Cementitious material mix proportion reverse design method based on physical constraint machine learning

Abstract

This invention relates to the field of intelligent mix design technology for cement-based materials, and particularly to a reverse design method for cement-based material mix proportions based on physical constraint machine learning. The method includes: acquiring target service performance parameters; determining initial weights using a combination of the analytic hierarchy process (AHP) and entropy weighting method according to the engineering scenario; determining the mix proportion variable vector and setting physical boundary constraints and cost constraints; establishing a combined prediction model including master prediction and residual correction, and applying physical monotonicity constraints to the master prediction part; constructing a satisfaction evaluation system with nonlinear deviation penalties, weighting to form a comprehensive optimization objective, and outputting candidate mix proportions through multi-objective optimization; experimentally verifying the candidate mix proportions, updating the weights and residual correction model based on measured deviations, and iterating until the termination condition is met to output the final mix proportion scheme. This invention can achieve multi-performance collaborative optimization while ensuring the physical rationality of the prediction.

Description

Technical Field

[0001] This invention relates to the field of intelligent mix design technology for cement-based materials, and in particular to a reverse design method for mix proportions of cement-based materials based on physical constraint machine learning. Background Technology

[0002] In recent years, machine learning methods have begun to be introduced into the field of cement-based material performance prediction, showing potential in areas such as concrete compressive strength prediction and mix design optimization. Some studies have used neural networks, ensemble learning, and other methods to establish the mapping relationship between mix design parameters and performance, and combined them with evolutionary algorithms such as NSGA-II for multi-objective optimization. However, existing methods still suffer from the following shortcomings when applied to the reverse design of mix proportions for high-toughness cement-based composite materials: current mix proportion design for high-toughness cement-based materials mainly relies on manual trial mixing, which is time-consuming and inefficient; existing methods mostly optimize single indicators such as strength or flowability, making it difficult to consider the synergistic requirements of multiple properties such as strength, toughness, flowability, and durability; weight allocation mostly relies on manual setting, lacks data support, and cannot adapt to the differences in failure modes in different engineering scenarios; purely data-driven models are prone to producing prediction results that violate physical laws, and existing methods mostly only screen the results after prediction, failing to fundamentally solve the problem from the model training level; penalty functions are mostly linear, which cannot reflect the non-linear growth characteristics of engineering risks when performance deviates from the target value; existing optimizations are mostly one-time outputs, lacking weight correction and model update mechanisms based on experimental and measured data, making it difficult for optimization results to converge automatically and resulting in insufficient reliability in implementation. Summary of the Invention

[0003] To overcome the above shortcomings, this invention provides a reverse design method for cement-based material mix proportions based on physical constraint machine learning. It aims to improve the problems in the existing technology, such as the lack of scenario-specific weight allocation, insufficient multi-performance collaborative optimization, the prediction model's tendency to violate physical laws, the penalty mechanism's neglect of nonlinear engineering risks, and the lack of experimental closed-loop feedback in the optimization results.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A reverse design method for cement-based material mix proportions based on physical constraint machine learning includes:

[0006] Obtain the target service performance parameters of the cement-based material to be designed, and determine the initial weight vector of each performance index by adopting a subjective and objective weighting method according to the engineering application scenario.

[0007] Based on the target service performance parameters, determine the vector of mix proportion variables that affect material properties, and set physical boundary constraints and cost constraints for each mix proportion variable;

[0008] Based on the aforementioned mix proportion variables and measured performance dataset, a combined prediction model including a main prediction component and a residual correction component is established, and a monotonicity constraint based on the physical correlation direction is applied to the main prediction component.

[0009] Based on the output of the combined prediction model, a satisfaction evaluation system with nonlinear deviation penalty is constructed. The satisfaction levels are weighted by the current weights to form a comprehensive optimization objective. Multi-objective optimization is performed under the physical boundary constraints and cost constraints to output candidate mix ratios.

[0010] The candidate mix proportions are experimentally verified. The current weight vector and the residual correction part are updated according to the measured deviation. The optimization solution and experimental verification are repeated until the termination condition is met, and the final mix proportion scheme is output.

[0011] Furthermore, the aforementioned subjective and objective combined empowerment method specifically includes:

[0012] The analytic hierarchy process (AHP) is used to calculate the subjective weights of each performance index based on the failure modes of the engineering application scenario.

[0013] The entropy weight method is used to calculate the objective weights of each performance index based on historical performance data;

[0014] The subjective weights and objective weights are linearly combined to obtain the initial weight vector.

[0015] Furthermore, the establishment of the combined prediction model, which includes a main prediction component and a residual correction component, specifically includes:

[0016] Using the aforementioned mix ratio variable as input and the aforementioned performance index as output, the master prediction part is trained based on the aforementioned measured performance dataset to establish an initial mapping relationship, and a monotonicity constraint based on the physical correlation direction is applied to the master prediction part.

[0017] Calculate the prediction residual of the main prediction part, and train the residual correction part based on the prediction residual;

[0018] The output of the main prediction part is linearly superimposed with the correction result of the residual correction part, and this superposition is used as the output of the combined prediction model.

[0019] Furthermore, applying a monotonicity constraint based on the physical correlation direction to the main prediction component specifically includes:

[0020] At each node split in the main prediction part, the trend of the predicted value change of the left and right child nodes in the dimension of the constraint variable is calculated;

[0021] If the preset monotonic direction is violated, a penalty term is added to the loss function of the current iteration to force the model to split in a direction that conforms to the monotonic direction.

[0022] Furthermore, the preset monotonic directions include at least the following: compressive strength decreases monotonically with the water-cement ratio, chloride ion diffusion coefficient increases monotonically with the water-cement ratio, ultimate tensile strain increases monotonically with fiber volume fraction, and flowability decreases monotonically with fiber volume fraction and increases monotonically with water-reducing agent dosage.

[0023] Furthermore, the steps for constructing a satisfaction evaluation system with nonlinear deviation penalty include:

[0024] Based on the optimization direction type of each performance indicator, a satisfaction function for each performance indicator is constructed respectively;

[0025] Construct a comprehensive penalty function that includes at least a variable out-of-bounds penalty term, a performance deviation penalty term, and a cost out-of-bounds penalty term;

[0026] For performance indicators with interval optimality characteristics, a nonlinear exponential penalty function is used to penalize predicted values ​​that deviate from the target range;

[0027] The satisfaction evaluation system is composed of the satisfaction function and the comprehensive penalty function.

[0028] Furthermore, the cost over-limit penalty is constructed based on material costs; the material costs are determined by a weighted sum of the unit price and usage of each raw material; the cost over-limit penalty is the squared penalty when the material costs exceed a preset upper limit.

[0029] Furthermore, the steps for solving the multi-objective optimization problem include:

[0030] The satisfaction levels are weighted and summed using the current weights, and then combined with the comprehensive penalty function to form a comprehensive optimization objective.

[0031] Within the search space defined by the physical boundary constraints and cost constraints, a multi-objective optimization algorithm with constraints is used to solve the comprehensive optimization objective. Based on the constraint dominance rules, non-dominated sorting is performed, and candidate mix ratio schemes are output.

[0032] Furthermore, the step of updating the current weight vector and the residual correction portion based on the measured deviation includes:

[0033] The candidate combination ratio is experimentally verified to obtain measured values. The deviation between the measured values ​​and the target values ​​is calculated, and the current weight vector is updated based on the deviation.

[0034] The weight of performance indicators that do not meet the target requirements is increased, while the weight of those that have met the target requirements is adjusted during normalization.

[0035] New test samples are added to the training set, and the residual correction part is incrementally updated. The main prediction part is retrained after the cumulative number of new samples reaches a preset proportion.

[0036] Further, the step of updating the current weight vector based on the deviation includes:

[0037] Based on the current weights of each performance indicator, the direction and degree of deviation are determined according to the measured deviations of each performance indicator.

[0038] A weighted update strategy is adopted to recalculate the weights of each performance index, and the recalculated weights are normalized. The normalized weights are used as the updated weight vector.

[0039] The present invention has the following beneficial effects:

[0040] 1. In this invention, subjective weights are calculated based on the failure modes of engineering scenarios using the analytic hierarchy process, and objective weights are calculated based on the dispersion of historical data using the entropy weight method. The two are then linearly fused and normalized, so that the weight allocation simultaneously reflects the scenario priority and the statistical regularity of the data, thus overcoming the defects of subjective arbitrariness or detachment from engineering reality in the single weighting method.

[0041] 2. In this invention, a penalty term is superimposed on the loss function of the gradient boosting tree node to achieve monotonic physical constraints. This forces the model to follow physical laws such as the inverse correlation between water-glue ratio and strength and the positive correlation with diffusion coefficient at the training layer, thus preventing the pure data-driven model from outputting prediction results that violate common sense due to sample noise. At the same time, Gaussian process regression is used to compensate and correct the local prediction residuals. The two are linearly superimposed to output the model, so that the model can maintain physical rationality while taking into account the accuracy of nonlinear fitting.

[0042] 3. In this invention, a triple penalty mechanism is established, including variable out-of-bounds, performance deviation, and cost over-limit. A nonlinear exponential penalty function is introduced for the interval optimal characteristic index to match the nonlinear growth characteristics of engineering risks. By actively increasing the weight of non-compliant indicators through experimental measurement deviations and passively adjusting compliant indicators during normalization, and by combining incremental updates of the residual correction part with staged retraining of the main prediction part, the prediction accuracy is gradually improved with iteration, and the combination scheme converges stably towards the target performance. Attached Figure Description

[0043] Figure 1 This is a flowchart of the reverse design method for cement-based material mix proportions based on physical constraint machine learning proposed in this invention.

[0044] Figure 2 This is a schematic diagram of the combined prediction structure of the GBDT master model and the GPR residual correction model proposed in this invention;

[0045] Figure 3 This diagram illustrates the construction of the satisfaction function and the variable out-of-bounds penalty, performance deviation penalty, and cost over-limit penalty functions proposed in this invention.

[0046] Figure 4 This is a flowchart illustrating the closed-loop iterative process of experimental verification, weight update, and residual model update proposed in this invention. Detailed Implementation

[0047] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] Example 1

[0049] This invention provides a reverse design method for cement-based material mix proportions based on physical constraint machine learning, such as... Figure 1 As shown, it includes the following steps:

[0050] S100: Obtain the target service performance parameters of the cement-based material to be designed, and determine the initial weight vector of each performance index by adopting a subjective and objective weighting method according to the engineering application scenario.

[0051] Furthermore, the aforementioned subjective and objective combined empowerment method specifically includes:

[0052] The analytic hierarchy process (AHP) is used to calculate the subjective weights of each performance index based on the failure modes of the engineering application scenario.

[0053] The entropy weight method is used to calculate the objective weights of each performance index based on historical performance data;

[0054] The subjective weights and objective weights are linearly combined to obtain the initial weight vector.

[0055] Specifically, when designing the mix proportions of high-toughness cement-based composite materials, it is first necessary to define the target service performance parameters of the material. In this embodiment, the target performance parameter vector... Defined as:

[0056] ;

[0057] in, Compressive strength; This represents the ultimate tensile strain. For fluidity; is the chloride ion diffusion coefficient.

[0058] Based on engineering requirements, compressive strength and ultimate tensile strain are considered optimally maximally, while chloride ion diffusion coefficient is considered optimally maximally ...

[0059] Subjective weights were determined using the analytic hierarchy process (AHP), and a performance index judgment matrix was constructed based on the main failure modes of four scenarios: marine engineering, thin-plate components, repair engineering, and reinforcement engineering. Experts then conducted pairwise comparisons based on the degree of influence of each index under specific failure modes. For marine engineering, the focus was on durability degradation caused by chloride ion corrosion, therefore, [the matrix was assigned specific weights]. Higher relative importance. For thin-plate members, due to their sensitivity to cracking, the ultimate tensile strain... To achieve master performance. Calculate the maximum eigenvalue and corresponding eigenvector of the judgment matrix, and ensure consistency is achieved within the specified range. Under the premise of obtaining the subjective weight vector .

[0060] Based on the entropy weight method, historical performance data for corresponding engineering scenarios are collected to determine objective weights. In this embodiment, the sample size is no less than 50 groups. The objective dispersion of the data is reflected by calculating the information entropy of each indicator. The smaller the information entropy, the higher the sensitivity of the indicator in the historical mix ratio evolution process, and the greater its contribution to performance evaluation, thus assigning it a higher objective weight. .

[0061] This embodiment uses a linear weighted combination method to fuse subjective experience with data features. The calculation formula is as follows:

[0062] ;

[0063] in, The subjective and objective weighting fusion coefficient has a value of [value missing]. In this embodiment, we take To balance the consistency between expert experience and historical data.

[0064] The initial weight range for each scenario is as follows:

[0065] Marine Engineering: , , , ;

[0066] Thin plate components: , , , ;

[0067] Repair work: , , , ;

[0068] Reinforcement Project: ; , , .

[0069] Finally, the initial weight vector is normalized:

[0070] ;

[0071] in, These correspond to compressive strength, ultimate tensile strain, fluidity, and chloride ion diffusion coefficient, respectively.

[0072] This embodiment takes a thin-plate component application scenario as an example, and sets its target performance as: compressive strength. Ultimate tensile strain The fluidity is between 200 mm and 230 mm, and the chloride ion diffusion coefficient is ≤ .

[0073] After calculation and normalization using the analytic hierarchy process (AHP) and entropy weight method, the initial weight vector is: , , , This weighting significantly highlights the central role of ultimate tensile strain in the design of thin-plate components.

[0074] By classifying the target service performance parameters into three categories according to the optimization direction—larger is better, smaller is better, and interval optimal—a foundation is laid for the subsequent differentiated construction of satisfaction and penalty functions. Simultaneously, the Analytic Hierarchy Process (AHP) is used to calculate subjective weights based on the failure modes of four engineering scenarios, while the entropy weight method calculates objective weights based on the objective dispersion of historical performance data. These two methods are then linearly fused and normalized, ensuring that the weight allocation reflects both the performance priority under specific engineering scenarios and conforms to the objective statistical laws of historical data. This overcomes the shortcomings of the single subjective weighting method (high arbitrariness) and the single objective weighting method (detachment from engineering reality).

[0075] S200: Based on the target service performance parameters, determine the vector of mix proportion variables that affect material properties, and set physical boundary constraints and cost constraints for each mix proportion variable;

[0076] Specifically, after clarifying the target performance, an eleven-dimensional mix ratio variable vector was constructed in this embodiment. This aims to comprehensively cover the core factors affecting the performance of high-toughness cement-based composite materials. The variable vector is defined as follows: ;in, The water-cement ratio determines the density and strength of the matrix; The sand-to-binder ratio is used to balance the volume stability and mechanical properties of the material. The total fiber integral is the key to achieving crack bridging and high toughness; The fiber length affects the bond length between the fiber and the matrix. The fiber aspect ratio determines the fiber's reinforcing and toughening efficiency; The dosage of water-reducing agent is used to adjust the working performance of the material; The amount of viscosity modifier added is adjusted to prevent segregation of the slurry under high fluidity conditions; The fly ash replacement rate; The silica ash replacement rate; The slag powder replacement rate; This represents the total amount of cementitious materials.

[0077] The physical boundary constraints selected for each component are as follows: , , , , , , , , , , .

[0078] To ensure the stability and long-term durability of the cementitious material system, the replacement rate of each mineral admixture must also meet the cumulative replacement rate constraint. Meanwhile, to balance economic efficiency in engineering applications, cost constraints are set. This includes the material cost per unit volume. The calculation formula is:

[0079] ;

[0080] in, This represents the total number of raw material types. For the first The unit price of the raw materials; For the mix proportion variable vector The determined first The amount of each raw material used per unit volume.

[0081] This formula uses the unit price of various raw materials. The amount of product per unit volume determined by the mix proportion variable The total cost of materials is obtained by linear weighted summation. During the optimization process, it is necessary to ensure... ,in This is a preset cost ceiling, usually set based on local market prices and project budget.

[0082] By constructing an eleven-dimensional mix proportion variable vector, covering multiple dimensions such as water-cement ratio, sand-cement ratio, fiber parameters, admixture dosage, mineral admixture substitution rate, and cementitious material dosage, physical boundary constraints are set for each variable, cumulative substitution rate constraints are set for mineral admixtures, and cost constraints are set. This limits the mix proportion optimization to a feasible domain that conforms to the laws of materials science and engineering economics, avoiding the problems of excessively large search space, generated mix proportion schemes that violate physical laws, or deviate from the actual cost controllable range in traditional empirical trial mixing.

[0083] S300: Based on the mix proportion variables and the measured performance dataset, establish a combined prediction model that includes a main prediction part and a residual correction part, and apply a monotonicity constraint based on the physical correlation direction to the main prediction part.

[0084] Furthermore, such as Figure 2 As shown, the establishment of the combined prediction model, which includes a main prediction component and a residual correction component, specifically includes:

[0085] Using the aforementioned mix ratio variable as input and the aforementioned performance index as output, the master prediction part is trained based on the aforementioned measured performance dataset to establish an initial mapping relationship, and a monotonicity constraint based on the physical correlation direction is applied to the master prediction part.

[0086] Calculate the prediction residual of the main prediction part, and train the residual correction part based on the prediction residual;

[0087] The output of the main prediction part is linearly superimposed with the correction result of the residual correction part, and this superposition is used as the output of the combined prediction model.

[0088] Furthermore, applying a monotonicity constraint based on the physical correlation direction to the main prediction component specifically includes:

[0089] At each node split in the main prediction part, the trend of the predicted value change of the left and right child nodes in the dimension of the constraint variable is calculated;

[0090] If the preset monotonic direction is violated, a penalty term is added to the loss function of the current iteration to force the model to split in a direction that conforms to the monotonic direction.

[0091] Specifically, after determining the mix proportion variable vector and its boundary constraints, this embodiment establishes a combined prediction model that includes a gradient boosting tree (GBDT) master prediction model and a Gaussian process regression (GPR) residual correction model. This aims to address the consistency between nonlinear mapping and physical laws under small sample data of cement-based materials. The model uses eleven-dimensional mix proportion variables... For input, the measured values ​​of each performance indicator. For output, train the GBDT master prediction model. To ensure that the prediction results conform to basic common sense in materials science, monotonic physical constraints are applied to the underlying model training.

[0092] The monotonic physical constraint is implemented by modifying the node splitting loss function of GBDT. During each node split in the tree growth process, the algorithm traverses candidate splitting features and splitting points, calculating the average predicted values ​​of the left and right child nodes in the constraint variable dimension. If the trend after the split violates the preset monotonic direction, a monotonicity penalty term is triggered. Modified loss function for:

[0093] ;

[0094] in, This is the original squared error loss function, used to ensure prediction accuracy; The value of the monotonic constraint penalty coefficient is within the range of [value range missing]. In this embodiment, we take ; The value is set to 1 if the splitting trend violates physical laws, and 0 otherwise.

[0095] Furthermore, the preset monotonic directions include at least the following: compressive strength decreases monotonically with the water-cement ratio, chloride ion diffusion coefficient increases monotonically with the water-cement ratio, ultimate tensile strain increases monotonically with fiber volume fraction, and flowability decreases monotonically with fiber volume fraction and increases monotonically with water-reducing agent dosage.

[0096] Specifically, based on the scientific principles of cement-based materials, the following preset monotonic direction constraints are applied to the master prediction model: compressive strength. With water-cement ratio Increases and monotonically decreases; chloride ion diffusion coefficient With water-cement ratio Increasing monotonically; ultimate tensile strain With the total fiber integral Increases monotonically; fluidity With the total fiber integral Increases and monotonically decreases with the dosage of water-reducing agent. It increases monotonically.

[0097] The aforementioned directional constraints are embedded in the model training process, guiding the splitting direction through a penalty term in the loss function. In this embodiment, a corresponding monotonic constraint vector is set for each performance metric, with the constraint variable having a non-zero element and the rest being zero.

[0098] While the main prediction model conforms to physical laws, it may have biases in capturing local nonlinear features. This embodiment calculates the measured values ​​of the training samples. Compared with the output value of the main prediction model The residuals between Using this residual as the training objective, a Gaussian process regression residual correction model is established. The model follows The model employs a radial basis kernel function:

[0099] ;

[0100] in, The variance of the signal; The kernel function length scale is used. Training is performed by minimizing the negative log-marginal likelihood function.

[0101] ;

[0102] in, Kernel matrix; For noise variance; It is the identity matrix; This represents the number of training samples.

[0103] Through the above training process, the GPR model can effectively capture local fluctuations in the data and compensate for the systematic bias of the main prediction model. Finally, the total output of the combined prediction model... Linear superposition of master forecast and residual correction .

[0104] In this embodiment, the accuracy requirements for the combined prediction model are shown in Table 1.

[0105] Table 1 Accuracy Requirements of Combined Prediction Model

[0106] Performance indicators Upper limit of average relative error compressive strength ≤8% Ultimate tensile strain ≤12% Flowability ≤7% Chloride ion diffusion coefficient ≤15%

[0107] In this embodiment, a thin plate component dataset is used as an example. The composition and purpose of the training samples are shown in Table 2.

[0108] Table 2. Dataset Composition and Usage

[0109] Data source Sample size / group Percentage / % use Historical test data 72 40.0 Establish basic mapping relationships and objectively assign weights using the entropy weight method. Orthogonal experimental data 72 40.0 Supplementing variable boundaries and performance gradients Iterative verification of experimental data 36 20.0 Update the residual model and verify the closed-loop effect. total 180 100 Model training, validation and testing

[0110] Without physical constraints, the ordinary GBDT model may exhibit abnormally high predicted compressive strength values ​​as the water-cement ratio increases within the range of 0.20 to 0.25 due to data noise interference, violating the fundamental physical laws of cement-based materials. After applying monotonic constraints, the prediction curve maintains physical rationality throughout the entire variable range, verifying the effectiveness of the constraint mechanism proposed in this invention.

[0111] After adopting the GBDT+GPR combined prediction model, the prediction accuracy of each performance index is improved compared with the single GBDT model, indicating that the residual correction mechanism can effectively compensate for the prediction bias of GBDT in the local nonlinear region.

[0112] By superimposing a penalty term into the GBDT node splitting loss function to achieve monotonic physical constraints, the model is forced to follow physical laws such as the inverse correlation between water-gel ratio and strength and the positive correlation with chloride ion diffusion coefficient at the training level. This fundamentally eliminates the possibility of pure data-driven models outputting prediction results that violate common sense in materials science due to sample noise. At the same time, GPR is used to compensate and correct the local prediction residuals of GBDT. The combined prediction result is output after the two are linearly superimposed, so that the model can take into account the nonlinear fitting accuracy while maintaining physical rationality.

[0113] S400: Based on the output of the combined prediction model, a satisfaction evaluation system with nonlinear deviation penalty is constructed. The satisfaction levels are weighted according to the current weights to form a comprehensive optimization objective. Multi-objective optimization is performed under the physical boundary constraints and cost constraints to output candidate mix ratios.

[0114] Furthermore, such as Figure 3 As shown, the steps for constructing a satisfaction evaluation system with nonlinear deviation penalty include:

[0115] Based on the optimization direction type of each performance indicator, a satisfaction function for each performance indicator is constructed respectively;

[0116] Construct a comprehensive penalty function that includes at least a variable out-of-bounds penalty term, a performance deviation penalty term, and a cost out-of-bounds penalty term;

[0117] For performance indicators with interval optimality characteristics, a nonlinear exponential penalty function is used to penalize predicted values ​​that deviate from the target range;

[0118] The satisfaction evaluation system is composed of the satisfaction function and the comprehensive penalty function.

[0119] Furthermore, the cost over-limit penalty is constructed based on material costs; the material costs are determined by a weighted sum of the unit price and usage of each raw material; the cost over-limit penalty is the squared penalty when the material costs exceed a preset upper limit.

[0120] Specifically, satisfaction functions are constructed for different types of performance metrics. Mapping predicted values ​​of different dimensions to Interval.

[0121] For indices where larger values ​​are always better, such as compressive strength and ultimate tensile strain, the satisfaction function is:

[0122] ;

[0123] in, This is the minimum acceptable value; The target value. When the predicted value is below the lower limit. The satisfaction rate was 0, which is higher than the target value. The initial satisfaction level is 1, and the intermediate part is a linear transition.

[0124] For indicators where smaller values ​​are better, such as the chloride ion diffusion coefficient, the satisfaction function is:

[0125] ;

[0126] in, This is the highest acceptable upper limit. When the predicted value is lower than the target value... The satisfaction level was 1, which is higher than the upper limit. The satisfaction rate was 0.

[0127] For the interval-optimal mobility index, the satisfaction function is:

[0128] ;

[0129] in, and These are the lower and upper limits of the target range, respectively; and These are the tolerances for the lower and upper deviations, respectively. The function operates within the target range. The value is 1 if it is within this range, and it decreases linearly to 0 if it deviates from this range.

[0130] To strictly constrain the search space, a method is constructed that includes a variable out-of-bounds penalty. Performance Deviation Penalty and cost over-limit penalties The comprehensive penalty items.

[0131] Variable out-of-bounds penalty: A squared penalty is applied to the mix proportion variable that exceeds the physical boundary constraints to ensure the feasibility of the scheme. When any combination ratio variable exceeds its preset range, a squared penalty is applied to that variable. The sum of the squared penalties for all variables exceeding the boundary constitutes the variable out-of-bounds penalty term.

[0132] Performance deviation penalty: Calculate the performance deviation penalty separately for both the larger-than-expected and smaller-than-expected indices; for the larger-than-expected indices... For indicators where smaller is better For the liquidity index, a non-linear exponential penalty function is used:

[0133] ;

[0134] in, This is a predicted value for fluidity. This is the flowability penalty coefficient, with a value range of [value missing]. .

[0135] When the predicted flowability value is within the target range, the flowability fully meets the construction requirements, and no penalty is imposed. When the flowability is below the lower limit or above the upper limit, the penalty value increases exponentially with the degree of deviation, simulating the actual engineering phenomenon where the construction difficulty increases sharply when the flowability deviates significantly. In this embodiment, the repair project takes... reinforcement project The performance deviation penalty function is the sum of the deviation penalties for each performance indicator. .

[0136] Cost exceeding limits penalty, calculating the cost of materials per unit volume. If it exceeds the preset limit Then a squared penalty term is introduced. .

[0137] Furthermore, the steps for solving the multi-objective optimization problem include:

[0138] The satisfaction levels are weighted and summed using the current weights, and then combined with the comprehensive penalty function to form a comprehensive optimization objective.

[0139] Within the search space defined by the physical boundary constraints and cost constraints, a multi-objective optimization algorithm with constraints is used to solve the comprehensive optimization objective. Based on the constraint dominance rules, non-dominated sorting is performed, and candidate mix ratio schemes are output.

[0140] Specifically, the satisfaction levels of each indicator are weighted and then all penalties are subtracted to form a comprehensive satisfaction function. :

[0141] ;

[0142] in, For the first The current weight of each performance metric; , , These are the penalty coefficients for variable out-of-bounds, performance deviation, and cost exceeding limits, respectively.

[0143] This embodiment uses the NSGA-II algorithm with constraints to solve the objective function. The constraint fitness function is:

[0144] ;

[0145] in, Total constraint violation rate:

[0146] ;

[0147] To constrain the penalty coefficient for violations.

[0148] This algorithm introduces constraint dominance rules in non-dominated sorting: if both individuals satisfy all constraints, they are sorted by overall satisfaction; if one is feasible and the other is infeasible, the feasible individual is prioritized; if neither is feasible, the total constraint violation is determined. Smaller values ​​take precedence. In this embodiment, the population size for the NSGA-II algorithm is [missing value]. The maximum number of generations is The crossover probability is The mutation probability is .

[0149] This embodiment takes a repair project scenario as an example, with a target mobility range of 230mm to 250mm. The aforementioned satisfaction evaluation system and NSGA-II optimization algorithm are used to solve the problem under the conditions of a population size of 150 and 200 generations. After optimization, candidate mix design schemes in the Pareto front are output. Each candidate scheme satisfies both physical boundary constraints and cost constraints. The scheme with the highest overall satisfaction proceeds to the subsequent experimental verification stage.

[0150] By constructing a differentiated satisfaction function, multi-dimensional performance prediction values ​​are uniformly mapped to comparable evaluation scales. A triple penalty mechanism, including variable out-of-bounds, performance deviation, and cost over-limit, is established to penalize schemes that violate constraints, ensuring that the optimization results conform to physical laws and economic requirements. Furthermore, a nonlinear exponential penalty function is introduced for interval optimal characteristic indicators such as flowability to match the nonlinear growth characteristics of risk when performance deviates in actual engineering. Finally, the NSGA-II algorithm with constraint dominance rules is used for solving the problem, prioritizing feasible schemes over infeasible schemes, thus overcoming the problem of traditional algorithms outputting infeasible schemes due to neglecting engineering constraints.

[0151] S500: Perform experimental verification on the candidate mix proportions, update the current weight vector and the residual correction part according to the measured deviation, and repeat the optimization solution and experimental verification until the termination condition is met, and output the final mix proportion scheme.

[0152] Furthermore, the step of updating the current weight vector and the residual correction portion based on the measured deviation includes:

[0153] The candidate combination ratio is experimentally verified to obtain measured values. The deviation between the measured values ​​and the target values ​​is calculated, and the current weight vector is updated based on the deviation.

[0154] The weight of performance indicators that do not meet the target requirements is increased, while the weight of those that have met the target requirements is adjusted during normalization.

[0155] New test samples are added to the training set, and the residual correction part is incrementally updated. The main prediction part is retrained after the cumulative number of new samples reaches a preset proportion.

[0156] Specifically, laboratory trials were conducted on the candidate mix design, and measured values ​​of various performance indicators were obtained according to standard testing methods. The measured values ​​were then... With target value Compare and calculate the performance deviation function. For indices where larger values ​​are always better, such as compressive strength and ultimate tensile strain, the deviation function is: A positive deviation occurs when the measured value is lower than the target value; the deviation is 0 when the measured value reaches or exceeds the target value.

[0157] For indices where smaller values ​​are better, such as the chloride ion diffusion coefficient, the deviation function is: A positive deviation occurs when the measured value is higher than the target value; the deviation is 0 when the measured value reaches or falls below the target value.

[0158] For the fluidity index, the deviation function is:

[0159] ;

[0160] in, For the first The measured values ​​of flowability during the iteration. The deviation is 0 when the measured value falls within the target range; when it is below the lower limit or above the upper limit, the deviation is calculated according to the proportion of deviation from the boundary.

[0161] Furthermore, such as Figure 4 As shown, the steps for updating the current weight vector based on the deviation include:

[0162] Based on the current weights of each performance indicator, the direction and degree of deviation are determined according to the measured deviations of each performance indicator.

[0163] A weighted update strategy is adopted to recalculate the weights of each performance index, and the recalculated weights are normalized. The normalized weights are used as the updated weight vector.

[0164] Specifically, based on the measured deviation, a weight correction algorithm is used to adjust the optimization priority of the next iteration. The weight update formula is:

[0165] ;

[0166] in, For the first In the first iteration The current weight of each performance metric; For the first In the first iteration Measured deviation of each performance indicator; This is the weighting adjustment coefficient, and its value range is... In this embodiment, we take .

[0167] If a certain performance indicator fails to meet the target requirements If the metric is already satisfactory, then in the next round of optimization, the weight of that metric will be proactively increased, forcing the optimization algorithm to shift its search focus towards that weak performance area; if the metric has already met the target... Its weight is not actively increased, but is passively adjusted only through the normalization of the denominator.

[0168] This embodiment employs a hierarchical update strategy for the combined prediction model, including incremental updates for the residual correction component and retraining of the main prediction component. Incremental updates for the residual correction component involve adding new samples obtained from each trial to the training set in real time, incrementally updating the GPR residual correction model, and using the new data to correct prediction biases in local regions of the main prediction model. Retraining of the main prediction component is triggered when the cumulative number of newly added trial samples reaches a preset proportion (e.g., 15%) of the original training set size, thereby updating the underlying global mapping relationships.

[0169] In this embodiment, the iteration termination condition is set to meet any of the following conditions: all four measured performance indicators meet the target requirements; overall satisfaction level is high. The average relative prediction error of each performance is reduced to below the preset threshold, with compressive strength ≤8%, ultimate tensile strain ≤12%, flowability ≤7%, and chloride ion diffusion coefficient ≤15%; the number of iterations reaches the preset upper limit, usually 5 to 10 times.

[0170] This embodiment takes a thin plate component scenario as an example. The performance data comparison before and after the first iteration is shown in Tables 3 and 4.

[0171] Table 3 Optimization results of thin plate components before iteration

[0172] index Predicted value Measured value target value deviation Does it meet the standard? Compressive strength / MPa 106 104 ≥100 +4.0% yes Ultimate tensile strain / % 3.05 2.95 ≥3.0 -1.7% no Flowability / mm 218 221 200～230 0 yes <![CDATA[Chloride ion diffusion coefficient / 10 -12 m 2 / s]]> 1.85 1.92 ≤2.0 0 yes

[0173] In the first iteration, the measured ultimate tensile strain of 2.95% was slightly lower than the target value of 3.0%, with a deviation of [missing information]. After calculation using the weight update formula, the weight of this indicator increased from 0.45 to 0.462.

[0174] Table 4. Optimization results of thin plate components after iteration

[0175] index Predicted value Measured value target value relative deviation Does it meet the standard? Compressive strength / MPa 109 108 ≥100 +8.0% yes Ultimate tensile strain / % 3.35 3.30 ≥3.0 +10.0% yes Flowability / mm 214 212 200～230 0 yes <![CDATA[Chloride ion diffusion coefficient / 10 -12 m 2 / s]]> 1.62 1.68 ≤2.0 0 yes

[0176] After weight adjustment, the algorithm shifted its search focus towards the ultimate tensile strain in the second round of optimization, successfully increasing the measured value to 3.30%, which met the design requirements. Furthermore, since the increase in ultimate tensile strain did not have a significant negative impact on other performance indicators, the overall satisfaction level was high. The value increased from 0.88 before iteration to 0.94 after iteration, verifying the effectiveness of the closed-loop adaptive iteration mechanism of the present invention.

[0177] When all measured performance indicators meet the target requirements, the iteration terminates and the current mix proportion scheme is output as the final optimal mix proportion scheme; if the termination condition is not met, the process returns to step S400, and the optimization solution and experimental verification are performed again with the updated weight vector and the updated combined prediction model until the termination condition is met and the final mix proportion scheme is output.

[0178] By obtaining measured values ​​through laboratory trials and comparing them with target values, the measured deviations of various performance indicators are calculated, providing a quantitative basis for weight updates. Based on the direction and degree of deviation, the weights of indicators that fail to meet the standards are proactively increased, while indicators that meet the standards are passively adjusted during normalization. This allows the optimization focus to adaptively shift towards weaker performance. Furthermore, by adding new experimental samples to the training set to incrementally update the residual correction part, and by retraining after the cumulative number of new samples in the main prediction part reaches the preset conditions, the prediction accuracy of the combined prediction model gradually improves with the iteration process. Finally, through a closed-loop iteration mechanism, the mix design scheme is stably converged to the target performance, overcoming the problem that one-time optimization results are difficult to implement.

[0179] Example 2

[0180] To verify the effectiveness of this method in engineering scenarios with different failure modes and varying performance control requirements, mix proportion optimization was performed using marine engineering, repair engineering, and reinforcement engineering as examples. This invention provides a reverse design method for cement-based material mix proportions based on physical constraint machine learning, including:

[0181] The target service performance parameters of the cement-based material to be designed are obtained, and an initial weight vector for each performance index is determined using a combined subjective and objective weighting method based on the engineering application scenario. Based on the target service performance parameters, the mix proportion variable vector affecting material performance is determined, and physical boundary constraints and cost constraints are set for each mix proportion variable. Based on the mix proportion variables and the measured performance dataset, a combined prediction model including a main prediction component and a residual correction component is established, and a monotonicity constraint based on the physical correlation direction is applied to the main prediction component. Based on the output of the combined prediction model, a satisfaction evaluation system with nonlinear deviation penalty is constructed. Each satisfaction level is weighted using the current weights to form a comprehensive optimization objective, and multi-objective optimization is performed under the physical boundary constraints and cost constraints to output candidate mix proportions. The candidate mix proportions are experimentally verified. The current weight vector and the residual correction component are updated based on the measured deviations, and this process of optimization and experimental verification is repeated until the termination condition is met, outputting the final mix proportion scheme.

[0182] Specifically, marine engineering projects are exposed to chloride ion corrosion environments for extended periods. Durability degradation caused by chloride ion corrosion is the primary failure mode, and the chloride ion diffusion coefficient is the main controlling performance indicator. The target performance requirements are: compressive strength ≥ 105 MPa, ultimate tensile strain ≥ 2.5%, flowability 190 to 220 mm, and chloride ion diffusion coefficient ≤ .

[0183] This embodiment uses the AHP-entropy weight method to calculate the initial weights, and the subjective weights of the analytic hierarchy process are... Objective weighting of entropy weighting method (based on 55 sets of historical marine engineering data): Combined weights ( ): Initial weights after normalization: ; The fluidity penalty coefficient is taken as The monotonic constraint penalty coefficient is taken as .

[0184] After optimization using this method, the performance indicators of the mix design schemes for marine engineering scenarios are shown in Table 5.

[0185] Table 5 Optimization Results of Marine Engineering

[0186] index Measured values ​​before iteration Measured values ​​after iteration target value Does it meet the standard? Compressive strength / MPa 109 112 ≥105 yes Ultimate tensile strain / % 2.7 2.9 ≥2.5 yes Flowability / mm 211 205 190～220 yes <![CDATA[Chloride ion diffusion coefficient / 10 -12 m 2 / s]]> 1.58 1.32 ≤1.5 yes

[0187] During the iteration process, the measured value of the ultimate tensile strain increased from 2.7% to 2.9%, and the measured value of the chloride ion diffusion coefficient increased from... Reduce to The overall satisfaction rate increased from 0.89 to 0.95. These results demonstrate that, in marine engineering scenarios where durability is paramount, this method can effectively balance the performance requirements between compressive strength, ultimate tensile strain, and chloride ion diffusion coefficient, outputting a mix design that meets the chloride ion diffusion coefficient limit while also considering mechanical properties.

[0188] Repair work requires high workability and early strength. Insufficient filling and insufficient early strength are the main failure modes. Workability and compressive strength are the primary control performance indicators. Target performance requirements are: compressive strength ≥ 90 MPa, ultimate tensile strain ≥ 2.0%, workability 230 to 250 mm, chloride ion diffusion coefficient ≤ .

[0189] This embodiment uses the AHP-entropy weighting method to calculate the initial weights: the subjective weights of the analytic hierarchy process are the subjective weights of the analytic hierarchy process. Entropy weight method objective weight (based on 50 sets of historical repair project data): Combined weights ( ): Initial weights after normalization: ; The fluidity penalty coefficient is taken as Repair projects have higher requirements for fluidity and stricter penalties; the monotonic constraint penalty coefficient is taken as... .

[0190] After optimization using this method, the performance indicators of the mix design scheme for the repair project scenario are shown in Table 6.

[0191] Table 6 Optimization Results of Repair Projects

[0192] index Predicted value Measured value target value Does it meet the standard? Compressive strength / MPa 98 96 ≥90 yes Ultimate tensile strain / % 2.5 2.4 ≥2.0 yes Flowability / mm 241 238 230～250 yes <![CDATA[Chloride ion diffusion coefficient / 10 -12 m 2 / s]]> 1.96 2.05 ≤2.5 yes

[0193] Overall satisfaction The above results demonstrate that, in repair engineering scenarios where fluidity is the primary control, this method, by employing a higher fluidity penalty coefficient, can achieve better results. It can effectively control the flowability within the target range of 230 to 250 mm, while also taking into account the compressive strength requirements, thus verifying the effective constraint effect of the nonlinear exponential penalty function on the interval optimal index.

[0194] Reinforcement projects require high load-bearing capacity and deformation coordination. Insufficient load-bearing capacity and interface deformation incompatibility are the main failure modes, with compressive strength and ultimate tensile strain being the primary control performance indicators. Target performance requirements are: compressive strength ≥ 110 MPa, ultimate tensile strain ≥ 3.0%, flowability 190 to 220 mm, and chloride ion diffusion coefficient ≤ .

[0195] This embodiment uses the AHP-entropy weighting method to calculate the initial weights: The subjective weights of the analytic hierarchy process are: Entropy weight method objective weights (based on 52 sets of historical data from reinforcement projects): Combined weights ( ): Initial weights after normalization: ; The fluidity penalty coefficient is taken as The monotonic constraint penalty coefficient is taken as .

[0196] After optimization using this method, the performance indicators of the mix proportion scheme for the reinforcement engineering scenario are shown in Table 7.

[0197] Table 7 Optimization Results of Reinforcement Projects

[0198] index Predicted value Measured value target value Does it meet the standard? Compressive strength / MPa 120 118 ≥110 yes Ultimate tensile strain / % 3.5 3.4 ≥3.0 yes Flowability / mm 208 205 190～220 yes <![CDATA[Chloride ion diffusion coefficient / 10 -12 m 2 / s]]> 1.50 1.56 ≤2.0 yes

[0199] Overall satisfaction The above results demonstrate that, in reinforcement engineering scenarios where bearing capacity is the primary factor, this method can prioritize ensuring that compressive strength and ultimate tensile strain meet higher target requirements, while also considering flowability and durability indicators, thus verifying the effectiveness of this method in the synergistic optimization of multiple performance indicators.

[0200] The optimization results of the above three engineering scenarios are summarized with those of the thin plate component in Example 1, as shown in Table 8.

[0201] Table 8 Summary of Optimization Results for Each Engineering Scenario

[0202] Scene Compressive strength / MPa Ultimate tensile strain / % Flowability / mm <![CDATA[Chloride ion diffusion coefficient / 10 -12 m 2 / s]]> Overall satisfaction Thin plate components 108 3.3 212 1.68 0.94 Marine Engineering 112 2.9 205 1.32 0.95 Repair work 96 2.4 238 2.05 0.92 reinforcement project 118 3.4 205 1.56 0.96

[0203] As shown in Table 8, the overall satisfaction scores of the four embodiments of the present invention range from 0.92 to 0.96, while the overall satisfaction scores of the six comparative examples range from 0.65 to 0.88. The lowest satisfaction score of the present invention, 0.92, is still higher than the highest value of 0.88 among all comparative examples, which verifies the comprehensive superiority of the present method in terms of prediction accuracy, physical rationality, construction feasibility, and implementation reliability.

[0204] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A reverse design method for cement-based material mix proportions based on physical constraint machine learning, characterized in that, include: Obtain the target service performance parameters of the cement-based material to be designed, and determine the initial weight vector of each performance index using a combination of subjective and objective weighting methods based on the engineering application scenario. Based on the target service performance parameters, determine the vector of mix proportion variables that affect material properties, and set physical boundary constraints and cost constraints for each mix proportion variable; Based on the aforementioned mix proportion variables and measured performance dataset, a combined prediction model including a main prediction component and a residual correction component is established, and a monotonicity constraint based on the physical correlation direction is applied to the main prediction component. Based on the output of the combined prediction model, a satisfaction evaluation system with nonlinear deviation penalty is constructed. The satisfaction levels are weighted by the current weights to form a comprehensive optimization objective. Multi-objective optimization is performed under the physical boundary constraints and cost constraints to output candidate mix ratios. The candidate mix proportions are experimentally verified. The current weight vector and the residual correction part are updated according to the measured deviation. The optimization solution and experimental verification are repeated until the termination condition is met, and the final mix proportion scheme is output.

2. The method for reverse design of cement-based material mix proportions based on physical constraint machine learning according to claim 1, characterized in that, The aforementioned combined subjective and objective empowerment method specifically includes: The analytic hierarchy process (AHP) is used to calculate the subjective weights of each performance index based on the failure modes of the engineering application scenario. The entropy weight method is used to calculate the objective weights of each performance index based on historical performance data; The subjective weights and objective weights are linearly combined to obtain the initial weight vector.

3. The reverse design method for cement-based material mix proportions based on physical constraint machine learning according to claim 1, characterized in that, The establishment of the combined prediction model, which includes a main prediction component and a residual correction component, specifically includes: Using the aforementioned mix ratio variable as input and the aforementioned performance index as output, the master prediction part is trained based on the aforementioned measured performance dataset to establish an initial mapping relationship, and a monotonicity constraint based on the physical correlation direction is applied to the master prediction part. Calculate the prediction residual of the main prediction part, and train the residual correction part based on the prediction residual; The output of the main prediction part is linearly superimposed with the correction result of the residual correction part, and this superposition is used as the output of the combined prediction model.

4. The reverse design method for cement-based material mix proportions based on physical constraint machine learning according to claim 1, characterized in that, The application of a monotonicity constraint based on the physical correlation direction to the main prediction component specifically includes: At each node split in the main prediction part, the trend of the predicted value change of the left and right child nodes in the dimension of the constraint variable is calculated; If the preset monotonic direction is violated, a penalty term is added to the loss function of the current iteration to force the model to split in a direction that conforms to the monotonic direction.

5. The reverse design method for cement-based material mix proportions based on physical constraint machine learning according to claim 4, characterized in that, The preset monotonic directions include at least the following: compressive strength and water-cement ratio are monotonically decreasing, chloride ion diffusion coefficient and water-cement ratio are monotonically increasing, ultimate tensile strain and fiber volume fraction are monotonically increasing, fluidity and fiber volume fraction are monotonically decreasing and monotonically increasing with water-reducing agent dosage.

6. The method for reverse design of cement-based material mix proportions based on physical constraint machine learning according to claim 1, characterized in that, The steps for constructing a satisfaction evaluation system with nonlinear deviation penalty include: Based on the optimization direction type of each performance indicator, a satisfaction function for each performance indicator is constructed respectively; Construct a comprehensive penalty function that includes at least a variable out-of-bounds penalty term, a performance deviation penalty term, and a cost out-of-bounds penalty term; For performance indicators with interval optimality characteristics, a nonlinear exponential penalty function is used to penalize predicted values ​​that deviate from the target range; The satisfaction evaluation system is composed of the satisfaction function and the comprehensive penalty function.

7. The method for reverse design of cement-based material mix proportions based on physical constraint machine learning according to claim 1, characterized in that, The cost over-limit penalty is constructed based on material costs; the material costs are determined by the weighted sum of the unit price and usage of each raw material; the cost over-limit penalty is the squared penalty when the material costs exceed a preset upper limit.

8. The method for reverse design of cement-based material mix proportions based on physical constraint machine learning according to claim 1, characterized in that, The steps for solving the multi-objective optimization problem include: The satisfaction levels are weighted and summed using the current weights, and then combined with the comprehensive penalty function to form a comprehensive optimization objective. Within the search space defined by the physical boundary constraints and cost constraints, a multi-objective optimization algorithm with constraints is used to solve the comprehensive optimization objective. Based on the constraint dominance rules, non-dominated sorting is performed, and candidate mix ratio schemes are output.

9. The method for reverse design of cement-based material mix proportions based on physical constraint machine learning according to claim 1, characterized in that, The steps of updating the current weight vector and the residual correction part based on the measured deviation include: The candidate combination ratio is experimentally verified to obtain measured values. The deviation between the measured values ​​and the target values ​​is calculated, and the current weight vector is updated based on the deviation. The weight of performance indicators that do not meet the target requirements is increased, while the weight of those that have met the target requirements is adjusted during normalization. New test samples are added to the training set, and the residual correction part is incrementally updated. The main prediction part is retrained after the cumulative number of new samples reaches a preset proportion.

10. The method for reverse design of cement-based material mix proportions based on physical constraint machine learning according to claim 9, characterized in that, The steps for updating the current weight vector based on the deviation include: Based on the current weights of each performance indicator, the direction and degree of deviation are determined according to the measured deviations of each performance indicator. A weighted update strategy is adopted to recalculate the weights of each performance index, and the recalculated weights are normalized. The normalized weights are used as the updated weight vector.

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