UHPC ratio reverse design method based on machine learning and global optimization algorithm

Abstract

The invention relates to a UHPC ratio reverse design method based on machine learning and a global optimization algorithm, and belongs to the technical field of building materials. The method comprises the following steps: firstly, establishing a UHPC performance prediction model through a machine learning method, and predicting fluidity, compressive strength and breaking strength by taking mix proportion parameters as input; secondly, constructing a multi-objective optimization loss function according to preset objective performance; searching by utilizing a global optimization algorithm to obtain a mix proportion candidate solution set meeting target performance constraints; and finally, screening and outputting a recommended mix proportion scheme from the candidate solution set according to a preset performance priority strategy. According to the method, local disturbance sampling is further combined to refine the candidate solution set, intelligent and data-driven reverse design of the UHPC mix proportion is achieved, the design period can be remarkably shortened, the mix proportion design precision and efficiency can be improved, the test cost can be reduced, and a UHPC mix proportion scheme with balanced performance or optimal specific performance can be flexibly generated according to engineering requirements; wide application prospects are realized.

Description

Technical Field

[0001] This invention belongs to the field of building materials technology, and specifically relates to a reverse design method for UHPC mix proportions based on machine learning and global optimization algorithms. Background Technology

[0002] Ultra-high performance concrete (UHPC) is widely used in bridge engineering, prefabricated buildings, and special structures due to its high strength, high toughness, and high durability. The performance of UHPC is influenced by a variety of parameters in the mix design, including the proportion of cementitious materials, water-cement ratio, admixture dosage, and fiber volume fraction. These parameters are generally coupled with each other, making mix design difficult. Despite the increasing demand for UHPC in engineering projects, its mix design still faces significant challenges.

[0003] Currently, UHPC mix design mainly relies on empirical methods, orthogonal experimental methods, or regression analysis. These methods typically require a large amount of experimental data, have long experimental cycles, and are costly. Furthermore, the design results are highly dependent on engineers' experience, making it difficult to guarantee design efficiency and stability when there are high parameter dimensions or complex performance requirements. Especially in new material research and development and large-scale application scenarios, traditional mix design methods are no longer sufficient to meet the needs of rapid, accurate, and scalable engineering design.

[0004] In recent years, machine learning methods have begun to be applied to predict the performance of unbalanced high-performance concrete (UHPC), estimating performance indicators such as flowability and compressive strength based on existing mix proportion data. However, existing research is mostly "forward prediction," that is, performance is extrapolated from the mix proportion, and it is still difficult to effectively achieve "reverse design" that automatically solves the corresponding mix proportion based on the target performance indicator. At the same time, there are generally competing relationships between different performance indicators in UHPC. For example, improved flowability may lead to a decrease in strength, and it is difficult to find the optimal solution that satisfies multiple objective constraints in the high-dimensional parameter space by relying solely on manual parameter tuning.

[0005] Therefore, there is an urgent need for an intelligent design method that can take the target performance as input, automatically search and recommend mix proportion parameters, and realize efficient and accurate reverse design of UHPC mix proportions to reduce experimental costs, improve design efficiency, and meet the needs of practical engineering applications. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a reverse design method for UHPC mix proportions based on machine learning and global optimization algorithms, which can quickly obtain mix proportion schemes that meet design performance requirements and have excellent constructability.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A UHPC coordination ratio reverse design method based on machine learning and global optimization algorithms, the specific steps of which are as follows:

[0009] 1) Establish performance prediction models: Using machine learning methods, with the mix proportion parameters of ultra-high performance concrete as input and the corresponding fluidity, compressive strength and flexural strength performance indicators as output, fluidity prediction models, compressive strength prediction models and flexural strength prediction models are trained.

[0010] 2) Constructing a multi-objective loss function: Based on the preset target fluidity, target compressive strength, and target flexural strength, the deviation between the output of the performance prediction model and the corresponding target performance indicators is constructed as a multi-objective optimization loss function;

[0011] 3) Global optimization search: Using the amount of each raw material in the mix proportion as the optimization variable and the multi-objective optimization loss function as the optimization objective, the global optimization algorithm is used to search for a set of candidate solutions for the mix proportion that meet the target performance constraints within the range of the raw material amounts.

[0012] 4) Recommended solution output: For each candidate solution in the candidate solution set of the mix proportion, the performance is evaluated and the deviation is calculated. According to the preset performance priority strategy, one or more recommended mix proportion schemes are selected from the candidate solution set as the design result.

[0013] Preferably, the method for establishing the performance prediction model in step 1) includes the following steps:

[0014] 1.1) Data collection: Collect the mix proportions of ultra-high performance concrete and their corresponding fluidity, compressive strength and flexural strength data to form the ultra-high performance concrete mix proportion-performance database;

[0015] 1.2) Data processing: Remove outlier data and fill in missing values ​​in the database; and divide the dataset into training set and test set;

[0016] 1.3) Model Training: Using the mix proportion parameters as input variables and the fluidity, compressive strength and flexural strength performance indicators as output variables, a machine learning regression model is used to train the training set to establish a fluidity prediction model, a compressive strength prediction model and a flexural strength prediction model.

[0017] Preferably, in step 1.2), the data processing sets precise value constraints or discrete value correction rules for specific raw material parameters in the mix proportion, such as water-cement ratio, cement content, total amount of cementitious materials and admixture dosage, to ensure that the mix proportion generated during the optimization process meets the performance requirements and workability requirements of ultra-high performance concrete.

[0018] Preferably, the machine learning regression model described in step 1.3) is trained using a random forest regression model, and the parameters are optimized through cross-validation and grid search to improve prediction accuracy and model generalization ability.

[0019] Preferably, the multi-objective loss function in step 2) is composed of the weighted sum of the squares of the liquidity prediction error, the compressive strength prediction error, and the flexural strength prediction error, and the weighting coefficients can be set according to the performance priority strategy.

[0020] Preferably, the global optimization algorithm in step 3) is a differential evolution algorithm, and the search range is controlled by an empirical constraint strategy in this field, so as to improve search efficiency and avoid infeasible design solutions.

[0021] Preferably, the candidate mix design obtained in step 3) is further screened by local perturbation sampling to obtain a refined candidate mix design that is closer to the target performance in the optimization space.

[0022] Preferably, the performance-priority strategy in step 4) is a multi-objective trade-off strategy, which selects one or more combination schemes with the smallest multi-objective loss function value.

[0023] Preferably, the cementitious material in the mix proportion includes one or more of cement, fly ash, slag, nano-silica, silica fume, and lime powder; the admixture is a polycarboxylate-based high-efficiency water-reducing agent; and the fiber is steel fiber or polystyrene fiber.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] This invention can quickly generate UHPC mix proportion schemes that meet design requirements based on target performance indicators. Combined with a performance-priority strategy, it can obtain concrete mix proportions with balanced performance or optimal specific performance. By combining machine learning models with global optimization, it not only shortens the design cycle but also improves the economy and constructability of mix proportion schemes. It is applicable to fields such as bridge engineering, prefabricated buildings, and special structures.

[0026] This data-driven approach can adapt to the introduction of new materials and changes in complex engineering requirements, providing a new intelligent, data-driven paradigm for UHPC design in fields such as bridge engineering, prefabricated buildings, and special structures, and has broad application prospects. Attached Figure Description

[0027] Figure 1 This is a flowchart of the intelligent design process for the UHPC mix proportion of the present invention. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings and embodiments:

[0029] This invention provides a UHPC fit ratio reverse design method based on machine learning and global optimization. The specific steps are as follows, and see also... Figure 1 :

[0030] 1) Establish performance prediction models: Using the mix proportion parameters of UHPC as input and their corresponding flowability, compressive strength and flexural strength performance indicators as output, flowability prediction models, compressive strength prediction models and flexural strength prediction models are trained by machine learning methods to characterize the mapping relationship between mix proportion parameters and performance indicators.

[0031] 2) Construct a multi-objective loss function: Based on the set target performance requirements, including target fluidity, target compressive strength and target flexural strength, construct a multi-objective loss function by the deviation between the model prediction value and the target value, which is used to measure the degree of deviation between the mix proportion scheme and the target performance.

[0032] 3) Global optimization search: The content of each raw material in the mix proportion (including but not limited to cement, silica fume, sand, water, admixtures and steel fiber) is set as the optimization variable. The multi-objective loss function is used as the optimization objective. The global optimization algorithm is used to search within its reasonable value range to obtain the candidate solution set of the mix proportion that meets the performance constraints.

[0033] 4) Recommended solution output: For each candidate solution in the candidate solution set of the mix proportion, the performance is evaluated and the deviation is calculated. According to the preset performance priority strategy, one or more recommended mix proportion schemes are selected from the candidate solution set as the design result.

[0034] Specifically, in step 1), the performance prediction model is established as follows:

[0035] 1.1) Data Collection: Mix proportions of ultra-high performance concrete (UHPC) and their corresponding flowability, compressive strength, and flexural strength data were collected to form an UHPC mix proportion-performance database. In this embodiment, by reviewing relevant domestic and international literature, publicly available experimental reports, and internal laboratory data accumulation, approximately 1228 sets of UHPC data with different mix proportion parameters and performance indicators were collected, forming an initial database (stored in a 1.xlsx file). These data cover various combinations of cementitious materials, aggregates, admixtures, and fibers, with mix proportion parameters serving as input features and corresponding performance indicators as output labels. The input features include 24 parameters, such as cement content, silica fume content, sand content, water content, water-reducing agent content, and steel fiber volume fraction, which are represented by columns 1 to 24 in the dataset. The collected data has good representativeness and diversity, effectively supporting the model's generalization ability.

[0036] 1.2) Data processing: The data in the database is cleaned, including removing outliers and completing missing items; then, the cleaned dataset is divided into training and test sets according to a preset ratio using the sklearn.model_selection.train_test_split function, with the training set accounting for 80% and the test set accounting for 20%, for machine learning training, optimization and final performance evaluation.

[0037] 1.3) Model Training: Using the mix proportion parameter as the input variable and the fluidity, compressive strength, and flexural strength performance indicators as the output variables, a random forest regression model was used to train the training set to establish a UHPC performance prediction model. The random forest regression model was chosen because of its excellent fitting ability to nonlinear data, good generalization performance, and robustness to noise and outliers. During model training, the 5-fold cross-validation and grid search method were implemented using the function sklearn.model_selection.GridSearchCV to optimize the key hyperparameters of the random forest model. The optimized hyperparameters and their search ranges include: the number of decision trees (n_estimators): searched between [200, 400]. The maximum depth (max_depth): searched between [10, 20, None] (None indicates no depth restriction). The minimum number of samples required for a leaf node (min_samples_split): searched between [2, 5]. The maximum number of features to be split (max_features): search within the range of ['sqrt', 0.7] ('sqrt' represents using the square root of the total number of features). After grid search and cross-validation optimization, the optimal parameter combination determined in this embodiment is as follows: for the compressive strength model, n_estimators is 400, max_depth is none, min_samples_split is 2, and max_features is 0.7. For the flexural strength model, n_estimators is 400, max_depth is none, min_samples_split is 2, and max_features is 0.7. For the fluidity model, n_estimators is 200, max_depth is 20, min_samples_split is 2, and max_features is 'sqrt'. Finally, three independent prediction models were established to predict fluidity, compressive strength, and flexural strength, respectively. These models were saved as .pkl files for later use.

[0038] Specifically, in step 2), the method for constructing the multi-objective loss function is as follows:

[0039] 2.1) Based on the flowability prediction model, compressive strength prediction model and flexural strength prediction model trained in step 1), the mix proportion to be optimized is used as input to predict its corresponding flowability (Pflow), compressive strength (Pcomp) and flexural strength performance values ​​(Pflex).

[0040] 2.2) Based on the set target performance requirements, such as target flowability (Tflow), target compressive strength (Tcomp), and target flexural strength (Tflex), calculate the deviation between the predicted performance value and the target performance value.

[0041] 2.3) The performance deviations are summed using a weighted or equally weighted method to form a multi-objective loss function, which is used to quantitatively characterize the degree of difference between the mix design and the target performance requirements. The mathematical expression of the multi-objective loss function is:

[0042] (1)

[0043] In this loss function, the weights of each performance metric are set to 1.0 by default. This setting is suitable for "multi-objective trade-off strategies," which prioritize the satisfaction of each performance metric during optimization. In practical applications, if it is necessary to emphasize a specific performance metric (for example, when a "single-objective optimal strategy" requires prioritizing compressive strength), the weights of the corresponding terms in the loss function can be modified to larger values, thereby guiding the global optimization algorithm to be more inclined to satisfy that priority metric.

[0044] Specifically, in step 3), the global optimization search is implemented as follows:

[0045] 3.1) The amount of each raw material in the mix proportion is used as an optimization variable, and its upper and lower limits are set according to the sample range in the database to ensure that the search results are engineering feasible.

[0046] 3.2) Using the multi-objective loss function constructed above as the optimization objective function, the Differential Evolution (DE) global optimization algorithm is implemented by calling the function scipy.optimize.differential_evolution. In a preferred embodiment, the key parameters of the DE algorithm are set as follows: population size (popsize) is 20, maximum number of iterations (maxiter) is 200, and the polish=True option is enabled to perform local fine-tuning after the iteration is completed. These parameter settings aim to balance search efficiency and solution accuracy, improving the ability to find the global optimum while ensuring the convergence of the algorithm.

[0047] 3.3) During the optimization search process, for mix proportion parameters such as cement strength grade and water-cement ratio that are discrete or constrained, range clipping or nearest neighbor rounding is used to ensure that they always meet the actual engineering requirements.

[0048] 3.4) The optimal solution best_x output by the differential evolution algorithm is used as the initial solution for the mix proportion. To obtain a refined set of candidate mix proportion solutions that more closely approximate the target performance in the optimization space, and to improve the flexibility and selection space of the recommended scheme, local perturbation sampling is performed centered on this initial solution. In a preferred embodiment, during 1500 perturbation samplings, for each mix proportion parameter of best_x, new mix proportion schemes are randomly generated within ±2% of the parameter value (achieved through relative range perturbation using np.random.normal(scale=0.02 * span)). These perturbed schemes are then ensured to remain within the original search boundary using np.clip(), and the discrete values ​​and ranges of the cement strength grade and water-cement ratio are corrected again, thereby generating a rich set of candidate mix proportion solutions that meet the constraints.

[0049] Specifically, in step 4), the recommended solution is output as follows:

[0050] 4.1) For each candidate solution in the mix ratio candidate solution set obtained from local perturbation sampling, input it into the trained performance prediction model to calculate its predicted performance, and calculate its deviation from the target performance and the total loss function value based on the target value. These results are compiled into a DataFrame file.

[0051] 4.2) Filter and rank candidate solutions according to a preset performance-priority strategy:

[0052] Multi-objective trade-off strategy: Under this strategy, the DataFrame is sorted in ascending order by its 'loss' value, and the five combinations with the smallest loss function values ​​are selected as recommended options. These options demonstrate the best overall balance across various performance metrics.

[0053] 4.3) The recommended combination schemes obtained from the screening are output to the recommended_multi_target.xlsx file. These files clearly list the specific combination parameters, prediction performance values, and corresponding loss function values ​​for each recommended scheme, making it convenient for users to select and refer to.

[0054] In a preferred embodiment, for the set target performance (e.g., target flowability: 190mm, target compressive strength: 128MPa, target flexural strength: 21MPa), a multi-target trade-off strategy is adopted, and the method of the present invention obtains the following recommended mix proportions and predicted performance, as shown in Table 1.

[0055] Table 1. Recommended UHPC Mate Ratios and Performance for Multi-Objective Priority

[0056] plan 1 2 3 4 5 6 7 8 9 10 <![CDATA[f c ]]> <![CDATA[f f ]]> SF loss 1 794.0 42.5 156.0 1081 2.36 174 21 1 0.18 13 190.09 128.76 21.03 <![CDATA[2.4×10 -5 ]]> 2 794.3 42.5 155.6 1083 2.36 174 21 1 0.18 13 190.09 128.73 21.06 <![CDATA[2.5×10 -5 ]]> 3 794.1 42.5 155.9 1080 2.36 174 21 1 0.18 13 190.09 128.77 21.06 <![CDATA[2.7×10 -5 ]]> 4 793.5 42.5 156.5 1080 2.36 174 21 1 0.18 13 190.09 129.10 21.19 <![CDATA[8.3×10 -5 ]]> 5 793.6 42.5 156.4 1083 2.36 174 21 1 0.18 13 190.09 129.10 21.19 <![CDATA[8.3×10 -5 ]]>

[0057] Note: 1 is cement dosage (kg / m3), 2 is cement compressive strength (MPa), 3 is silica fume content (kg / m3), 4 is quartz sand content (kg / m3), 5 is maximum aggregate size (mm), 6 is moisture content (kg / m3), 7 is high-efficiency water-reducing agent content (kg / m3), 8 is steel fiber content (%), 9 is steel fiber diameter (mm), 10 is steel fiber length (mm), fc is compressive strength (MPa), ff is flexural strength (MPa), SF is fluidity (mm), and loss is total loss value.

[0058] As can be seen from Table 1, the method of the present invention can effectively identify the UHPC mix design that meets the target performance requirements. All predicted performance indicators are highly close to the target values, and the total loss values ​​are all on the order of 10⁻⁵, which proves the effectiveness and accuracy of the method.

[0059] To further verify the engineering applicability and accuracy of the reverse design method described in this invention, the recommended mix proportion scheme (Scheme 1) with the best comprehensive evaluation in Table 1 above was selected for laboratory trial mixing verification. First, specimen preparation was carried out. The experimental raw materials were selected from those with similar physicochemical properties to those in the model database. Specifically, P·I 42.5 silicate cement and silica fume were used as cementitious materials, high-purity quartz sand was used as aggregate, polycarboxylate superplasticizer with a solid content of 40% was used as admixture, and straight copper-plated steel fibers were used as reinforcing materials. The specimens were stirred and molded according to the standard UHPC preparation process. After molding for 24 hours, the specimens were demolded and subjected to standard steam curing at 90℃ for 48 hours. Second, performance tests and comparisons were conducted on the specimens. The measured performance results are as follows: flowability (spreadability) was 242 mm, compressive strength was 134.0 MPa, and flexural strength was 16.4 MPa. The measured results were compared and analyzed with the set target values ​​(flowability 190 mm, compressive strength 128 MPa, flexural strength 21 MPa) and the model prediction values.

[0060] Based on the above test results, the analysis is as follows:

[0061] Regarding compressive strength, the measured value (134 MPa) is slightly higher than the target value (128 MPa), with a relatively small error. This indicates that the mix proportion generated by this invention has high reliability in the design of cementitious material systems, can effectively guarantee structural strength requirements, and has a certain safety margin.

[0062] Regarding flowability, the measured value (242 mm) was higher than the target value. This deviation was mainly due to the difference in sensitivity between the admixture used in the laboratory and the database samples. In practical engineering, this positive deviation is a favorable factor, meaning that costs can be further reduced by appropriately lowering the water-reducing agent dosage.

[0063] Regarding flexural strength, the measured value (16.4 MPa) differs somewhat from the target value. Given that the flexural strength of UHPC is significantly affected by steel fiber orientation and vibration compaction process, rather than being solely determined by the mix proportions, this recommended scheme already provides good matrix properties; only minor adjustments to the molding process are needed to meet the requirements.

[0064] In summary, the verification experiments show that, compared with the traditional method of blindly trying different mixes based on experience, the method of this invention can directly output a mix design with performance indicators close to the design requirements, which greatly shortens the design cycle, reduces the experimental cost, and has significant engineering practical value.

[0065] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A UHPC matching reverse design method based on machine learning and global optimization algorithms, characterized in that, Includes the following steps: 1) Establish performance prediction models: Using machine learning methods, with the mix proportion parameters of ultra-high performance concrete as input and the corresponding fluidity, compressive strength and flexural strength performance indicators as output, fluidity prediction models, compressive strength prediction models and flexural strength prediction models are trained. 2) Constructing a multi-objective loss function: Based on the preset target fluidity, target compressive strength, and target flexural strength, the deviation between the output of the performance prediction model and the corresponding target performance indicators is constructed as a multi-objective optimization loss function; 3) Global optimization search: Using the amount of each raw material in the mix proportion as the optimization variable and the multi-objective optimization loss function as the optimization objective, the global optimization algorithm is used to search for a set of candidate solutions for the mix proportion that meet the target performance constraints within the range of the raw material amounts. 4) Recommended solution output: For each candidate solution in the candidate solution set of the mix proportion, the performance is evaluated and the deviation is calculated. According to the preset performance priority strategy, one or more recommended mix proportion schemes are selected from the candidate solution set as the design result.

2. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 1, characterized in that, The method for establishing the performance prediction model described in step 1) includes the following steps: 1.1) Data collection: Collect the mix proportions of ultra-high performance concrete and their corresponding fluidity, compressive strength and flexural strength data to form the ultra-high performance concrete mix proportion-performance database; 1.2) Data processing: Remove outlier data and fill in missing values ​​in the database; and divide the dataset into training set and test set; 1.3) Model Training: Using the mix proportion parameters as input variables and the fluidity, compressive strength and flexural strength performance indicators as output variables, a machine learning regression model is used to train the training set to establish a fluidity prediction model, a compressive strength prediction model and a flexural strength prediction model.

3. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 2, characterized in that, In step 1.2), during data processing, precise value constraints or discrete value correction rules are set for specific raw material parameters in the mix proportion, such as water-cement ratio, cement content, total amount of cementitious materials, and admixture dosage, to ensure that the mix proportion generated during the optimization process meets the performance and workability requirements of ultra-high performance concrete.

4. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 2, characterized in that, The machine learning regression model described in step 1.3) is trained using a random forest regression model, and the parameters are optimized through cross-validation and grid search to improve prediction accuracy and model generalization ability.

5. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 1, characterized in that, The multi-objective loss function mentioned in step 2) is composed of the weighted sum of the squares of the liquidity prediction error, the compressive strength prediction error, and the flexural strength prediction error. The weighting coefficients can be set according to the performance priority strategy.

6. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 1, characterized in that, The global optimization algorithm described in step 3) is the differential evolution algorithm, and it is combined with the empirical constraint strategy in this field to control the search range, so as to improve the search efficiency and avoid infeasible design solutions.

7. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 1, characterized in that, The candidate mix design obtained in step 3) is further screened by local perturbation sampling to obtain a refined candidate mix design that more closely approximates the target performance in the optimization space.

8. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 1, characterized in that, The performance-first strategy in step 4) is a multi-objective trade-off strategy, which selects one or more matching schemes with the smallest multi-objective loss function value.

9. The UHPC matching reverse design method based on machine learning and global optimization algorithm according to claim 3, characterized in that, The cementitious material in the mix proportion includes one or more of cement, fly ash, slag, nano silica, silica fume, and lime powder; the admixture is a polycarboxylate-based high-efficiency water-reducing agent; and the fiber is steel fiber or polystyrene fiber.

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