptive weights, it overcomes the limitations of single-objective global regression in existing technologies. This not only improves the parameter fitting accuracy and stability of the obtained parameters but also enhances the balance of fitting accuracy among different modified cements, thereby improving the accuracy of parameter calibration. This, in turn, improves the accuracy of the calibrated isotherm model in predicting the amount of bound chloride ions, providing an accurate assessment basis for the service life of modified cements under chloride erosion environments. Furthermore, by constructing a phase-separated superimposed isotherm model, it facilitates the establishment of a shared parameter collaborative identification framework for multiple modified cements, ensuring that the final calibrated parameters are applicable to all types of cements, rather than being optimal only for a single dominant modified cement.

[0073] In an optional embodiment, the phase-separated superimposed isotherm model is formed by combining a first isothermal adsorption model for the CSH phase, a second isothermal adsorption model for the AFm phase, and a third isothermal adsorption model for the HT phase; and the phase-separated superimposed isotherm model includes: ; The first isothermal adsorption model includes: ; The second isothermal adsorption model includes: ; The third isothermal adsorption model includes: ; in, To predict the amount of bound chloride ions, The concentration of free chloride ions. The type of hydration product phase, For the first Mass fraction of the hydration product phase. For the first Predicting the amount of bound chloride ions by subclasses of hydrochemical product phases. , , , , , , , , , These are the parameters to be optimized.

[0074] As can be seen, this optional embodiment can more accurately quantitatively characterize the chloride ion binding capacity of each hydration product phase by constructing a phase-separated superimposed isotherm model including the CSH phase (Langmuir model), AFm phase (Freundlich model), and HT phase (two-site Langmuir-Freundlich model). This is beneficial for distinguishing the contribution of each hydration product phase and assigning corresponding isotherm model parameters to them, thereby improving the accuracy of establishing the phase-separated superimposed isotherm model. In turn, it is beneficial for improving the accuracy of subsequent prediction of the amount of bound chloride ions through an accurate isotherm model.

[0075] In another optional embodiment, the target optimization module 303, based on a phase-separated superimposed isotherm model, calculates the goodness of fit of each modified cement under the parameters to be optimized using the experimental data of each modified cement in the following specific ways: For each type of modified cement, the free chloride ion concentration of the modified cement is input into the phase-separated superimposed isotherm model for prediction, and the predicted bound chloride ion content of the modified cement under the parameters to be optimized is obtained. Based on the predicted bound chloride ion content of the modified cement and the measured bound chloride ion content of the modified cement, calculate the sum of squared residuals of the modified cement under the parameters to be optimized. Based on the measured bound chloride ion content of the modified cement and the calculated measured average value, the total sum of squares of deviations of the modified cement under the parameters to be optimized is calculated. The measured average value is the average of the measured bound chloride ion content of all modified cements. The goodness of fit of the modified cement under the parameters to be optimized is calculated based on the sum of squared residuals of the modified cement under the parameters to be optimized and the sum of squared total deviations of the modified cement under the parameters to be optimized.

[0076] As can be seen, this optional embodiment can input the free chloride ion concentration of each modified cement into the phase-separated superimposed isotherm model for prediction, obtaining the predicted bound chloride ion content of the modified cement under the parameters to be optimized; and calculate the residual sum of squares of the modified cement under the parameters to be optimized based on the predicted bound chloride ion content and the measured bound chloride ion content of the modified cement; calculate the total deviation sum of squares of the modified cement under the parameters to be optimized based on the measured bound chloride ion content and the calculated measured average value, where the measured average value is the average of the measured bound chloride ion content of all modified cements; and calculate the goodness of fit of the modified cement under the parameters to be optimized based on the residual sum of squares and the total deviation sum of squares of the modified cement under the parameters to be optimized. This can improve the accuracy and reliability of calculating the residual sum of squares and the total deviation sum of squares of each modified cement, thereby improving the accuracy and reliability of calculating the goodness of fit of each modified cement, which is beneficial to improving the accuracy and reliability of subsequently establishing a multi-objective optimization problem and calculating adaptive weights.

[0077] In yet another optional embodiment, the objective optimization module 303 calculates the adaptive weight of each modified cement in the multi-objective optimization problem based on the goodness of fit of each modified cement in the following specific ways: For each type of modified cement, the goal is to maximize the goodness of fit of the modified cement. This is achieved by performing single-objective pre-optimization on the parameters to be optimized, thus obtaining the maximum goodness of fit of the modified cement. Based on the maximum goodness of fit of the modified cement, calculate the adaptive weight of the modified cement in the multi-objective optimization problem; The formula for calculating the adaptive weights is as follows: ; in, For the first Adaptive weights for modified cement, For the first The maximum goodness of fit of the modified cement. This represents the total amount of modified cement. less than or equal to Positive integers.

[0078] As can be seen, this optional embodiment aims to maximize the goodness of fit of each modified cement. By performing single-objective pre-optimization on the parameters to be optimized, the maximum goodness of fit of the modified cement is obtained. Based on the maximum goodness of fit of the modified cement, the adaptive weight of the modified cement in the multi-objective optimization problem is calculated. Compared with the shortcomings of the prior art, which suffers from "fit imbalance" due to ignoring the differences in data volume, noise characteristics and model adaptability among modified cements, this scheme is based on the adaptive weighting mechanism of the independent fitting upper limit (i.e., the maximum goodness of fit). By independently pre-optimizing each modified cement to obtain its achievable maximum goodness of fit, the weight of each modified cement in the multi-objective optimization problem is constructed. This makes the voice of each modified cement in the final decision dynamically determined by its own fitting potential, rather than by the amount of data or subjective preference.

[0079] In another optional embodiment, the multi-objective optimization solution algorithm includes at least two of the following: a guided multi-objective genetic algorithm based on dominance relations, a multi-objective particle swarm optimization algorithm based on swarm intelligence, and a multi-objective evolutionary algorithm based on decomposition; the number of times the solution operation is run is greater than or equal to a preset number; Furthermore, the parameter calibration module 304 performs the solution operation corresponding to the multi-objective optimization problem according to the adaptive weights and the preset multi-objective optimization solution algorithm, and the specific methods for obtaining the optimal trade-off solution include: The multi-objective optimization problem is solved according to the preset multi-objective optimization algorithm to generate a Pareto optimal solution set; and the optimal trade-off solution is determined from the Pareto optimal solution set according to the adaptive weight.

[0080] As can be seen, this optional embodiment can solve the multi-objective optimization problem according to the preset multi-objective optimization solution algorithm to generate a Pareto optimal solution set; and determine the optimal trade-off solution from the Pareto optimal solution set according to the adaptive weight. Solving the multi-objective optimization problem by using the multi-objective optimization solution algorithm can improve the accuracy of obtaining the Pareto optimal solution set, thereby improving the accuracy of determining the optimal trade-off solution, and further improving the accuracy of calibrating the isotherm model parameters.

[0081] In this optional embodiment, as an optional implementation method, the parameter calibration module 304 solves the multi-objective optimization problem according to a preset multi-objective optimization algorithm to generate a Pareto optimal solution set in the following specific ways: When the multi-objective optimization solution algorithm includes a guided multi-objective genetic algorithm, the initial parameter solution is obtained by pre-optimizing the parameters to be optimized by calculating the average goodness of fit of all modified cements; based on the initial parameter solution, a guided initial population is generated, and the guided initial population is used as the initial candidate solution set of the multi-objective optimization problem. The initial candidate solution set is optimized to obtain the Pareto candidate solution set of the guided multi-objective genetic algorithm. When the multi-objective optimization algorithm includes a multi-objective particle swarm optimization algorithm, the particle swarm is initialized, and an external archive is established to store non-dominated solutions. The position of each particle in the swarm represents a candidate parameter solution for the multi-objective optimization problem. The external archive is updated based on the objective function vector corresponding to each particle in the multi-objective optimization problem. The objective function vector includes the goodness-of-fit of each modified cement. After each iteration of the multi-objective optimization problem, the crowding distance of the non-dominated solutions stored in the external archive is calculated and cleaned to obtain a cleaned crowding distance. Based on the cleaned crowding distance, a global guide is selected from the external archive to guide the next iteration of the multi-objective optimization problem. The current velocity and position of the particles are updated based on the global guide and the historical best positions of each particle. The objective function vector corresponding to the multi-objective optimization problem is recalculated based on the updated particle positions to update the historical best positions and the external archive, thus obtaining the Pareto candidate solution set of the multi-objective particle swarm optimization algorithm. When the multi-objective optimization algorithm includes a multi-objective evolutionary algorithm, multiple weight vectors are generated for the multi-objective optimization problem, and neighbor relationships are established based on the distance between each weight vector. Based on the weight vectors, the multi-objective optimization problem is decomposed into multiple sub-problems, and offspring individuals corresponding to the neighbor solutions of each sub-problem are generated. Based on the goodness of fit of each modified cement corresponding to the offspring individuals under the multi-objective optimization problem, the ideal point and neighbor solutions are updated to obtain the Pareto candidate solution set of the multi-objective optimization algorithm. By integrating all Pareto candidate solution sets, we obtain the Pareto optimal solution set.

[0082] As can be seen, this optional implementation method can solve multi-objective optimization problems using various solution algorithms, obtain Pareto candidate solution sets for each algorithm, and integrate these Pareto candidate solution sets to obtain the Pareto optimal solution set. This diversified approach improves the accuracy and flexibility of solving multi-objective optimization problems, thereby enhancing the accuracy and flexibility of obtaining Pareto candidate solution sets and ultimately improving the accuracy of obtaining the Pareto optimal solution set. Furthermore, compared to traditional single-regression methods, which cannot assess the reliability of calibration results (e.g., whether the obtained parameters fluctuate significantly due to initial value selection or algorithm randomness, whether the parameters are consistent across different algorithm systems, and cannot quantify the root mean square error of each modified cement), this method offers a more comprehensive solution. To address the shortcomings of RMSE (Resolution for Evolutionary Models) such as its balance, this scheme integrates three different paradigms (dominant G-MOGA-WI, swarm intelligence MOPSO, and decompositional MOEA / D) for collaborative solution and cross-validation. The consistency of Pareto solutions obtained from different paradigms helps provide objective criteria for the reliability of subsequent calibration results. Furthermore, by repeatedly running the algorithm independently and extracting statistical central trends (median, kernel density estimation peak, quantiles), the scheme effectively solves the problem of parameter non-uniqueness caused by model parameter compensation effects. This ensures that the output median parameter has the highest probability of occurrence in all independent runs, and provides a quantifiable indicator of parameter reliability through quantile intervals, which helps improve the reproducibility of calibration results.

[0083] In yet another optional embodiment, the Pareto optimal solution set includes one or more Pareto optimal solutions. Furthermore, the parameter calibration module 304 determines the optimal trade-off solution from the Pareto optimal solution set using adaptive weights in the following specific manner: For each Pareto optimal solution, calculate the weighted Euclidean distance between the Pareto optimal solution and the preset ideal goodness of fit; and select the Pareto optimal solution with the smallest weighted Euclidean distance from all Pareto optimal solutions as the optimal trade-off solution; or... The Pareto optimal solution set is calculated using the entropy weight method to obtain the objective weight of each Pareto optimal solution. Based on the objective weight of each Pareto optimal solution, the relative closeness between each Pareto optimal solution and the preset ideal goodness of fit is calculated. The Pareto optimal solution with the largest relative closeness is selected from all Pareto optimal solutions as the optimal trade-off solution.

[0084] As can be seen, this optional embodiment can calculate the weighted Euclidean distance between each Pareto optimal solution and a preset ideal goodness of fit; and select the Pareto optimal solution with the smallest weighted Euclidean distance from all Pareto optimal solutions as the optimal trade-off solution, which can improve the accuracy of the weighted Euclidean distance calculation and thus improve the accuracy of the optimal trade-off solution selection; or, the Pareto optimal solution set can be calculated using the entropy weight method to obtain the target objective weight of each Pareto optimal solution, and the relative closeness between each Pareto optimal solution and the preset ideal goodness of fit can be calculated based on the target objective weight of each Pareto optimal solution; and select the Pareto optimal solution with the largest relative closeness from all Pareto optimal solutions as the optimal trade-off solution, which can improve the accuracy of the relative closeness calculation between each Pareto optimal solution and the ideal goodness of fit and thus improve the accuracy of the optimal trade-off solution selection, and the selection of the optimal solution by using weighted Euclidean distance or relative closeness can improve the flexibility and efficiency of the optimal trade-off solution selection.

[0085] Example 4 Please see Figure 4 , Figure 4 This is a schematic diagram of another multiphase combined isotherm parameter calibration system for cement-based materials disclosed in an embodiment of the present invention. Figure 4 As shown, the multiphase combined isotherm parameter calibration system for this cement-based material may include: Memory 401 storing executable program code; Processor 402 coupled to memory 401; The processor 402 calls the executable program code stored in the memory 401 to execute the steps in the method for calibrating the multiphase combination isotherm parameters of cement-based materials as described in Embodiment 1 or Embodiment 2 of the present invention.

[0086] Example 5 This invention discloses a computer storage medium storing computer instructions. When these computer instructions are invoked, they are used to execute the steps in the method for calibrating the multiphase combined isotherm parameters of cement-based materials as described in Embodiment 1 or Embodiment 2 of this invention.

[0087] Example 6 This invention discloses a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program, and the computer program is operable to cause a computer to perform the steps in the method for calibrating the multiphase combined isotherm parameters of cement-based materials described in Embodiment 1 or Embodiment 2.

[0088] The system embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0089] Through the detailed description of the above embodiments, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, including read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically-Erasable Programmable Read-Only Memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, disk storage, magnetic tape storage, or any other computer-readable medium that can be used to carry or store data.

[0090] Finally, it should be noted that the multiphase combination isotherm parameter calibration method and system for cement-based materials disclosed in the embodiments of the present invention are merely preferred embodiments of the present invention, and are only used to illustrate the technical solutions of the present invention, not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of multiphase combined isotherm parameter calibration of a cementitious material, characterized by, The method includes: Experimental data and hydration product phase data for each of the various modified cements were obtained. The experimental data included the concentration of free chloride ions and the measured amount of bound chloride ions. The hydration product phase data included the mass fraction of various hydration product phases, all of which included CSH phase, AFm phase and HT phase. Based on the experimental data and the hydration product phase data, a phase-separated superimposed isotherm model is constructed, wherein the isotherm model parameters of each hydration product phase included in the phase-separated superimposed isotherm model are used as parameters to be optimized. Based on the phase-separated superimposed isotherm model, the goodness of fit of each modified cement under the parameters to be optimized is calculated according to the experimental data of each modified cement; and a multi-objective optimization problem is established according to the goodness of fit of each modified cement; and the adaptive weight of each modified cement in the multi-objective optimization problem is calculated according to the goodness of fit of each modified cement. Based on the adaptive weights and the preset multi-objective optimization algorithm, the solution operation corresponding to the multi-objective optimization problem is executed to obtain the optimal trade-off solution. Based on the optimal trade-off solution, the isothermal model parameters of each hydration product phase are calibrated.

2. The method for calibrating the multiphase combined isotherm parameters of cement-based materials according to claim 1, characterized in that, The phase-separated superimposed isotherm model is formed by combining the first isothermal adsorption model of the CSH phase, the second isothermal adsorption model of the AFm phase, and the third isothermal adsorption model of the HT phase; and the phase-separated superimposed isotherm model includes: ； The first isothermal adsorption model includes: ； The second isothermal adsorption model includes: ； The third isothermal adsorption model includes: ； in, To predict the amount of bound chloride ions, The concentration of free chloride ions. The type of the hydration product phase, For the first Mass fraction of the hydration product phase. For the first Predicting the amount of bound chloride ions by subclasses of hydrochemical product phases. , , , , , , , , , These are the parameters to be optimized.

3. The method for calibrating the multiphase combined isotherm parameters of cement-based materials according to claim 2, characterized in that, Based on the phase-separated superimposed isotherm model, and according to the experimental data of each modified cement, the goodness of fit of each modified cement under the parameters to be optimized is calculated, including: For each type of modified cement, the free chloride ion concentration of the modified cement is input into the phase-separated superimposed isotherm model for prediction, and the predicted bound chloride ion content of the modified cement under the parameters to be optimized is obtained. Based on the predicted bound chloride ion content of the modified cement and the measured bound chloride ion content of the modified cement, calculate the sum of squared residuals of the modified cement under the parameters to be optimized. Based on the measured amount of bound chloride ions in the modified cement and the calculated average value, the total sum of squares of deviations of the modified cement under the parameters to be optimized is calculated, where the average value is the average of the measured amount of bound chloride ions in all the modified cements. The goodness of fit of the modified cement under the parameters to be optimized is calculated based on the sum of squared residuals of the modified cement under the parameters to be optimized and the sum of squared total deviations of the modified cement under the parameters to be optimized.

4. The method for calibrating the multiphase combined isotherm parameters of cement-based materials according to claim 3, characterized in that, The step of calculating the adaptive weight of each modified cement in the multi-objective optimization problem based on the goodness of fit of each modified cement includes: For each type of modified cement, with the goal of maximizing the goodness of fit of the modified cement, the maximum goodness of fit of the modified cement is obtained by performing single-objective pre-optimization on the parameters to be optimized. Based on the maximum goodness of fit of the modified cement, the adaptive weight of the modified cement in the multi-objective optimization problem is calculated. The formula for calculating the adaptive weight is as follows: ； in, For the first Adaptive weights for modified cement, For the first The maximum goodness of fit of the modified cement. This represents the total amount of modified cement. less than or equal to Positive integers.

5. The method for calibrating the multiphase combined isotherm parameters of cement-based materials according to any one of claims 1-4, characterized in that, The multi-objective optimization solution algorithm includes at least two of the following: a guided multi-objective genetic algorithm based on dominance relations, a multi-objective particle swarm optimization algorithm based on swarm intelligence, and a multi-objective evolutionary algorithm based on decomposition; the number of times the solution operation is run is greater than or equal to a preset number; And, the step of performing the solution operation corresponding to the multi-objective optimization problem according to the adaptive weights and the preset multi-objective optimization solution algorithm to obtain the optimal trade-off solution includes: The multi-objective optimization problem is solved according to a preset multi-objective optimization algorithm to generate a Pareto optimal solution set; And based on the adaptive weights, the optimal trade-off solution is determined from the Pareto optimal solution set.

6. The method for calibrating the multiphase combined isotherm parameters of cement-based materials according to claim 5, characterized in that, The step of solving the multi-objective optimization problem according to a preset multi-objective optimization algorithm to generate a Pareto optimal solution set includes: When the multi-objective optimization solution algorithm includes the guided multi-objective genetic algorithm, the parameters to be optimized are pre-optimized by calculating the average goodness of fit of all the modified cements to obtain the initial parameter solution; based on the initial parameter solution, a guided initial population is generated, and the guided initial population is used as the initial candidate solution set of the multi-objective optimization problem. The initial candidate solution set is optimized to obtain the Pareto candidate solution set of the guided multi-objective genetic algorithm. When the multi-objective optimization algorithm includes the multi-objective particle swarm optimization algorithm, the particle swarm is initialized, and an external archive for storing non-dominated solutions is established, wherein the position of each particle in the particle swarm represents a candidate parameter solution of the multi-objective optimization problem; the external archive is updated according to the objective function vector corresponding to each particle under the multi-objective optimization problem, the objective function vector including the goodness of fit of each modified cement; after each iteration of the multi-objective optimization problem, the crowding distance of the non-dominated solutions stored in the external archive is calculated, and the crowding distance is cleaned to obtain a cleaned crowding distance; based on the cleaned crowding distance, a global guide is selected from the external archive to guide the next solution of the multi-objective optimization problem; the current velocity and current position of the particles are updated according to the global guide and the historical best position of each particle, and the objective function vector corresponding to the multi-objective optimization problem is recalculated according to the updated current position of the particles to update the historical best position and the external archive, thereby obtaining the Pareto candidate solution set of the multi-objective particle swarm optimization algorithm; When the multi-objective optimization algorithm includes the multi-objective evolutionary algorithm, multiple weight vectors of the multi-objective optimization problem are generated, and neighbor relationships are established based on the distance between each weight vector; based on the weight vectors, the multi-objective optimization problem is decomposed into multiple objective sub-problems, and offspring individuals corresponding to the neighbor solutions of each objective sub-problem are generated; based on the goodness of fit of each modified cement corresponding to the offspring individuals under the multi-objective optimization problem, the ideal point and neighbor solutions are updated to obtain the Pareto candidate solution set of the multi-objective optimization algorithm; By integrating all the Pareto candidate solution sets, the Pareto optimal solution set is obtained.

7. The method for calibrating the multiphase combined isotherm parameters of cement-based materials according to claim 6, characterized in that, The Pareto optimal solution set includes one or more Pareto optimal solutions; And, determining the optimal trade-off solution from the Pareto optimal solution set using the adaptive weights includes: For each Pareto optimal solution, calculate the weighted Euclidean distance between the Pareto optimal solution and the preset ideal goodness of fit; And from all the Pareto optimal solutions, select the one with the smallest weighted Euclidean distance as the optimal trade-off solution; or... The Pareto optimal solution set is calculated using the entropy weight method to obtain the target objective weight of each Pareto optimal solution. Based on the target objective weight of each Pareto optimal solution, the relative closeness between each Pareto optimal solution and the preset ideal goodness of fit is calculated. The Pareto optimal solution with the largest relative closeness is selected from all Pareto optimal solutions as the optimal trade-off solution.

8. A calibration system for multiphase combined isotherm parameters of cement-based materials, characterized in that, The system includes: The data acquisition module is used to acquire experimental data and hydration product phase data for each of the various modified cements. The experimental data includes the concentration of free chloride ions and the measured amount of bound chloride ions. The hydration product phase data includes the mass fraction of various hydration product phases, and all the hydration product phases include CSH phase, AFm phase and HT phase. The model building module is used to construct a phase-separated superimposed isotherm model based on the experimental data and the hydration product phase data, wherein the isotherm model parameters of each hydration product phase included in the phase-separated superimposed isotherm model are used as parameters to be optimized. The objective optimization module is used to calculate the goodness of fit of each modified cement under the parameters to be optimized based on the phase-separated superimposed isotherm model and the experimental data of each modified cement; and to establish a multi-objective optimization problem based on the goodness of fit of each modified cement; and to calculate the adaptive weight of each modified cement in the multi-objective optimization problem based on the goodness of fit of each modified cement. The parameter calibration module is used to perform the solution operation corresponding to the multi-objective optimization problem according to the adaptive weight and the preset multi-objective optimization solution algorithm, to obtain the optimal trade-off solution, and to calibrate the isothermal model parameters of each of the hydration product phases according to the optimal trade-off solution.

9. A calibration system for multiphase combined isotherm parameters of cement-based materials, characterized in that, The system includes: Memory containing executable program code; A processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the multiphase combination isotherm parameter calibration method for cement-based materials as described in any one of claims 1-7.

10. A computer storage medium, characterized in that, The computer storage medium stores computer instructions, which, when invoked, are used to execute the method for calibrating the multiphase combined isotherm parameters of cement-based materials as described in any one of claims 1-7.

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