Ultra-high performance concrete compressive strength prediction method based on grey wolf optimization algorithm

Abstract

The invention discloses an ultra-high performance concrete compressive strength prediction method based on a grey wolf optimization algorithm. The method mainly solves the technical problem that it is difficult to comprehensively, accurately and efficiently predict the compressive strength of the ultra-high performance concrete through existing empirical formulas or numerical simulation. According to the method, the initial threshold value and the weight value of the BP neural network model are optimized through the grey wolf optimization algorithm (GWO), the problem that the model falls into local optimum can be effectively avoided, then the robustness and generalization ability of the model are improved, and the prediction precision is higher. And the SHAP feature importance method is adopted to identify the feature which contributes the greatest to the prediction result, so that the simplification of the quantity of variables is realized, the redundancy caused by potential correlation among the variables is avoided, the extracted input variables have the minimum redundancy, and the prediction accuracy and the prediction efficiency of the neural network model are effectively improved after parameter optimization.

Description

Technical Field

[0001] The present invention relates to the field of concrete, and specifically to a method for predicting the compressive strength of ultra-high performance concrete based on the Grey Wolf optimization algorithm. Background Art

[0002] Ultra-high performance concrete (UHPC) has excellent mechanical properties and durability. It is an ultra-high strength cement-based material with high strength, high toughness and low porosity. It minimizes the defects (pores and microcracks) inside the material by increasing the fineness and activity of the components, thereby possessing ultra-high strength and high durability. It has the characteristics of low water-cement ratio, high cementitious material content, and high particle packing density. Its compressive strength can usually reach two to three times that of traditional concrete. It has been widely used in important infrastructure such as bridges, railways, super high-rise buildings, and harsh environments such as severe cold, high salinity and oceans.

[0003] The raw materials of UHPC mainly include cement, mineral admixtures, fine aggregates, steel fibers, water reducing agents, etc. The tensile strength and impact resistance of ultra-high performance concrete are improved by adding an appropriate amount of steel fibers, and the mechanical and durability properties of ultra-high performance concrete are improved by adding an appropriate amount of nanomaterials. However, for ultra-high performance concrete with different mix ratios, there are large differences in cost, workability, mechanical properties and durability. Accurate and reliable evaluation of the mechanical properties of ultra-high performance concrete is an important prerequisite for its widespread application in various building structures, and compressive resistance is one of the important characteristics for evaluating the mechanical properties of ultra-high performance concrete.

[0004] The mix design of ultra-high performance concrete known to the inventors is generally based on stacking models and semi-empirical methods, such as the Balomi formula that evaluates the compressive strength of concrete at standard age based on the water-cement ratio. However, more mineral admixtures are used in the preparation of ultra-high performance concrete, and the components of cementitious materials are complex. Relying solely on the water-cement ratio to express the ratio of cementitious materials to water will cause large errors in the mix design of ultra-high performance concrete. The inventors are aware of a method that takes both the water-cement ratio and the water-binder ratio into consideration at the same time in order to reduce errors in this regard. This method designs multiple groups of UHPC mixes with different water-binder ratios and water-cement ratios for testing, and analyzes the effects of the two on ultra-high performance concrete with a strength of 100 to 130 MPa. However, after fitting the relationship between the three, it was found that the R 2 It is relatively low, which means that the compressive strength of UHPC is affected by many complex factors and cannot be simply expressed by the water-binder ratio or water-cement ratio.

[0005] In addition, the inventors found in long-term research and practice that due to the complex components of ultra-high performance concrete, obvious regional differences in raw materials, and diverse mixing processes and maintenance systems, these factors are coupled with each other, and it is difficult to describe their impact on the compressive strength of UHPC through simple empirical formulas or numerical simulations. And based on traditional concrete strength tests, it is difficult to fully consider the above factors through a large number of tests, and traditional tests require a lot of time, manpower and resources, resulting in a long cycle and low efficiency for the optimization design, production practice and performance evaluation of UHPC.

[0006] The information disclosed in this background technology section is only used to deepen the understanding of the background technology of the present disclosure, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art known to those skilled in the art. Summary of the invention

[0007] In view of at least one of the above technical problems, the present disclosure provides a method for predicting the compressive strength of ultra-high performance concrete based on the Grey Wolf optimization algorithm, which mainly solves the technical problem that the existing empirical formula or numerical simulation is difficult to comprehensively, accurately and efficiently predict the compressive strength of ultra-high performance concrete.

[0008] According to one aspect of the present disclosure, a method for predicting the compressive strength of ultra-high performance concrete based on the Grey Wolf optimization algorithm is provided, which comprises the following steps: (1) Establish a multi-source data set with raw material ratio, cube size, and curing conditions as input variables and compressive strength as output variable; (2) Optimizing the initial threshold and weight of the BP neural network based on the GWO swarm intelligence algorithm, and establishing a GWO-BP neural network model based on the multi-source data set; (3) Based on the input combination and the corresponding output prediction results of the GWO-BP neural network model, the SHAP feature importance value is used to identify the feature that contributes most to the prediction result, and the optimal mix ratio of ultra-high performance concrete is determined.

[0009] In some embodiments of the present disclosure, in the step (1), the raw material ratio includes water dosage, steel fiber dosage, cement dosage, silica fume dosage, fly ash dosage, slag dosage, fine aggregate dosage, coarse aggregate dosage, high-efficiency water reducing agent dosage, steel fiber parameters, and water-cement ratio; the curing conditions include curing days and curing temperature.

[0010] In some embodiments of the present disclosure, in step (2), k groups of data from n groups of data in the multi-source data set are randomly selected as training set data, and the remaining nk groups of data are selected as test set data.

[0011] In some embodiments of the present disclosure, in step (2), the number of input layer nodes of the BP neural network is the same as the number of input variables, the number of initial hidden layer nodes is 5, and the number of output layer nodes is 1.

[0012] In some embodiments of the present disclosure, step (3) further includes the following sub-steps: (31) Importance analysis of ultra-high performance concrete compressive strength based on single input variables to determine the main input variables affecting the compressive strength of ultra-high performance concrete; (32) Based on the SHAP main effect values ​​corresponding to the main input variables, the corresponding main input variables are optimized.

[0013] One or more technical solutions provided in the embodiments of the present application have at least any of the following technical effects or advantages: 1. Optimizing the initial threshold and weight of the BP neural network model through the Grey Wolf Group Intelligent Algorithm (GWO) can effectively avoid the problem of the BP neural network model falling into the local optimal state, thereby improving the robustness and generalization ability of the model and achieving higher prediction accuracy.

[0014] 2. The SHAP feature importance method is used to identify the input variables (features) that contribute most to the prediction results, and the specific impact of each input variable (feature) on the prediction results is intuitively explained through visualization methods, thereby reducing the number of variables and avoiding redundancy caused by potential correlation between variables. The extracted input variables have minimal redundancy, and after parameter optimization, the prediction accuracy and efficiency of the neural network model are effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 1 is a data distribution statistical diagram of a multi-source data set in an embodiment of the present application; wherein (a) is a pie chart of the distribution range of UHPC compressive strength data; and (b) is a statistical diagram of the frequency of occurrence of each input variable.

[0016] Figure 2 This is a marginal histogram of the effects of various input variables on the compressive strength of UHPC in one embodiment of the present application.

[0017] Figure 3 This is a heat map of the correlation between each input variable and the compressive strength of UHPC in an embodiment of the present application.

[0018] Figure 4 It is an iteration curve diagram of the fitness values ​​of the PSO-BP and GWO-BP models in one embodiment of the present application.

[0019] Figure 5 Graph showing the prediction performance of the BP neural network model in one embodiment of the present application; (a) is a fitting effect graph; and (b) is a comparison graph between the predicted value and the true value.

[0020] Figure 6 Graph showing the prediction performance of the PSO-BP model in one embodiment of the present application; (a) is a fitting effect graph; and (b) is a comparison graph between the predicted value and the true value.

[0021] Figure 7 1 is a diagram of the prediction performance of the GWO-BP model in one embodiment of the present application; (a) is a fitting effect diagram; (b) is a comparison diagram of the predicted value and the true value.

[0022] Figure 8 This is a comparison chart of the prediction results of the BP neural network model, the PSO-BP model and the GWO-BP model in one embodiment of the present application.

[0023] Fig. 9 This is a global feature importance analysis diagram of UHPC compressive strength in one embodiment of the present application; (a) is a feature significance diagram; (b) is a SHAP summary diagram.

[0024] Fig.10 This is an importance analysis diagram of the local characteristics of UHPC compressive strength in one embodiment of the present application.

[0025] Fig.11 This is a SEM image of the lightweight UHPC hydration product under different curing conditions in an experimental example of this application. DETAILED DESCRIPTION

[0026] The programs involved or relied upon in the following embodiments are all conventional programs or simple programs in the technical field, and those skilled in the art can make conventional selections or adaptive adjustments according to specific application scenarios. In order to better understand the technical solution of this application, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods. Example

[0027] In order to solve the technical problem that it is difficult to comprehensively, accurately and efficiently predict the compressive strength of ultra-high performance concrete based on the existing empirical formula or numerical simulation when predicting the compressive strength of ultra-high performance concrete in the prior art, this example discloses a method for predicting the compressive strength of ultra-high performance concrete based on the gray wolf optimization algorithm, which specifically includes the following steps: (1) A multi-source data set was established with raw material ratio, cube size, and curing conditions as input variables and compressive strength as output variable.

[0028] In order to realize the training of the ultra-high performance concrete compressive strength prediction model, in this embodiment, a multi-source data set is first established. In this embodiment, the ultra-high performance concrete raw material ratios including water content (CW), steel fiber content (CSF), cement content (CC), silica fume content (CSE), fly ash content (CFH), slag content (CSP), fine aggregate content (CFA), coarse aggregate content (CCA), high-efficiency water reducer content (CSR), steel fiber parameters (SFP), and water-cement ratio (W / B) are used as independent variables. In addition, in this example, considering the influence of size effect and curing conditions on compressive strength, the cube size (CSZ), curing days (CDS) and curing temperature (CT) are also used as input variables of the model to participate in the training and prediction of the model, and the compressive strength is used as the output variable.

[0029] Specifically, in this embodiment, a total of 338 sets of experimental data were collected, and the statistical distribution of each input variable and output variable is shown in Table 1 and Figure 1 and Figure 2 , and the heat map of the correlation between each input variable and compressive strength can be found in Figure 3 In addition, in this embodiment, k groups of data from the n groups of data in the multi-source data set are randomly selected as training set data, and the remaining nk groups of data are used as test set data.

[0030] .

[0031] (2) The initial threshold and weight of the BP neural network are optimized based on the GWO swarm intelligence algorithm, and the GWO-BP neural network model is established based on multi-source data sets.

[0032] BP neural network is a multi-layer feedforward neural network. The network model is trained based on the back propagation algorithm. It includes an input layer, several hidden layers and an output layer, which can realize nonlinear mapping. It is based on the gradient descent method. By using the gradient search method, the parameters of the model are updated in the opposite direction of the gradient of the loss function, which can maximize the reduction of the mean square error between the actual output value and the expected output value of the model. In this embodiment, the number of input layer nodes of the BP neural network is the same as the number of input variables, the initial number of hidden layer nodes is selected to be 5, and the number of hidden nodes is adjusted according to the prediction error according to experiments with different hidden layer nodes. In addition, since the BP neural network predicts a single target variable in this example, the number of output layer nodes is set to 1.

[0033] However, the inventors found in the process of implementing this embodiment that the BP neural network, due to the use of the gradient descent algorithm, is prone to fall into the dilemma of local optimum during its optimization process and cannot obtain the global minimum. Therefore, in order to improve the robustness and generalization ability of the prediction neural network model, in this embodiment, a swarm intelligence algorithm is used to optimize the initial threshold and weight of the BP neural network model.

[0034] In this embodiment, the particle swarm optimization algorithm and the grey wolf optimization algorithm are used to optimize the BP neural network respectively, so as to explain the advantages of the GWO-BP neural network model in the present invention.

[0035] Specifically, the particle swarm optimization algorithm (PSO) is an algorithm proposed based on the communication and cooperation mechanism of bird flocks or fish schools. It designs a massless particle to simulate individuals in a bird flock. In this embodiment, let the dimension of the search space be D and the number of populations be n. Then i The particles include the speed representing the speed of movement V i and the position representing the direction of movement X i Two properties, each particle in the search space according to the fitness function F ( i ) independently seek the optimal solution and record the optimal solution as the extreme value of the current individual P i And share it with other particles in the entire particle swarm, so that the optimal individual extreme value is used as the current global optimal solution of the entire particle swarm P g , then all particles in the particle swarm are based on their current individual extreme values P i and the shared current global optimal solution P g Adjust the speed and position of the individual to achieve search optimization in the global space, thereby avoiding falling into the local optimal solution. Among them, the speed attribute represents the momentum of the particle. If t is a certain moment, the new particle position can be calculated by adding the speed vector to the current position. The update method of the particle speed and coordinates is based on equations (1) and (2): v id k+1 =w·v id k +c 1 ·r 1 ( P id k -x id k) +c 2 ·r 2 ( P gd k -x gd k ) (1).

[0036] X id k+1 =X id k +v id k+1 (2).

[0037] In the formula, w represents the weight of the corresponding particle; k represents the number of iterations of the corresponding particle, v id k Represents iteration k Second is the particle i exist d The velocity component in the dimension; P id k Represents iteration k Secondary particles i The individual extreme point P i of d Dimensional component; P gd k Represents iteration k The next group extreme point P g of d Dimensional component; X id k Represents iteration k The individual extreme point d Dimensional component; x gd k Represents iteration k The group extreme point d Dimensional component; c 1 and c 2 are learning factors that are non-negative constants respectively; r 1 and r 2 is a random value in the range [0, 1].

[0038] In addition, the Gray Wolf Optimization (GWO) algorithm is a swarm intelligence algorithm based on the wolf pack hierarchy and hunting process. It simulates different hierarchies by dividing the gray wolves into four types: α The wolf is the leader of the group and is at the first level. It is mainly responsible for making various decisions and passing them down to the entire group. β The wolf is a subordinate wolf, at the second level, responding α The wolf gave the order and passed it to the γ Wolf and ω wolves, and supervise them; γ Wolves include scout wolves, guard wolves, old wolves and predator wolves, which are at the third level and are responsible for assisting α Wolf and β The wolf completes the roundup of its prey; ω The wolf is at the fourth level and must obey the wolves at other levels to maintain the stability of the population structure. Correspondingly, the position of each wolf represents a set of solutions to the problem. In this embodiment, in each iteration, the most suitable solution is set as α , the second and third optimal solutions are β and γ The remaining solutions are ω ,but: X w = ( X α +X β +X γ ) / 3 (3).

[0039] In the formula, X w for ω The location of the wolf iteration; X α , X β , X γ They are α、β , γ Wolf Pair ω The wolf's location estimate, where: X α = X 1 − A 1 ·D α (4).

[0040] Xβ = X 2 − A 2 ·D β (5).

[0041] X γ = X 3 − A 3 ·D γ (6).

[0042] In the formula, X 1 , X 2 and X 3 Respectively represent α、β , γ The current position of the wolf, A represents the convergence factor. When |A|>1, the search range is expanded and the prey is searched globally; when |A|<1, the search range is narrowed and the prey is approached; D represents the distance vector between the gray wolf individual and the prey, specifically: D=|K·X p (t)−X(t)| (7).

[0043] A=2a·rd 2 −a (8).

[0044] K=2rd 1 (9).

[0045] a=2−2t / max (10).

[0046] In the formula, X p (t) Represents the location of prey; X(t) represents the position vector of the gray wolf in the wolf pack; a is the control factor, and a decreases linearly from 2 to 0 as the number of iterations increases; K is the random vector coefficient; rd 1 and rd 2 is a random value in the range of [0, 1]; t represents the current number of iterations, and max represents the maximum number of iterations. The random vector coefficients are used to display random search behavior from the initial iteration to the final iteration optimization process, providing a global search of the decision space and preventing the algorithm from falling into a local optimum.

[0047] In this embodiment, the optimization results of the particle swarm optimization algorithm (PSO) and the gray wolf optimization algorithm (GWO) for the BP neural network are shown in Figure 4 As shown by Figure 4 It can be seen that the particle swarm optimization algorithm (PSO) still decreases in the 32nd generation after a long number of iterations, while the fitness value of the grey wolf optimization algorithm (GWO) decreases more simply and quickly. When it iterates to the 15th generation, the fitness value has stabilized. Therefore, in this embodiment, a more advantageous GWO-BP neural network model is established based on a multi-source data set, and the model is used to predict the compressive strength of the corresponding ultra-high performance concrete under the corresponding mix ratio.

[0048] In addition, in this embodiment, in order to further accurately evaluate the performance of the algorithm, the mean absolute error (MAE), mean absolute percentage error (MAPE), and determination coefficient (R 2 ), root mean square error (RMSE) are used to evaluate the prediction performance of BP neural network model, PSO-BP neural network model and GWO-BP neural network model respectively. Specifically: (11).

[0049] The evaluation results are shown in Table 2 and Figures 5 to 8 .

[0050] .

[0051] From the data in Table 2, we can see that all three models have achieved good training results, but the generalization ability of the BP neural network is weak, so the BP neural network is optimized by the particle swarm optimization algorithm (PSO) or the gray wolf optimization algorithm (GWO) to improve the prediction accuracy of the test set. Figure 5 to Figure 7 It can be found that the prediction points of the GWO-BP neural network model are ideally close to the fitting line, the effect of the PSO-BP neural network model is second, and the prediction results of the BP neural network model are the most scattered. In addition, Figure 8 Specifically, the error analysis diagram of the predicted compressive strength of the validation set samples by the BP neural network model, the PSO-BP neural network model, and the GWO-BP neural network model and the actual compressive strength of the validation set samples shows that in the validation set, the absolute error between the predicted value and the actual value of the GWO-BP neural network model is the smallest, followed by the PSO-BP neural network model, and the BP neural network model has the largest absolute error.

[0052] (3) Based on the input combination and the corresponding output prediction results of the GWO-BP neural network model, the SHAP feature importance value is used to identify the features that contribute most to the prediction results, and the optimal mix ratio of ultra-high performance concrete is determined.

[0053] Due to the large number of input variables, in order to effectively streamline the input variables to save computing time, avoid redundancy caused by potential correlation between the input variables, and reasonably eliminate some input variables that have no contribution or little contribution to the prediction results, in this embodiment, feature engineering is used to optimize the variables, thereby extracting features (variables) that can reflect the changes in the output variables from the input variables, so that the extracted features have minimal redundancy, thereby making the prediction model more accurate and efficient.

[0054] Specifically, in this embodiment, in order to explain the necessity of using feature engineering for variable optimization, 11 different input combinations are designed. The prediction results corresponding to different input combinations based on the GWO-BP neural network model are shown in Table 3 (X in the table is 1 is the steel fiber parameter, X 2 is the water-binder ratio, X 3 For water, X 4 For steel fiber, X 5 For cement, X 6 is silica fume, X 7 is fly ash, X 8 is slag, X 9 is fine aggregate, X 10 is coarse aggregate, X 11 is a water reducing agent, X 12 For maintenance conditions, X 13 is the cube size).

[0055] .

[0056] From the prediction results shown in Table 4, it can be seen that combination 1 has the highest accuracy because it provides as much information input as possible; combination 9 has the lowest accuracy because it has only seven input variables and does not consider several other important input variables. However, it is not difficult to find from Table 4 that the accuracy of the model does not simply increase with the increase in the number of input variables. For example, although combination 11 has only four input variables (steel fiber parameters, water-cement ratio, curing conditions and cube size), its performance evaluation results are higher than those of other combinations except combination 1. Therefore, it is necessary to optimize the input variables and reduce redundancy.

[0057] In this embodiment, the Grey Wolf Optimization algorithm (GWO) is used to improve the prediction accuracy and generalization ability of the BP neural network model. However, since its prediction method involves multiple single models and integrated voting / combination algorithms, it faces a black box problem. In order to effectively identify redundant input variables, in this example, the SHAP feature importance method is used to identify the features (input variables) that contribute the most to the results among the input variables, and reflect the degree of influence of each feature on a specific prediction. Specifically, SHAP calculates the marginal contribution of features to the model output, and can decompose the prediction result into the sum of the contributions of each input variable. Its output is a data set containing SHAP values ​​and with the same dimensions as the model training set. The SHAP value can reveal the degree of influence (importance) of the input variables on the prediction results of the GWO-BP neural network model. In this example, the SHAP feature importance identification includes the following sub-steps: (31) Importance analysis of ultra-high performance concrete compressive strength based on single input variables was conducted to determine the main input variables affecting the compressive strength of ultra-high performance concrete.

[0058] See also Fig. 9 The global importance analysis diagram of UHPC compressive strength based on a single feature is shown in the figure. Fig. 9 (a) reveals the overall importance of each input variable, among which the curing condition has the highest SHAP value of +12.78, indicating that the curing condition has the highest contribution to the compressive strength of UHPC. The water-binder ratio and steel fiber parameters show SHAP values ​​of +7.51 and +6.75, respectively, which indicates that the water-binder ratio and steel fiber parameters also have high importance in estimating the compressive strength of UHPC. Silica fume, cube size, water reducer, etc. have medium levels of SHAP values, indicating that the importance of this variable in predicting the compressive strength of UHPC is at a medium level. Fig. 9 (b) is a SHAP summary diagram, which can reflect the positive or negative impact of each input variable on the output. The color of the point in the figure indicates its impact intensity, where blue represents a smaller value and red represents a larger value. For example, the red point of the water-binder ratio (water_binder_ratio) in the figure appears on the negative semi-axis, indicating that the water-binder ratio has a significant negative impact on the compressive strength of UHPC, that is, an increase in the value of the water-binder ratio will significantly reduce the compressive strength of UHPC. Therefore, the overall importance of each input variable on the output variable can be reflected through feature global importance analysis, and the positive or negative impact of each input variable on the output prediction can be determined.

[0059] In this example, curing conditions, steel fiber parameters, water-cement ratio, silica fume and cube size are determined as important input variables of the model. Ignoring these five variables will lead to a sharp drop in prediction accuracy (R 2From 0.94417 to 0.37892). Among them, the appropriate curing temperature and curing days can promote the cement hydration reaction, so that the strength of concrete can be fully exerted. If the curing conditions are insufficient or inappropriate, the porosity in the concrete will increase, resulting in a decrease in the compressive strength of UHPC. Parameters such as the type, shape, length and dosage of steel fibers will also affect the compressive strength of ultra-high performance concrete. Reasonable selection of steel fiber parameters can improve the toughness and crack resistance of concrete, thereby improving the compressive strength of UHPC; the smaller the water-binder ratio, the higher the strength of concrete is usually. Appropriately reducing the water-binder ratio can reduce the porosity and void ratio in the concrete and improve the compressive strength. Silica fume is a high-quality concrete admixture that can improve the early strength and durability of concrete. Adding an appropriate amount of silica fume can improve the microstructure of concrete, reduce porosity, and increase compressive strength; due to the size effect of concrete, the size of the concrete specimen also has a certain influence on the compressive strength test results.

[0060] (32) Based on the SHAP main effect values ​​corresponding to the main input variables, the corresponding main input variables are optimized.

[0061] After determining the effective and reasonable main input variables and the positive or negative impact of the main input variables on the prediction, in order to further optimize the parameters of the main input variables, see Fig.10 The SHAP main effect value diagram corresponding to each input variable parameter shown reflects the degree of influence of the change of a single feature (input variable) on the result in model prediction. Parameter optimization is performed based on the influence of the variable parameter change reflected by the SHAP main effect value corresponding to the main input variable on the prediction result, thereby improving the model prediction accuracy and efficiency.

[0062] Experimental example In order to verify the effectiveness of the prediction of the GWO-BP neural network model, UHPC specimens of different sizes were designed in this case and compressive strength tests were carried out after curing under various curing conditions.

[0063] Specifically, in this experimental example, the cement in the UHPC cementitious material is P·O42.5 cement, silica fume, first-grade fly ash and S95-grade blast furnace granulated slag, wherein the density of cement, silica fume, fly ash and slag is 3150 kg / m 3 、670 Kg / m 3 , 2600 Kg / m 3 、2960 Kg / m 3; The fine aggregate is quartz sand with a particle size range of 1.25-2.36 mm; the additive is a UHPC-specific polycarboxylic acid high-performance water-reducing agent with a maximum water reduction rate greater than 45% and a solid content of 25%; the fiber is a copper-plated long straight fiber (13 mm long, 0.2 mm in diameter). In this experimental example, the water-cement ratio is 0.18, the water-reducing agent is 3% (as a percentage of the cementitious material), and steel fibers with an aspect ratio of 65 are used, the volume yield is 2.0%, and the specific UHPC matrix mix ratio is shown in Table 4.

[0064] .

[0065] In addition, in this experimental example, three temperatures were designed: room temperature, 40°C, and 90°C; three curing times: 1 day, 3 days, and 7 days; three cube specimen sizes: 40 mm, 70.7 mm, and 100 mm; a total of 81 specimens. For the specific test plan, see Table 5.

[0066] .

[0067] In this experimental example, when making the cubic test block, the cementitious material and fine aggregate (quartz sand) were first mixed and stirred for 3 minutes, then the water reducer was added and stirred for 2 minutes, and then water was added and stirred for 6 minutes until it was in a fluid state, and steel fibers were added to the material and stirred for 6 minutes. After the steel fibers were evenly distributed, the material was poured into the mold to form a cubic test block. After 24 hours, the mold was removed and the test blocks were taken out and placed in a high-temperature curing box at 40℃ and 90℃ and a standard curing room at 20℃ for curing. The high-temperature curing box was heated to 40℃ and 90℃ at a heating rate of 10℃ / h, respectively, and the temperature was maintained for 1 day, 3 days and 7 days, and the test blocks that reached the curing time were taken out and cooled to room temperature, that is, the curing was completed.

[0068] The test blocks cooled to room temperature were tested in accordance with the GB / T 31387-2015 "Reactive Powder Concrete" specification, where the test blocks were first subjected to a flexural test and then a compression test using a fixture. In this case, a YAW-5000 5000KN pressure testing machine was used to continuously and uniformly load at a rate of 1.0MPa / s. The test results are shown in Table 6 and Fig.11 .

[0069] .

[0070] Since concrete is a composite material composed of aggregate, water and silicate cement, under standard curing conditions, its main hydration products are calcium silicate hydrate (CSH) gel, calcium hydroxide (CH), ettringite (AFt) and monosulfide calcium sulfoaluminate hydrate (AFm). Fig.11It can be seen that under different curing conditions, due to the lower water-cement ratio of UHPC, the cement paste matrix is ​​relatively dense, it is difficult to find large pore structures in the hardened cement paste matrix, and there are a large number of flocculent CSH gels in the cement paste matrix. Under standard curing, a small amount of needle-rod-like AFt grows in an interlaced manner in UHP, and CH crystals grow in a plate-like manner; under steam curing, it can be seen that UHPC has flaky CH.

[0071] Specifically, under standard curing conditions, the hydration products of UHPC mainly include CSH gel, calcium hydroxide (CH), calcium sulfoaluminate (AFt) and monosulfide hydrated calcium sulfoaluminate (AFm). Under such curing conditions, due to the relatively low temperature and humidity, the hydration reaction rate is slow, resulting in a relatively high content of CH. In addition, the Ca / Si ratio of CSH gel is high, which indicates that under standard curing, the reaction degree of silicate is low, the molecular chain length of CSH gel is short, and the microstructure is relatively loose.

[0072] In contrast, steam curing significantly promotes the hydration process of UHPC. Under high temperature conditions, AFt is more easily decomposed to form AFm, because high temperature promotes the phase transition of AFt to AFm. At the same time, steam curing accelerates the depolymerization of silicon-oxygen tetrahedrons in mineral admixtures from polymers to monomers and dimers, thereby promoting the process of secondary hydration reactions. This process not only accelerates the conversion of CH to CSH gel, but also consumes CH and generates more CSH gel. After steam curing, silica fume and fly ash in UHPC are consumed in large quantities, because under autoclaving conditions, the SiO in these materials 2 The activity was stimulated, which promoted the reaction with CH and formed more CSH gel.

[0073] Under steam curing, the average molecular chain length of CSH gel is the longest, while that under standard curing is the shortest. This phenomenon indicates that with the increase of curing temperature, the average molecular chain length of CSH gel gradually increases. High temperature stimulates SiO 2 The activity of the UHPC gel paste makes the hydration of the UHPC gel paste produce more silicon-oxygen tetrahedrons and silicon-oxygen dimers to form polymers. In addition, the high temperature also promotes the breakage of aluminum-oxygen hexahedrons, generating more aluminum-oxygen tetrahedrons and pentahedrons, which bridge with the silicon-oxygen in the polymer, further increasing the length of the CSH gel molecular chain.

[0074] In summary, steam curing promotes cement hydration and activates SiO 2 The activity of CSH gel is increased, more CSH gel is generated, and the average molecular chain length of CSH gel is increased, thereby improving the microstructure and performance of UHPC.

[0075] The UHPC compressive strength predicted by the GWO-BP algorithm is compared with the measured compressive strength, and the results are shown in Table 7. As shown in Table 7, the GWO-BP neural network model can accurately predict the compressive strength of UHPC under different mix ratios, and has high prediction accuracy and reliability.

[0076] .

[0077] Although some preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0078] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the inventive concept. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for predicting the compressive strength of ultra-high performance concrete based on the Grey Wolf optimization algorithm, characterized in that: The steps include: (1) Establish a multi-source data set with raw material ratio, cube size, and curing conditions as input variables and compressive strength as output variable; (2) Optimizing the initial threshold and weight of the BP neural network based on the GWO swarm intelligence algorithm, and establishing a GWO-BP neural network model based on the multi-source data set; (3) Based on the input combination and the corresponding output prediction results of the GWO-BP neural network model, the SHAP feature importance value is used to identify the feature that contributes most to the prediction result, and the optimal mix ratio of ultra-high performance concrete is determined.

2. The method for predicting the compressive strength of ultra-high performance concrete according to claim 1, characterized in that: In the step (1), the raw material ratio includes water dosage, steel fiber dosage, cement dosage, silica fume dosage, fly ash dosage, slag dosage, fine aggregate dosage, coarse aggregate dosage, high-efficiency water reducing agent dosage, steel fiber parameters, and water-cement ratio; the curing conditions include curing days and curing temperature.

3. The method for predicting the compressive strength of ultra-high performance concrete according to claim 1, characterized in that: In the step (2), k groups of data from the n groups of data in the multi-source data set are randomly selected as training set data, and the remaining nk groups of data are used as test set data.

4. The method for predicting the compressive strength of ultra-high performance concrete according to claim 1, characterized in that: In step (2), the number of input layer nodes of the BP neural network is the same as the number of input variables, the number of initial hidden layer nodes is 5, and the number of output layer nodes is 1.

5. The method for predicting the compressive strength of ultra-high performance concrete according to claim 1, characterized in that: The step (3) further includes the following sub-steps: (31) Importance analysis of ultra-high performance concrete compressive strength based on single input variables to determine the main input variables affecting the compressive strength of ultra-high performance concrete; (32) Based on the SHAP main effect values ​​corresponding to the main input variables, the corresponding main input variables are optimized.

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