Cooperative optimization control method and system for expansion degree and strength of flow-state solidified soil

Abstract

The invention relates to the technical field of cooperative control, in particular to a cooperative optimization control method and system for the expansion degree and strength of flow-state solidified soil, and the method comprises the steps: designing a sample according to all influence factors, measuring performance data, and forming test data; constructing a correlation matrix through preprocessing such as abnormal value elimination, variable standardization and virtual variable conversion; screening significant influence items through a variance analysis model and quantifying weights; constructing a dual-output prediction model based on a random forest algorithm, and performing training verification optimization; taking the prediction model as a constraint, and combining economy and convenience to screen an optimal parameter combination; on-site trial mixing verification is carried out, deviation reaches the standard, parameters are determined, and otherwise, data are complemented to update the model to resolve. According to the method, the single factor and the interaction effect are effectively removed, the problem of collaborative prediction under negative correlation of the expansion degree and the strength is solved, collaborative optimization of the expansion degree and the strength is realized, and the scientificity and efficiency of construction parameter determination are improved.

Description

Technical Field

[0001] This invention relates to the field of collaborative control technology, specifically to a method and system for collaborative optimization control of the spread and strength of fluidized solidified soil. Background Technology

[0002] The spread and strength of fluidized solidified soil are influenced by many factors, including cement content, curing agent ratio, mixing time, curing period, and construction location. Spread is affected by fluidity, while strength is constrained by both mix proportion and curing time. There is a potential negative correlation between spread (fluidity index) and strength (mechanical index). For example, increasing water content may increase spread but weaken strength. Furthermore, it is affected by the interaction of multiple variables such as mix proportion, mixing time, and curing period. For instance, the degree of influence of mixing time on spread varies with different cement contents. Existing technologies make it difficult to separate the effects of single factors and interactions through multivariate regression, orthogonal experimental data analysis, and it is difficult to avoid ignoring key coupling terms during modeling. Summary of the Invention

[0003] The purpose of this invention is to provide a method for synergistic optimization control of the spread and strength of fluidized solidified soil, and at the same time, to provide a control system for synergistic optimization control of the spread and strength of fluidized solidified soil, so as to solve the problems mentioned in the background art.

[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution: The first aspect is a method for synergistic optimization and control of the spread and strength of fluidized solidified soil, including the following steps: For fluidized solidified soil, samples were designed based on all influencing factors. Parallel samples were prepared for each group. The spread and strength of the fluidized solidified soil were measured, and the variable parameters and corresponding performance data were recorded to form test data. The Grubbs criterion is used to remove outliers from the test data, the numerical variables of the test data are standardized, the categorical variables of the test data are converted into dummy variables, the correlation coefficient is calculated to determine the variable association, and a correlation matrix is ​​formed. A variance analysis model was constructed, including main effect terms and interaction effect terms, and significant influencing terms were screened. The contribution of each significant term was calculated by partial correlation coefficient, and the influence weight was determined. Using significant impact factors as input, a dual-output prediction model is constructed using the random forest algorithm. The model is trained and its accuracy is verified by dividing the training set and the test set. If the model does not meet the standard, it is re-optimized. The expansion and strength optimization objectives are set, the prediction model is used as a constraint, the optimization algorithm is used to solve the problem, and the parameter combination is selected from the optimal solution set based on the construction economy and convenience. The fluidized solidified soil was mixed and poured on-site according to the optimal parameters. The actual performance data was measured and compared with the predicted values. If the deviation met the standard, the parameters were determined. Otherwise, the data was supplemented, the model was updated, and the solution was obtained again.

[0005] Furthermore, the design of samples for fluidized solidified soil based on all influencing factors involves preparing parallel samples for each group, measuring the spread and strength of the fluidized solidified soil, and recording the variable parameters and corresponding performance data to form test data. Specifically, this includes: determining all influencing factors and the value range of each variable for the spread and strength of the fluidized solidified soil; designing samples according to the principle of full factorial design, preparing parallel samples for each variable combination to ensure data reliability; using standard instruments to measure the spread and compressive strength of the fluidized solidified soil at each curing cycle; recording the variable parameters corresponding to each sample group and the simultaneously measured spread and strength data, and systematically organizing this information to form complete test data.

[0006] Furthermore, the method of using Grubbs' criterion to remove outliers from the test data specifically involves: statistically analyzing the expansion and intensity data of each group of samples, calculating the mean and standard deviation, and, according to Grubbs' criterion, identifying samples whose detected values ​​deviate from the group mean by more than 3 times the standard deviation as outliers; finally, outliers are removed and valid data is retained.

[0007] Furthermore, the standardization of numerical variables in the test data specifically involves: determining the range of numerical variables, including influencing factors and their extent and intensity; calculating the mean and standard deviation of the sample data for each numerical variable; and using a standardization formula to transform the original data to obtain standardized values, so that all variables are on the same order of magnitude.

[0008] Furthermore, the process of converting categorical variables in the test data into dummy variables, calculating correlation coefficients to determine variable associations, and forming a correlation matrix specifically involves: identifying the categorical variables of construction sites in the test data and converting them into dummy variables suitable for subsequent processing; determining the range of variables participating in the correlation coefficient calculation, including the converted dummy variables, standardized numerical influencing factors, and the two target indicators of extent and intensity; calculating the linear correlation coefficients between each influencing factor and extent and intensity, determining the association direction by the sign of the coefficient, and judging the association strength by the absolute value; and organizing the correlation coefficient results among all variables to construct a complete correlation matrix, presenting the basic association characteristics of the variables.

[0009] Furthermore, the construction of the variance analysis model, including main effect terms and interaction effect terms, and screening for significant influencing terms, specifically involves: constructing an variance analysis model to isolate the single and interaction effects of each influencing factor, providing core variables for the main model; the main effect terms include the influencing factors of the spread and strength of the fluidized solidified soil, and the interaction effect terms include the second-order product of any two variables in the main effect terms and the third-order product of specific three variables; two independent models are constructed with spread and strength as dependent variables and the main effect terms and interaction effect terms as independent variables, respectively; the F-value and P-value of each effect term are obtained through variance analysis, with the F-value reflecting the degree of influence and the P-value determining the statistical significance; significant influencing terms are screened with a P-value less than 0.05 as the criterion, and the sets of significant influencing terms affecting spread and strength are determined separately, which are used to determine the objects for quantifying contribution.

[0010] Furthermore, the step of calculating the contribution of each significant item using partial correlation coefficients and determining the influence weights involves the following steps: The significant influence items are the calculation objects, including main effect items, second-order and third-order interaction effect items that significantly affect the extent or intensity, and forming independent sets according to extent and intensity; partial correlation coefficients are introduced to control interference from other items, quantifying the net association between a single significant item and the target indicator; the contribution of each significant item is calculated using the ratio of the partial sum of squares to the total sum of squares, yielding the contribution of significant items in extent and intensity respectively; the contribution is converted into influence weights, and a quantitative result table containing the name, contribution, and weight of the significant items is formed by sorting them by contribution.

[0011] Furthermore, the process of constructing a dual-output prediction model using a random forest algorithm with significant impact items as input, and dividing the data into training and test sets for model training and accuracy verification, specifically involves: using the selected significant impact items in terms of expansion and intensity as input, and expansion and intensity as output, to construct a dual-output prediction model using a random forest algorithm; setting the core parameters of the model, and dividing the preprocessed sample data into training and test sets; using the training set for iterative optimization of model parameters, and the test set for model prediction verification; using the root mean square error and coefficient of determination as accuracy evaluation indicators, if the accuracy is not up to standard, returning to re-select significant impact items, optimizing the input variable set, reconstructing the model, and repeating the training and verification process.

[0012] Furthermore, the setting of expansion and strength optimization objectives, with the prediction model as a constraint, and the use of optimization algorithms to solve the problem, specifically involves: determining the synergistic optimization objectives of expansion and strength, determining the key construction variables as decision variables, and using the prediction model with the required accuracy as a constraint; selecting an algorithm adapted to multi-objective optimization as the solution algorithm, starting the algorithm to iteratively update the parameter combination, calculating the corresponding performance values ​​based on the prediction model, and selecting the optimal solution set that meets the optimization objectives.

[0013] Secondly, the synergistic optimization control system for the spread and strength of fluidized solidified soil includes: The data preprocessing module is used for outlier removal, variable standardization and dummy variable transformation, and to calculate correlation coefficients to form a correlation matrix; The ANOVA module is used to construct ANOVA models containing main effects and interaction effects, screen significant items, and determine the weights of influence. The prediction model building module is used to build a dual-output model based on random forest, and to perform dataset partitioning for training and accuracy verification and optimization. The parameter optimization and filtering module is used to set optimization objectives, solve the problem with the prediction model as a constraint, and filter parameter combinations based on economic considerations. The on-site verification and update module is used to compare actual and predicted data, determine parameters if they meet the criteria, or supplement data to update the model.

[0014] Compared with existing technologies, this invention has the following advantages: This application ensures the reliability of basic data through a full-factor sample design and system data preprocessing. It incorporates main effects and interaction effects using an analysis of variance model, accurately screening significant influencing factors and quantifying their weights, effectively separating the single and interaction effects of each factor, and avoiding the omission of key coupling terms during modeling. The random forest dual-output prediction model constructed with significant influencing factors improves the accuracy of synergistic prediction of expansion and intensity, solving the problem of synergistic prediction under negative correlation between the two. Based on the prediction model and optimization algorithm, parameters are selected based on construction economy and convenience, realizing the transformation of expansion and intensity from potentially negative correlation to synergistic optimality. The on-site verification and model update mechanism optimizes the model and parameters through feedback from actual data, further improving the reliability and applicability of parameters, ensuring that the final parameters not only meet the performance requirements of both indicators but also adapt to actual engineering needs, improving the scientific rigor and efficiency of determining construction parameters for fluidized solidified soil. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to the present invention; Figure 2 This is a block diagram of the fluidized solidified soil expansion and strength synergistic optimization control system of the present invention. Detailed Implementation

[0016] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] This application discloses a method for synergistic optimization and control of the spread and strength of fluidized solidified soil, such as... Figure 1 The steps include: S1. Design samples for fluidized solidified soil according to all influencing factors, prepare parallel samples for each group, measure the spread and strength of fluidized solidified soil, and record variable parameters and corresponding performance data to form test data; S2. Use the Grubbs criterion to remove outliers from the test data, standardize the numerical variables of the test data, convert the categorical variables of the test data into dummy variables, calculate the correlation coefficient to determine the variable association, and form a correlation matrix. S3. Construct an analysis of variance model, include main effect terms and interaction effect terms, screen for significant influencing terms, calculate the contribution of each significant term using partial correlation coefficients, and determine the influence weights; S4. Using significant impact items as input, construct a dual-output prediction model using the random forest algorithm, divide the model into training and test sets for training and accuracy verification, and re-optimize if the model does not meet the requirements. S5. Set the expansion and strength optimization objectives, use the prediction model as a constraint, and use the optimization algorithm to solve the problem. Based on the construction economy and convenience, select the parameter combination from the optimal solution set. S6. Perform on-site trial mixing and pouring of fluidized solidified soil according to the optimal parameters, measure the actual performance data and compare it with the predicted value. If the deviation meets the standard, determine the parameters; otherwise, supplement the data, update the model, and solve it again.

[0018] In S1, samples were designed for fluidized solidified soil based on all influencing factors. Parallel samples were prepared for each group, and the spread and strength of the fluidized solidified soil were measured. Variable parameters and corresponding performance data were recorded to form test data. Specifically, in implementation, the all influencing factors and the value ranges of each variable for the spread and strength of the fluidized solidified soil were first determined. Specifically, the cement dosage was set at 8%-15% of the fluidized solidified soil mass, with 5 gradients; the ratio of curing agent to cement mass was set at 0.05-0.2, with 4 gradients; the mixing time was set at 60s-180s, with 4 gradients; and the curing cycle was set at 1d, 3d, 7d, and 28d, with 4 levels. The construction location was selected as the foundation pit filling... Two typical scenarios for roadbed subbase were studied. Samples were then designed according to the full factorial design principle, with three parallel samples prepared for each variable combination to ensure data reliability. Next, a standard slump spread meter was used to measure the spread of the fluidized solidified soil, with a measurement accuracy to 1 mm. Simultaneously, a universal pressure testing machine was used to measure the compressive strength of the fluidized solidified soil under each curing cycle, with a measurement accuracy to 0.01 MPa. Finally, detailed records were kept of the cement content, curing agent ratio, mixing time, curing cycle, construction location variables, and the simultaneously measured spread and strength data for each sample group. This information was systematically organized to form complete test data.

[0019] In S2, the Grubbs criterion is used to remove outliers from the test data. Specifically, the range of test data from which outliers need to be removed is first determined. This mainly targets the spread data measured by the standard slump spread meter and the compressive strength data for each curing cycle measured by the universal pressure testing machine. These data are the core basis for subsequent analysis and their reliability must be guaranteed. The spread data for each group of samples consists of the test values ​​of 3 parallel samples, and the strength data consists of the compressive strength test values ​​of 3 parallel test blocks under the corresponding curing cycle. Outliers are screened separately for each group.

[0020] Subsequently, the expansion and intensity data corresponding to each group of samples were statistically processed, and the mean of each group of data was calculated, i.e., x. mean and standard deviation, i.e., x std During the calculation process, three decimal places are retained to ensure statistical accuracy. At the same time, it is confirmed that the sample size of each data group is not less than 3. If a group of samples has less than 3 valid data due to detection errors, the sample group is re-prepared for detection and supplementation.

[0021] Next, outlier removal criteria are set according to Grubbs' criterion. First, it is determined whether each group of data conforms to an approximately normal distribution. This can be assisted by a data distribution histogram or a normality test. Under the premise that the data conforms to the characteristics of a normal distribution, when the absolute deviation of the expansion or intensity detection value of a certain sample from the mean of the group of data exceeds 3 times the standard deviation, the sample data is determined to be an outlier. If two or more outliers appear in the same group, the accuracy of the detection instrument and the operation procedure are re-checked. After eliminating systematic errors, the group of samples is re-tested.

[0022] Finally, data identified as outliers are removed from the original test data. For the remaining valid data after removing outliers, if the number is less than 3, parallel samples of the variable combination are prepared again for supplementary testing to ensure that each group retains no less than 3 valid data. Only valid data that meets the accuracy requirements are retained to provide high-quality data support for subsequent data standardization processing and variable correlation analysis.

[0023] In S2, the standardization of numerical variables in the test data is implemented by first determining the range of numerical variables in the test data. This primarily includes cement content, hardener ratio, mixing time, curing cycle, and measured spread and strength data. Categorical variables such as construction location are excluded to ensure accuracy. Then, for each numerical variable, its mean in the sample data is calculated, i.e., x. mean and standard deviation, i.e., x std , where x mean x is the average of all valid sample data for this variable. std This is a statistic that reflects the dispersion of the sample data for this variable.

[0024] Then, a standardized processing formula is used. The original data of each numerical variable are transformed, where x is the original detection value of the variable. This is the standardized value after conversion.

[0025] This process eliminates interference caused by differences in the units and magnitudes of different numerical variables, bringing all variables to the same order of magnitude. This provides a standardized data foundation for subsequent construction of variance analysis models, calculation of correlation coefficients, and establishment of predictive models, ensuring that each variable has equal weight and influence in the analysis process.

[0026] In step S2, the categorical variables of the test data are converted into dummy variables, the correlation coefficient is calculated to determine the variable association, and a correlation matrix is ​​formed. Specifically, in practice, the type of categorical variable in the test data is first determined. In this application, the categorical variable is the construction location, which includes two typical scenarios: foundation pit filling and roadbed subbase. The categorical variable is converted into a dummy variable to adapt to the subsequent data processing requirements. The foundation pit filling scenario is recorded as 1, and the roadbed subbase scenario is recorded as 0.

[0027] Subsequently, the range of variables involved in the correlation coefficient calculation was determined, including the transformed construction site dummy variable, as well as standardized numerical variables such as cement content, curing agent ratio, mixing time, and curing cycle, while also incorporating the two target indicators of spread and strength.

[0028] Next, we calculate the linear correlation coefficients between each influencing factor (including dummy variables and standardized numerical variables) and its extent, and between each influencing factor and its intensity. We determine the direction of the association between variables by the positive or negative value of the correlation coefficient, and judge the intensity of the association by the magnitude of the absolute value of the correlation coefficient.

[0029] Finally, the correlation coefficients of all variables were systematically organized to construct a complete correlation matrix, clearly presenting the basic association characteristics between variables and providing a basis for subsequent quantitative analysis of multivariate interaction effects.

[0030] In S3, an analysis of variance model is constructed, including main effect terms and interaction effect terms, and significant influencing terms are screened. Specifically, the construction goal of the analysis of variance model is first determined, that is, to accurately separate the single effect and interaction effect of each influencing factor, so as to provide core variables for subsequent model construction.

[0031] Subsequently, the main effect terms and interaction effect terms of the model were determined. The main effect terms include five categories of known influencing factors on the spread and strength of fluidized solidified soil: cement content, curing agent ratio, mixing time, curing period, and construction location. The specific attributes of each main effect term were clarified. Cement content, curing agent ratio, mixing time, and curing period are numerical variables, while construction location is a categorical variable (corresponding to the converted dummy variable). All main effect terms are included in the model in the form of preprocessed standardized numerical values ​​or dummy variables. The interaction effect terms consist of two parts. One part is the product of any two variables in the above main effect terms, which serves as the second-order interaction effect term. For example, all pairwise combinations such as the product of cement content and mixing time, the product of curing agent ratio and curing period, and the product of the dummy variable of construction location and cement content are included. The other part is the product of cement content, mixing time, and curing period, which serves as the third-order interaction effect term to comprehensively cover the interaction between multiple variables.

[0032] Next, using expansion and intensity as the dependent variables of the model, and the main effect term and interaction effect term as the independent variables, two independent analysis of variance models for expansion and intensity were constructed. During the construction, all independent variables were first tested for collinearity. If there were variable combinations with a variance inflation factor greater than 10, redundant interaction terms were removed before model fitting to ensure model stability.

[0033] The model was then calculated using the analysis of variance algorithm to obtain the F-values ​​and P-values ​​for each main effect item and interaction effect item. The F-value reflects the degree of influence of the effect item on the dependent variable; the larger the F-value, the more significant the influence. The P-value is used to determine whether the influence of the effect item is statistically significant; the smaller the P-value, the higher the statistical significance.

[0034] Finally, a significance criterion was established, and effect items with a P-value less than 0.05 were judged as having a significant impact on the extent or intensity. The F-value was used to assist in the judgment process. For effect items with a P-value less than 0.05 but an F-value less than 1, the data preprocessing process and the rationality of the model construction were re-examined. After confirming that there were no errors, they were included in the set of significant impact items. Finally, the sets of significant impact items affecting the extent and the sets of significant impact items affecting the intensity were determined, providing a definite object for subsequent quantification of the contribution of each significant item.

[0035] In S3, the contribution of each significant item is calculated using the partial correlation coefficient to determine the influence weight. Specifically, in implementation, the calculation object is first determined to be the screened significant influence items. These items include main effect items, second-order interaction effect items, and third-order interaction effect items that have a significant effect on the extent or intensity. They have been formed into independent sets of significant influence items according to the extent and intensity. Duplicate and overlapping effect items are explicitly removed from the set to ensure that each significant item corresponds to only a single influence dimension and to avoid weight superposition bias during calculation.

[0036] Subsequently, the partial correlation coefficient analysis method is introduced. This method can accurately quantify the net correlation between a single significant item and its extent or intensity, while controlling for interference from other significant influencing items. This lays the foundation for contribution calculation. In practice, for each significant item, all other significant items in the same set are used as control variables. By fixing the values ​​of these control variables, the individual correlation between the target significant item and the indicator is analyzed in isolation, avoiding correlation bias caused by interference from multiple factors.

[0037] The core of the contribution calculation is the ratio of partial sum of squares to total sum of squares. The partial sum of squares refers to the amount of variation of the dependent variable (expansion or intensity) explained by a significant effect in the analysis of variance model, while the total sum of squares is the total variation of the dependent variable. This ratio can directly reflect the actual contribution of each significant item to the target indicator. During the calculation, professional statistical analysis tools are used to extract the partial sum of squares of the corresponding effect items from the output of the analysis of variance model, and the total sum of squares is the total variation of the dependent variable after model fitting, ensuring that the data source is completely consistent with the model output.

[0038] In practice, statistical analysis tools are used to calculate the partial sum of squares of each effect in the set of items significantly affected by the expansion degree and the total sum of squares of the set. Then, the contribution of each significant item to the expansion degree is obtained by ratio calculation. Four decimal places are retained during the calculation to ensure the accuracy of the contribution value. The contribution of each effect in the set of items significantly affected by the intensity degree is calculated in the same way, and the two sets of calculations are performed independently to avoid cross-referencing of the significant item data of expansion degree and intensity degree.

[0039] Finally, the contribution values ​​of each significant item are converted into corresponding influence weights. During the conversion, the sum of the contributions of all significant items under the same indicator is used as the benchmark. The contribution of a single significant item is divided by the sum to obtain the corresponding weight, ensuring that the sum of the weights of all significant items for the same target indicator is 1. If there is a deviation of ±0.01 in the total weight after calculation, the weights of each significant item are adjusted proportionally to correct it, ensuring the rationality of the weight logic. The significant items are then sorted from high to low contribution to form a quantitative result table containing the name of the significant item, its corresponding contribution, and its influence weight. This provides a core basis for determining the priority of input variables when constructing the coupled prediction model.

[0040] In step S4, a dual-output prediction model is constructed using the random forest algorithm with significant impact terms as input. Training and testing sets are then used for model training and accuracy verification. Specifically, the input and output variables of the model are first determined. The input variables are sets of significant impact terms selected for expansion and intensity, including significant main effect terms, second-order interaction effect terms, and third-order interaction effect terms. The output variables are the expansion and intensity of the fluidized solidified soil. This constructs a dual-output prediction model capable of simultaneously predicting two target indicators. The random forest algorithm is chosen as the model algorithm because it has strong anti-interference capabilities and nonlinear fitting capabilities, making it suitable for prediction needs under multi-variable interactive influences.

[0041] Next, the core parameters of the random forest model were determined. The number of decision trees was set to 100-200 to balance model accuracy and computational efficiency. The splitting of decision tree nodes was based on the Gini coefficient, and the minimum number of samples per leaf node was set to 5 to avoid overfitting.

[0042] The processed sample data was then randomly and hierarchically divided into training and test sets in a 7:3 ratio. This hierarchical division ensures that the distribution characteristics of the variable combinations in the training and test sets remain consistent, improving the reliability of model training. The training set data was input into the initially constructed random forest model for iterative parameter training. The model performance was optimized by continuously adjusting parameters such as the growth rules of the decision tree and the priority of feature selection. The model's fitting effect on the training set was monitored in real time during training. After the model training was completed, the test set data was input into the model for prediction to obtain the predicted values ​​of scalability and strength.

[0043] Using root mean square error (RMSE) and coefficient of determination (R²) 2 As a core evaluation metric for model accuracy, RMSE is used to quantify the average deviation between predicted and actual values. 2 Used to measure a model's ability to explain data variation, when the model's prediction R-value for expansion is... 2 ≥0.92, Predicted intensity R 2 If the accuracy is ≥0.95, the model is considered to meet the accuracy requirements. If the prediction accuracy of any target indicator does not meet the standard, the significant impact items are re-screened. The input variable set can be optimized by expanding the screening range of interaction effect items and adding higher-order interaction effect items. Then, the model is rebuilt based on the new significant impact items and training and validation work is carried out until the model accuracy meets the established standard.

[0044] If the target is not met in S4, the model will be re-optimized. Specifically, in implementation, if the accuracy of the dual-output prediction model constructed using the random forest algorithm fails to meet the target, i.e., the expansion prediction R... 2 <0.92 or intensity prediction R 2When the value is less than 0.95, return to the multivariate interaction effect quantitative analysis stage and re-screen for significant influencing terms. This can be achieved by expanding the scope of interaction effect term screening, such as including more product terms of two variables in the second-order interaction effect term consideration, or adding new third-order interaction effect terms such as cement admixture-hardener ratio-curing cycle, to optimize the input variable set. After determining the new set of significant influencing terms for expansion and strength, use this new set as the input variables to reconstruct the dual-output prediction model. Divide the training and test sets in a 7:3 ratio, and retrain and verify the model accuracy. Repeat this process until the expansion prediction R value is obtained. 2 ≥0.92 and intensity prediction R 2 ≥0.95, to ensure the model accuracy meets the requirements.

[0045] In S5, expansion and strength optimization targets are set, and the optimization algorithm is used to solve the problem with the prediction model as a constraint. In practice, the optimization targets are first determined by combining the construction application requirements and mechanical performance standards of the fluidized solidified soil. The expansion needs to meet the construction fluidity requirements of 200mm-350mm, and the 28-day strength needs to meet the mechanical performance requirements of ≥3MPa. The core is to achieve the optimal synergy between expansion and strength within this range, so as to ensure that it meets the flow requirements during construction and pouring, and also ensures the load-bearing capacity of the solidified structure.

[0046] Next, the core elements of the optimization problem were determined, with cement content, curing agent ratio, mixing time, and curing cycle as decision variables. These variables directly affect the mix proportion and construction process of the fluidized solidified soil and are the key control objects for achieving the optimization goal. At the same time, the completed and accurate prediction model was used as a constraint condition. This model can accurately reflect the quantitative relationship between decision variables and expansion and intensity, providing a reliable basis for optimization solution.

[0047] Subsequently, the non-dominated sorting genetic algorithm, which is adapted to the needs of multi-objective optimization, was selected as the core solution algorithm. This algorithm can efficiently search the Pareto optimal solution set under multiple constraints, which meets the needs of scalability and intensity dual-objective collaborative optimization.

[0048] During algorithm execution, the population size is set to 100 to ensure the coverage of the search space; the number of iterations is set to 500 to give the algorithm sufficient time to converge to the optimal solution region; the crossover probability is set to 0.8 to improve the diversity and evolutionary ability of the population; and the mutation probability is set to 0.05 to introduce appropriate mutations while maintaining population stability to avoid local optima.

[0049] Finally, the algorithm is launched to optimize the solution. Through genetic operations such as selection, crossover, and mutation, the parameter combinations in the population are continuously updated iteratively. Combined with the coupled prediction model, the expansion and strength values ​​corresponding to each parameter combination are calculated in real time. Finally, the Pareto optimal solution set that meets the optimization objective is selected, which provides a basis for subsequent parameter selection.

[0050] In practice, the non-dominated sorting genetic algorithm has two limitations: first, when dealing with the strong interaction characteristics of multivariate fluidized solidified soil, it is prone to getting trapped in local optima due to excessive decay of population diversity, thus missing the optimal parameter combination of "low cement content - high synergistic performance"; second, the convergence speed is limited by the number of iterations, making it difficult to quickly output usable parameters in urgent engineering scenarios. Therefore, this application further proposes an "adaptive weighted particle swarm optimization and gradient descent hybrid algorithm," which achieves efficient global spatial exploration through particle swarm optimization and completes accurate local area excavation by combining gradient descent. This not only meets the dual-objective collaborative optimization requirements but also specifically addresses the core contradiction in the parameter optimization of fluidized solidified soil: "no omissions in global search and high precision in local optimization." The details are as follows: First, considering the construction application requirements and mechanical performance standards of fluidized solidified soil, a synergistic optimization objective is determined. For example, the spread must meet the construction fluidity requirement of 200mm-350mm, and the 28-day strength must meet the mechanical performance requirement of ≥3MPa. A bi-objective optimization function with constraint penalty terms is constructed to achieve synergistic optimality and avoid invalid parameters being substituted into the calculation. The mathematical expression of the bi-objective optimization function is: ; In the formula, X is the decision variable vector (X=[c,r,t,T], where c is the cement content, r is the curing agent ratio, t is the mixing time, and T is the curing period); E(X) is the expansion of the prediction model output; f 28 (X) represents the 28-day intensity output by the prediction model; ω1 and ω2 are weighting coefficients (both set to 0.5 to achieve balanced optimization of the two objectives); 350mm is the upper limit of the expansion range, and 150mm is the target range span of the expansion range; f 28,max This represents the maximum intensity value in the sample over 28 days.

[0051] The constraints include the range of values ​​for decision variables and the constraints for the prediction model. The range of values ​​for decision variables includes c∈[8%,15%], r∈[0.05,0.2], t∈[60s,180s], T∈{1d,3d,7d,28d}; the constraints for the prediction model refer to E(X), f 28 (X) is calculated by a random forest dual-output model with compliant accuracy, ensuring the accuracy of the performance correlation.

[0052] The first stage uses an adaptive weighted particle swarm optimization algorithm for global optimization, including the following steps: The input data consists of a set of significant influencing terms selected through analysis of variance, the range of decision variables, a bi-objective optimization function, and constraints. The adaptive weighted particle swarm optimization algorithm updates position and velocity by simulating the particle flight process, configuring inertial weights that dynamically adjust with the iteration process and particle performance to balance global exploration and local convergence capabilities.

[0053] The inertia weight calculation employs a nonlinear adaptive weight formula, which reduces the weight of high-performing particles to focus on local areas, and decreases the weight in the later stages of iteration to accelerate convergence. The inertia weight calculation formula is as follows: ; In the formula, ω(k) is the inertia weight of the k-th iteration; ω max The initial weights are ω. max A value of 0.9 ensures global exploration, ω min For minimum weight, ω min A value of 0.4 ensures convergence in later stages; k is the current iteration number, K max Let K = 300, where F is the total number of iterations. i (k) is the fitness value of the i-th particle in the k-th iteration (determined by the optimization function F). X Calculation); F avg F represents the average fitness of all particles in the k-th iteration; min (k) represents the optimal fitness in the k-th iteration; (To avoid a denominator of 0.)

[0054] The particle velocity and position are updated by combining individual optimal and global optimal information. The update formula is as follows: ; ; In the formula, v i (k+1) represents the velocity of the i-th particle in the (k+1)-th iteration; x i (k+1) represents the position of the i-th particle in the (k+1)-th iteration; For individual learning factors, c2 r1 and r2 are random numbers in the interval [0,1]; p best,i The historical best position of the i-th particle; g best This represents the globally optimal position for all particles.

[0055] Iteration termination and candidate set output: When the number of iterations reaches K max =300, or the change in the global optimal fitness over 20 consecutive iterations. When the iteration stops, select the population that satisfies the condition. , The positions of the particles form a candidate solution set S, and global optimization is completed.

[0056] The second stage involves local refinement using gradient descent, including the following steps: The input data is the set of candidate solutions S output from the first stage. The gradient information of the objective function is used to fine-tune each candidate solution to improve parameter accuracy. Since the maintenance period T in the decision variable is a discrete value, gradient optimization is only performed on the continuous variables c, r, and t, while T remains unchanged.

[0057] Gradient calculation is performed by taking the partial derivatives of the continuous variables in the optimization function F(X) to obtain the gradient vector, which reflects the direction of the influence of parameter changes on the objective function. The gradient calculation formula is: ; F1 and F2 are the expansion and strength sub-objectives of the optimization function, respectively. The partial derivatives are calculated through numerical differentiation of the random forest model, i.e., by applying small perturbations to the parameters. Calculate the change in the objective function.

[0058] The parameter update uses the momentum gradient descent formula, introducing a momentum term to accelerate convergence and suppress oscillations. The parameter update formula is as follows: ; In the formula, X new For the updated parameters; X old η is the current parameter; η is the learning rate, controlling the step size, so that η = 0.001; α is the momentum coefficient, so that α = 0.9; X prev These are the parameters from the last update.

[0059] Local optimization terminates when 50 gradient updates are performed for each candidate solution, or when the parameter changes... Stop when the time is right, add the optimized parameters to a temporary set, and finally remove the parameters that do not meet the constraints to form a refined Pareto optimal solution set.

[0060] In S5, parameter combinations are selected from the optimal solution set based on construction economy and convenience. Specifically, in implementation, the core criteria for determining construction economy and convenience are first determined. Among them, the principle of minimizing cement content is given to the economic aspect, since cement is a key material in the cost composition of fluidized solidified soil, and reducing the cement content can directly reduce raw material procurement expenditures. The principle of controlling the mixing time to 90s-120s is given to the convenience aspect. This time range can ensure that the components of fluidized solidified soil are mixed evenly, and can be adapted to the operating efficiency of conventional construction equipment, avoiding uneven mixing due to too short a mixing time, or affecting the construction progress due to too long a mixing time.

[0061] For the Pareto optimal solution set obtained from multi-objective optimization, parameter combinations with mixing times in the range of 90s-120s are first screened to form a candidate subset that meets the requirements of construction convenience. Then, the parameter combinations in this candidate subset are sorted by cement content, and the parameter combination with the lowest cement content is selected as the preliminary optimization result. If there are multiple parameter combinations with the same cement content in the candidate subset, a second screening is conducted by combining the economy of the curing agent ratio (prioritizing the lower ratio while meeting performance requirements) and the rationality of the curing cycle (prioritizing conventional curing cycles that match the project schedule, such as 7 days or 28 days). Finally, an optimal construction parameter combination that simultaneously meets the requirements of economy, convenience, and basic expansion and strength is determined, ensuring that the screening result not only meets the actual needs of the project but also remains consistent with the overall collaborative optimization objective.

[0062] In S6, the on-site trial mixing and pouring of fluidized solidified soil is carried out according to the optimal parameters. Specifically, the details of the optimal combination of construction parameters are first determined, including the specific percentage of cement content, the precise value of the curing agent ratio, the determined number of seconds for mixing time, and the determined number of days for curing period. In addition, the actual scenario of the construction site (foundation pit filling or roadbed subbase) is considered to make good preparations for the early stage of construction.

[0063] Before construction, check the quality certificates of all raw materials (cement, curing agent, aggregate, etc.) to ensure they meet relevant standards. Simultaneously, thoroughly debug the mixing equipment (such as a forced mixer) and calibrate its metering system to ensure the metering accuracy of components such as cement, curing agent, and water. The metering error for cement and curing agent should be controlled within ±1%, and the metering error for mixing water within ±0.5%. Then, add the aggregate, cement, curing agent, and other dry materials to the mixing equipment sequentially according to the optimal parameters. First, dry mix for 30 seconds to achieve initial uniformity. Then, add the specified amount of water for wet mixing, strictly controlling the wet mixing time to the optimal mixing time. Observe the material state during mixing to ensure the mixture has a uniform color and is free of lumps or segregation.

[0064] In step S6, actual performance data is measured and compared with predicted values. If the deviation meets the standard, the parameters are determined; otherwise, supplementary data is added, the model is updated, and the solution is recalculated. Specifically, after the on-site trial mixing and pouring of the fluidized solidified soil is completed according to the optimal parameters, representative test blocks are promptly selected to prepare standard test blocks. At the same time, the spread of the on-site mixture is directly measured using a standard slump spread meter, accurate to 1 mm. The standard test blocks are then cured according to the corresponding curing cycle. The curing process strictly follows relevant specifications to control temperature and humidity conditions. The compressive strength is measured using a universal pressure testing machine at curing nodes such as 1 day, 3 days, 7 days, and 28 days, accurate to 0.01 MPa. The spread data and strength data of each curing cycle obtained from the actual tests are fully recorded, and the actual construction parameters, on-site ambient temperature, raw material batches, and other related information during the trial mixing and pouring are simultaneously compiled.

[0065] Subsequently, the actual measured expansion and strength data are compared one by one with the corresponding predicted values ​​output by the coupled prediction model, and the deviation between the two is calculated. The expansion deviation is calculated as the absolute value of the difference between the actual measured value and the predicted value, and the strength deviation is calculated as the absolute value of the difference between the actual compressive strength and the corresponding predicted value in each maintenance cycle.

[0066] Based on the preset deviation standard, if the expansion deviation is ≤5mm and the strength deviation of each key curing cycle (especially 28d) is ≤0.1MPa, the deviation is deemed to meet the standard. The optimal parameters of this set are then formally determined as construction parameters, incorporated into the project construction technical documents, and used to guide subsequent batch construction. If the expansion deviation exceeds 5mm or the strength deviation of any key curing cycle exceeds 0.1MPa, the deviation is deemed not to meet the standard. In this case, the complete parameter information of this trial mixing, actual test data, and on-site environmental records are added to the original training set. The data source is marked as "on-site verification supplementary data" to ensure traceability. Then, the process returns to the prediction model construction stage. The model is retrained and the parameters are optimized using the supplemented training set. After the model is updated, the multi-objective optimization parameter solution step is executed again to obtain a new parameter combination. Subsequently, the on-site trial mixing, performance testing, and deviation comparison process are repeated according to the new parameters until the deviation between the actual test value and the model prediction value meets the standard. Finally, the qualified construction parameters are determined.

[0067] This application also protects a control system for the coordinated optimization of the spread and strength of fluidized solidified soil, such as... Figure 2As shown, it includes: a data preprocessing module for outlier removal, variable standardization and dummy variable transformation, and calculation of correlation coefficients to form a correlation matrix; an analysis of variance module for constructing an analysis of variance model containing main effects and interaction effects, screening significant terms and determining their weights; a prediction model construction module for building a dual-output model based on random forest, dividing the dataset for training and accuracy verification and optimization; a parameter optimization and selection module for setting optimization objectives, solving the model with the prediction model as constraints, and selecting parameter combinations based on economic considerations; and a field verification and update module for comparing actual and predicted data, determining parameters to meet the criteria, or supplementing data to update the model.

[0068] This application also protects a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method for synergistic optimization control of the expansion and strength of fluidized solidified soil as provided in the embodiments of the present invention.

[0069] The computer storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, system, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, system, or device.

[0070] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which can send, propagate, or transmit programs for use by or in conjunction with an instruction execution system, system, or device.

[0071] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including—but not limited to—wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0072] The above description is merely one specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for synergistic optimization and control of the spread and strength of fluidized solidified soil, characterized in that, Including the following steps: For fluidized solidified soil, samples were designed based on all influencing factors. Parallel samples were prepared for each group. The spread and strength of the fluidized solidified soil were measured, and the variable parameters and corresponding performance data were recorded to form test data. The Grubbs criterion is used to remove outliers from the test data, the numerical variables of the test data are standardized, the categorical variables of the test data are converted into dummy variables, the correlation coefficient is calculated to determine the variable association, and a correlation matrix is ​​formed. A variance analysis model was constructed, including main effect terms and interaction effect terms, and significant influencing terms were screened. The contribution of each significant term was calculated by partial correlation coefficient, and the influence weight was determined. Using significant impact factors as input, a dual-output prediction model is constructed using the random forest algorithm. The model is trained and its accuracy is verified by dividing the training set and the test set. If the model does not meet the standard, it is re-optimized. The expansion and strength optimization objectives are set, the prediction model is used as a constraint, the optimization algorithm is used to solve the problem, and the parameter combination is selected from the optimal solution set based on the construction economy and convenience. The fluidized solidified soil was mixed and poured on-site according to the optimal parameters. The actual performance data was measured and compared with the predicted values. If the deviation met the standard, the parameters were determined. Otherwise, the data was supplemented, the model was updated, and the solution was obtained again.

2. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The method involves designing samples for fluidized solidified soil based on all influencing factors, preparing parallel samples for each group, measuring the spread and strength of the fluidized solidified soil, and recording the variable parameters and corresponding performance data to form test data. Specifically, this includes: determining all influencing factors and the value range of each variable for the spread and strength of the fluidized solidified soil; designing samples according to the principle of full factorial design, preparing parallel samples for each variable combination; measuring the spread and compressive strength of the fluidized solidified soil at each curing cycle using standard instruments; recording the variable parameters corresponding to each group of samples and the simultaneously measured spread and strength data, and compiling the variable parameters corresponding to each group of samples and the simultaneously measured spread and strength data to form complete test data.

3. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The method of using Grubbs' criterion to remove outliers from the test data is as follows: the expansion and intensity data of each group of samples are statistically analyzed, the mean and standard deviation are calculated, and according to Grubbs' criterion, samples whose test values ​​deviate from the group mean by more than 3 times the standard deviation are identified as outliers; finally, outliers are removed and valid data are retained.

4. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The standardization process for numerical variables in the test data specifically involves: determining the range of numerical variables, including influencing factors and their extent and intensity data; calculating the mean and standard deviation of the sample data for each numerical variable; and using standardization formulas to transform the original data to obtain standardized values, so that all variables are on the same order of magnitude.

5. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The process of converting categorical variables in the test data into dummy variables, calculating correlation coefficients to determine variable associations, and forming a correlation matrix involves: identifying the categorical variables of construction sites in the test data and converting them into dummy variables suitable for subsequent processing; determining the range of variables involved in the correlation coefficient calculation, including the converted dummy variables, standardized numerical influencing factors, and the two target indicators of extent and intensity; calculating the linear correlation coefficients between each influencing factor and extent and intensity, determining the association direction by the sign of the coefficient, and judging the association strength by the absolute value; and organizing the correlation coefficient results among all variables to construct a complete correlation matrix, presenting the basic association characteristics of the variables.

6. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The construction of the variance analysis model, including main effect terms and interaction effect terms, and screening for significant influencing terms, specifically involves: constructing an variance analysis model to isolate the single and interaction effects of each influencing factor, providing core input variables for the dual-output prediction model; the main effect terms include the influencing factors of the spread and strength of the fluidized solidified soil, and the interaction effect terms include the second-order product of any two variables in the main effect terms and the third-order product of specific three variables; two independent models are constructed with spread and strength as dependent variables and the main effect terms and interaction effect terms as independent variables, respectively; the F-value and P-value of each effect term are obtained through variance analysis, with the F-value reflecting the degree of influence and the P-value determining the statistical significance; significant influencing terms are screened with a P-value less than 0.05 as the criterion, and the sets of significant influencing terms affecting spread and strength are determined respectively.

7. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The method of calculating the contribution of each significant item using partial correlation coefficients and determining the influence weights involves the following steps: The significant influence items are the calculation objects, including main effect items, second-order and third-order interaction effect items that have a significant effect on expansion or intensity, and are formed into independent sets according to expansion and intensity respectively; partial correlation coefficients are introduced to control interference from other items and quantify the net association between a single significant item and the target indicator; the contribution of each significant item is calculated using the ratio of the partial sum of squares to the total sum of squares, yielding the contribution of expansion and intensity significant items respectively. The contribution level is converted into an influence weight, and the results are sorted by contribution level to form a quantitative result table containing the name of the significant item, the contribution level, and the weight.

8. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The process involves using significant impact items as input and constructing a dual-output prediction model using the random forest algorithm. The model is then divided into training and test sets for training and accuracy verification. Specifically, this involves using selected significant impact items (based on expansion and strength) as input and expansion and strength as outputs, and constructing a dual-output prediction model using the random forest algorithm. Core model parameters are set, and the preprocessed sample data is hierarchically divided into training and test sets. The training set is used for iterative optimization of model parameters, and the test set is used for model prediction verification. The root mean square error and coefficient of determination are used as accuracy evaluation metrics. If the accuracy is not up to standard, the process is repeated: significant impact items are re-selected, the input variable set is optimized, the model is rebuilt, and the training and verification process is repeated.

9. The method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to claim 1, characterized in that, The aforementioned optimization objectives for scalability and strength are set, constrained by the prediction model, and solved using an optimization algorithm. Specifically, the objectives for scalability and strength optimization are determined, key construction variables are determined as decision variables, and a prediction model with satisfactory accuracy is used as a constraint. An algorithm adapted to multi-objective optimization is selected as the solution algorithm, the algorithm is started to iteratively update the parameter combination, the corresponding performance values ​​are calculated based on the prediction model, and the optimal solution set that meets the optimization objectives is selected.

10. A system utilizing the method for synergistic optimization and control of the spread and strength of fluidized solidified soil according to any one of claims 1-9, characterized in that, include: The data preprocessing module is used for outlier removal, variable standardization and dummy variable transformation, and to calculate correlation coefficients to form a correlation matrix; The ANOVA module is used to construct ANOVA models containing main effects and interaction effects, screen significant items, and determine the weights of influence. The prediction model building module is used to build a dual-output model based on random forest, and to perform dataset partitioning for training and accuracy verification and optimization. The parameter optimization and filtering module is used to set optimization objectives, solve the problem with the prediction model as a constraint, and filter parameter combinations based on economic considerations. The on-site verification and update module is used to compare actual and predicted data, determine parameters if they meet the criteria, or supplement data to update the model.

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