Foam concrete mechanical property prediction model optimization method considering economy

Abstract

The invention provides a foam concrete mechanical property prediction model optimization method considering economy, which comprises the following steps of: establishing a three-dimensional mesoscopic finite element model of foam concrete, then selecting material parameters and external loading condition parameters to carry out regularity analysis, and taking the parameters with relatively high influence factors as deep learning input variables; and then, a combined neural network combining a convolutional neural network (CNN) and a bidirectional gating cycle unit (BiGRU) is adopted as a prediction model, a data sample is obtained through reliable numerical model analysis, and accurate prediction of the mechanical properties of the foam concrete is realized based on the CNN-BiGRU. And finally, according to the deep learning model, setting an objective function of the compressive strength and the energy absorption capacity of the foam concrete, solving the optimal design characteristics of the foam concrete in the aspects of the compressive strength and the energy absorption capacity, and obtaining an optimal performance design scheme of the foam concrete.

Description

Technical Field

[0001] The invention relates to the field of foam concrete performance research, and in particular to a foam concrete mechanical performance prediction model optimization method considering economy. Background Art

[0002] As a porous and lightweight material, foaming agent is added to the system during the preparation process to produce a large number of closed pores in the system. It has high specific strength while being light in weight, good thermal insulation and sound absorption performance, and strong resistance to freezing and thawing. Foamed concrete is mainly composed of cement, fine aggregate, water and foaming agent. Its pore structure leads to a wide range of density (300kg / m3-1600kg / m3) and low compressive strength (0.2MPato20MPa). The energy absorption capacity of foamed concrete is also reflected in the application of tunnel engineering. In the past few decades, a large number of large-scale facilities have been built around the world. However, the production of cement consumes a lot of energy and emits carbon. Carbon dioxide accounts for 74% of the total greenhouse gas emissions. Therefore, the construction industry, which is heavily dependent on raw materials, urgently needs to make a low-carbon transformation. As a green energy alternative to traditional concrete, foamed concrete has attracted attention from the sustainable development industry. Its strength is mainly provided by the matrix. Improving the compressive strength per unit mass can obtain higher-strength foamed concrete materials while maintaining lightness and reducing carbon emissions. Energy absorption in structural vibrations such as large tunnel engineering and aircraft braking systems is also a serious problem.

[0003] Chinese patent application CN202410704522.3 discloses a method for optimizing the prediction model of the mechanical properties of foamed concrete. A three-dimensional microscopic finite element model of foamed concrete is established, and then material parameters and external loading condition parameters are selected for regularity analysis, and the parameters with higher influencing factors are used as deep learning input variables. Then, a combined neural network combining convolutional neural network (CNN), gated recurrent unit (GRU) and attention mechanism (Attention) is used as a prediction model, and data samples are obtained through numerical model analysis, and the mechanical properties of foamed concrete are predicted based on the combined neural network of CNN-GRU-Attention. This method emphasizes that the macroscopic compressive strength and energy absorption capacity of foamed concrete are affected by six factors (density, elastic modulus, Poisson's ratio, shear dilatancy angle, friction coefficient and loading rate), and predictions are made to seek the optimal solution. However, this method only analyzes the compressive strength, which will result in the lower the porosity, the higher the strength. In extreme cases, the macroscopic compressive strength of solid concrete must be the highest when other factors are consistent. The optimized result is bound to cause economic waste. It can be seen that this method fails to take economic efficiency into consideration and cannot meet engineering requirements with the least carbon emissions and the least amount of concrete.

[0004] Therefore, further research to improve the energy efficiency of building materials and reduce carbon emissions is an urgent issue that needs to be addressed. Summary of the invention

[0005] In order to solve the shortcomings of the prior art, the present invention provides an optimization method for the prediction model of the mechanical properties of foamed concrete taking into account economy, establishes a three-dimensional microscopic finite element model of foamed concrete, then selects material parameters and external loading condition parameters for regularity analysis, and uses the parameters with higher influencing factors as deep learning input variables. Then, a combined neural network combining convolutional neural network (CNN) and bidirectional gated recurrent unit (BiGRU) is used as a prediction model, and data samples are obtained through reliable numerical model analysis, and accurate prediction of the mechanical properties of foamed concrete is achieved based on CNN-BiGRU. Finally, the objective functions of the compressive strength and energy absorption capacity of foamed concrete are set according to the deep learning model, the optimal design features of foamed concrete in terms of compressive strength and energy absorption capacity are solved, and the optimal performance design scheme of foamed concrete is obtained.

[0006] The embodiment of the present invention provides the following solution: An embodiment of the present invention provides a method for optimizing a prediction model for mechanical properties of foamed concrete taking economic efficiency into consideration, the method comprising: Step 1: Establish a finite element matrix void structure model of foam concrete; Step 2: Generate data set: Use various working conditions as input parameters, apply them to the foam concrete finite element matrix void structure model, and output the unit mass compressive strength under different working conditions. s u and energy absorption value W EA , and obtain the unit mass compressive strength under different working conditions s u and energy absorption value W EA As output parameters, the input parameters and output parameters under each same working condition are a set of samples; each set of working condition combination includes density, elastic modulus, Poisson's ratio, shear dilation angle, friction coefficient, loading rate and porosity; part of the samples in the data set are used as training data sets, and the other part of the samples are used as test data sets; Step 3: Use CNN-BiGRU combined neural network to establish a foam concrete performance prediction model; Step 4: Use a multi-objective optimization method to optimize the parameters of the foam concrete performance prediction model to obtain an optimized foam concrete mechanical properties prediction model.

[0007] In an optional embodiment, step 1 uses the following steps to establish a foam concrete finite element matrix void structure model: S1.1, continuously photograph the foam concrete specimens by X-ray computed tomography to obtain a set of pore structure images; S1.2, performing bilinear interpolation processing on the pore structure image, reducing the image size, and representing the reduced set of pore structure images with a three-dimensional stacking matrix; S1.3, set the grayscale threshold, perform binarization on each grayscale value in the three-dimensional stacking matrix, reset the grayscale value of pixels greater than the grayscale threshold to the maximum value, indicating cement paste, reset the grayscale value of pixels less than or equal to the grayscale threshold to 0, indicating pore structure, and obtain a binary stacking matrix image file; S1.4, generate solid parts, divide the solid parts into networks, write the divided mesh model files into the INPUT file (input file), and complete the modeling of the initial dense concrete model; S1.5, reconstructing the foam concrete model using the binary stacked matrix image file and the initial dense concrete model; S1.6. Define the contact relationship between each unit in the dense concrete model, where the normal contact relationship between the units is hard contact, and the tangential contact relationship is controlled by the friction coefficient.

[0008] In an optional embodiment, step 2 of generating a data set includes the following process: using the ABAQUS system, using the control variable method to take different working conditions as input parameters of the foam concrete finite element matrix void structure model, extracting the ODB file results, and obtaining the unit mass compressive strength under different working conditions s u and energy absorption value W EA As output parameters, the input parameters and output parameters under each identical working condition are a set of samples.

[0009] In an optional embodiment, the foamed concrete performance prediction model described in step 3 includes an input layer, a CNN layer, a BiGRU layer and a fully connected layer, and the processing process of the foamed concrete performance prediction model includes the following steps: S3.1, input the input parameters from the input layer; S3.2, CNN layer extracts dynamic coupling characteristics from input parameters; S3.3, BiGRU layer models the dynamic changes of dynamic coupling characteristics and captures the unit mass compressive strength s u and energy absorption value W EA The temporal compliance relationship of S3.4. Compressive strength per unit mass s u and energy absorption value WEA The temporal compliance relationship of is output through the fully connected layer to obtain the final prediction result.

[0010] In an optional embodiment, the CNN layer described in step S3.1 includes a convolutional layer and a pooling layer.

[0011] In an optional embodiment, the number of convolution kernels in the convolution layer is 32, the convolution kernel size is 1×1, and the activation function is ReLU; in the pooling layer, the pool size is 1; the CNN layer outputs the feature sequence through the Dropout layer as the input of the second BiGRU layer, and finally outputs the prediction sequence through the Dense layer; the Dropout layer parameter is set to 0.2, and the number of neurons in the second BiGRU layer is set to (64, 128); wherein the model parameter BiGRU hidden layer activation function is set to ReLU, the Dropout layer parameter is 0.2, the Dense fully connected layer activation function is linear, the learning rate is 0.001, epochs=1000, batch_size=500, the loss function is MAE, and the optimizer is adam.

[0012] In an optional embodiment, step 4 includes the following process: S4.1. Use the input parameters as input variables to establish the first objective function And the second objective function : , Among them, the first objective function The purpose is to maximize the compressive strength per unit mass s u , the second objective function The purpose is to maximize the energy absorption value W EA , represents the input parameters to be optimized, x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6, x 7 ], x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6, x 7 ] is the set of input parameters, the first objective function And the second objective function The constraints are: ; S4.2. Determine an initial population of size N, obtain a first-generation offspring population of size N after selection, crossover, and mutation operations, merge the two populations, and obtain a population of size 2N; S4.3, non-dominated sorting 2N-scale population, determine the non-dominated level of individuals, and retain individuals in descending order of dominance level until the set of offspring in the next generation is larger than the size of the initial population, and record the non-dominated level L at this time; S4.4. Use crowding distance to sort the individuals in the L layer, select relatively sparse points, and avoid local maximum and minimum values. The calculation formula of crowding distance CD is: , in, M is the total number of individuals in the same layer, is the distance between the ith individual and its neighbors in order of m dimensions, is the crowding distance between the i-th individuals; S4.5. After selecting the next generation parent population, a new generation population is obtained by performing selection, crossover and mutation operations again; S4.6, looping step S4.3 to step S4.5 until the number of iterations reaches the set number of iterations, obtaining the Pareto optimal solution set; S4.7. Use the TOPSIS method to obtain the optimal solution in the Pareto optimal solution set.

[0013] In an optional embodiment, the crossover probability and the mutation probability are set to 0.6 and 0.05 respectively, the initialization population size is 100, and the maximum evolutionary generation and the stop generation are 100.

[0014] In an optional embodiment, step S4.7 includes the following process: determining the maximum unit mass compressive strength s u And maximize the energy absorption value W EA and input parameters The positive ideal solution and negative ideal solution of the optimal solution set are then obtained, and the Euclidean distance between each solution in the optimal solution set and the positive ideal solution and the negative ideal solution is then calculated. The degree of closeness between each solution and the optimal solution is thus obtained, and the solution closest to the optimal solution is taken as the optimal solution.

[0015] The beneficial effects of the present invention based on its technical solution are: (1) The present invention provides an optimization method for predicting the mechanical properties of foamed concrete with consideration of economy. First, the microscopic pore structure of foamed concrete is captured by X-ray computed tomography (X-CT), and the ABAQUS finite element calculation software is redeveloped by Python program to reconstruct the three-dimensional microscopic finite element model of foamed concrete. The numerical results are compared with the indoor experimental data to verify the reliability of the model. Then, based on the reliable numerical method, the material parameters and external loading condition parameters are selected for regularity analysis, and the parameters with higher influencing factors are used as deep learning input variables. Then, the CNN-BiGRU combined neural network is used as the prediction model. The data samples are obtained through reliable numerical model analysis, and the mechanical properties of foamed concrete are accurately predicted based on CNN-BiGRU. Finally, the objective functions of the compressive strength and energy absorption capacity of foamed concrete are set according to the deep learning model, and the optimal design features of foamed concrete in terms of compressive strength and energy absorption capacity are solved by the non-dominated sorting genetic algorithm II (NSGA-II), so as to achieve the optimal performance design of foamed concrete.

[0016] (2) If only compressive strength is analyzed, the lower the porosity, the higher the strength. In extreme cases, the macroscopic compressive strength of solid concrete is definitely the highest when other factors are the same, which is bound to cause economic waste. Considering that porosity is the main factor affecting the unit mass compressive strength, the present invention provides an optimization method for predicting the mechanical properties of foamed concrete considering economy, which introduces the unit mass compressive strength index and adds the porosity as a training factor, so as to improve economy and reduce carbon emissions while ensuring performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 The present invention is a flow chart of a foam concrete mechanical property prediction model optimization method taking economy into consideration.

[0019] Figure 2 is a schematic diagram of numerical simulation of crack development. Figure 2 2-1, 2-2, 2-3 and 2-4 are schematic diagrams of the effects when the parameter Frame in the simulation software is set to 25, 45, 75 and 100 respectively.

[0020] Figure 3 It is a schematic diagram of the foam concrete performance prediction model.

[0021] Figure 4 It is a schematic diagram of the optimal solution set. DETAILED DESCRIPTION

[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention belong to the scope of protection of the embodiments of the present invention.

[0023] The embodiment of the present invention provides a method for optimizing the prediction model of mechanical properties of foamed concrete taking into account economy, referring to Figure 1 , the method comprising: Step 1: Establish a finite element matrix void structure model of foam concrete.

[0024] S1.1. Continuously photograph the foam concrete specimens by X-ray computed tomography to obtain a set of pore structure images.

[0025] S1.2. Perform bilinear interpolation processing on the pore structure image to reduce the image size, and represent the reduced set of pore structure images with a three-dimensional stacking matrix.

[0026] S1.3. Set the grayscale threshold, binarize each grayscale value in the three-dimensional stacking matrix, reset the pixel grayscale values ​​greater than the grayscale threshold to the maximum value, indicating cement paste, reset the pixel grayscale values ​​less than or equal to the grayscale threshold to 0, indicating pore structure, and obtain a binary stacking matrix image file.

[0027] S1.4. Generate solid components, divide the solid components into networks, write the divided mesh model files into the INPUT file, and complete the modeling of the initial dense concrete model.

[0028] S1.5. Reconstruct the foam concrete model using the binarized stacked matrix image file and the initial dense concrete model.

[0029] S1.6. Define the contact relationship between each unit in the dense concrete model, where the normal contact relationship between the units is hard contact, and the tangential contact relationship is controlled by the friction coefficient.

[0030] The foam concrete specimens were subjected to uniaxial compression tests, and the foam concrete finite element matrix void structure model was subjected to uniaxial loading. The strain results of the two were well matched. In addition, the cracks of the foam concrete specimens extended diagonally as the compression progressed, and the corresponding fracture modes also occurred in the numerical simulation results of the foam concrete finite element matrix void structure model, such as Figure 2 As shown, 2-1, 2-2, 2-3 and 2-4 respectively show the effects when the parameter Frame in the simulation software is set to 25, 45, 75 and 100, proving the effectiveness of the model.

[0031] Step 2: Generate data set: Using ABAQUS system, 268 groups of working conditions (each group of working conditions includes density (Density, kg / m 3 ), elastic modulus (Modulus, MPa), Poisson's ratio (Poisson), dilatancy angle (Angle, °), friction coefficient (Friction), loading rate (Loading, mm / s) and porosity) are used as input parameters of the finite element matrix void structure model of foam concrete, and the ODB file results are extracted to obtain 268 sets of unit mass compressive strength s u and energy absorption value W EA As output parameters, the input parameters and output parameters under each identical working condition are a set of samples, and a total of 268 sets of samples are obtained.

[0032] Energy absorption value W EA It represents the external load consumed by foam concrete when it deforms. Its expression is the sum of the envelope area between the stress-strain curve and the horizontal axis, and is defined as:

[0033] Compressive strength per unit mass s u It is defined by distributing the macroscopic compressive strength of the foam concrete model to one unit:

[0034] The compressive strength s c is the first peak reached by the stress-strain curve.

[0035] According to the calculation results, the following conclusions can be drawn: (1) The influence of elastic modulus on the mechanical behavior of foam concrete is mainly reflected in the elastic stage and peak compressive strength. The larger the elastic modulus, the better the foam concrete model. s u The higher it is, the faster it reaches the peak. s u As the elastic modulus increases, s u They increased by 9.8%, 13.5%, 15.5% and 21.6% respectively. s uThe increase in energy absorption also leads to an increase in W EA They increased by 7.8%, 10.2%, 12.3% and 16.6% respectively. It can also be seen from the stress distribution cloud diagram that the increase in elastic modulus leads to more obvious stress concentration.

[0036] (2) The density of the material matrix mainly affects the mass and dynamic effect of the model, but has little effect on the mechanical response of the foam concrete model in the quasi-static process. s u and W EA Both have increased with the increase of density, increasing by 5.5% and 3.4% respectively. s u It increases with the decrease of density, which illustrates the lightweight characteristics of foam concrete as a porous material.

[0037] (3) As the Poisson's ratio increases, the foam concrete model s u It increased by 4.7%. s u It also increases with the increase of Poisson's ratio.

[0038] (4) The change in friction coefficient is mainly reflected in the mechanical behavior of the pore structure after contact, which has an impact on the foam concrete. s u Almost no impact, s u It is also almost unaffected by the coefficient of friction. W EA As the friction coefficient increases, it increases by 7.0%, 7.6%, 8.0%, and 8.4% respectively. Under greater deformation W EA The growth rate will also increase significantly.

[0039] (5) Different loading rates lead to certain dynamic effects in the model, and as the loading rate increases, s u and W EA There are certain improvements. s u They increased by 2.2%, 4.9%, 8.6% and 14.0% respectively. W EA The energy absorption capacity of the foam concrete model under dynamic effects was significantly improved, with increases of 31.8%, 35.9%, 39.7% and 49.2% respectively. s u It also increases with the increase of loading rate.

[0040] (6) Shear dilatancy angle s u and W EA Have a significant impact, s u They increased by 6.9%, 14.8%, 25.1% and 53.9% respectively. W EA They increased by 9.2%, 18.8%, 34.9%, and 81.9% respectively. The shaded area indicates W EA The difference. s u It also increases with the increase of dilatancy angle.

[0041] (7) Effect of porosity on foam concrete model s u and W EA The impact is huge. s u As the porosity increases, the model s u and W EA The stress decreases significantly, and due to the increase in the pore structure, the mutual contact behavior begins to occur earlier, resulting in a limited stress drop. s u They decreased by 34.2%, 43.7%, 39.5% and 48.7% respectively. s u They decreased by 25.8%, 34.8%, 28.2% and 37.9% respectively.

[0042] The Latin hypercube sampling method (LHS) was used to select 1000 sets of design parameter combination samples of the foam concrete finite element matrix void structure model as the finite element input parameters, and the results of the ODB file calculated by ABAQUS software were extracted to obtain 1000 sets of s u and W EA The result is used as the output parameter.

[0043] In this embodiment, 80% of the samples are set as the training data set in the model training process, and the remaining 20% ​​are used as the test data set.

[0044] The input parameter settings are shown in the following table:

[0045] Step 3: Use the CNN-BiGRU combined neural network to establish a foam concrete performance prediction model. Figure 3As shown in the figure, the foam concrete performance prediction model consists of an input layer, a CNN layer, a BiGRU layer, and a fully connected layer. The CNN layer includes a convolution layer and a pooling layer. The number of convolution kernels in the convolution layer is 32, the convolution kernel size is 1×1, and the activation function is ReLU; in the pooling layer, the pool size is 1; the CNN layer outputs the feature sequence through the Dropout layer as the input of the second BiGRU layer, and finally outputs the prediction sequence through the Dense layer; the Dropout layer parameter is set to 0.2, and the number of neurons in the second BiGRU layer is set to (64, 128); among them, the model parameters are set to set the activation function of the BiGRU hidden layer to ReLU, the Dropout layer parameter to 0.2, the activation function of the Dense fully connected layer to linear, the learning rate to 0.001, epochs=1000, batch_size=500, the loss function to MAE, and the optimizer to adam.

[0046] The processing of the foam concrete performance prediction model includes the following steps: S3.1, input the input parameters from the input layer; S3.2, CNN layer extracts dynamic coupling characteristics from input parameters; S3.3, BiGRU layer models the dynamic changes of dynamic coupling characteristics and captures the unit mass compressive strength s u and energy absorption value W EA The temporal compliance relationship of S3.4. Compressive strength per unit mass s u and energy absorption value W EA The temporal compliance relationship of is output through the fully connected layer to obtain the final prediction result.

[0047] The prediction results are shown in the following table:

[0048] It can be seen that the R of the training set of the CNN-BiGRU model 2 are 0.970 and 0.984, which are accurate enough for optimization use.

[0049] Step 4: Optimize the parameters of the foam concrete performance prediction model using a multi-objective optimization method to obtain an optimized foam concrete mechanical properties prediction model. This includes the following processes: S4.1. Use the input parameters as input variables to establish the first objective function And the second objective function : , Among them, the first objective function The purpose is to maximize the compressive strength per unit mass s u , the second objective function The purpose is to maximize the energy absorption value W EA , represents the input parameters to be optimized, x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6, x 7 ], x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6, x 7 ] is the set of input parameters, the first objective function And the second objective function The constraints are:

[0050] S4.2. Determine an initial population of size N. After selection, crossover, and mutation operations, obtain a first-generation offspring population of size N. Merge the two populations to obtain a population of size 2N.

[0051] S4.3. Non-dominated sorting: For a population of size 2N, determine the non-dominated level of the individuals and retain the individuals in descending order of dominance level until the set of offspring in the next generation is larger than the size of the initial population. Record the non-dominated level L at this time.

[0052] S4.4. Use crowding distance to sort the individuals in the L layer, select relatively sparse points, and avoid local maximum and minimum values. The calculation formula of crowding distance CD is: , in, M is the total number of individuals in the same layer, is the distance between the ith individual and its neighbors in order of m dimensions, is the crowding distance between the i-th individuals.

[0053] S4.5. After selecting the next generation parent population, a new offspring population is obtained after selection, crossover and mutation operations again; in this embodiment, the crossover probability and mutation probability are set to 0.6 and 0.05 respectively, the initialization population size is 100, and the maximum evolutionary generation and stop generation are 100.

[0054] S4.6. Repeat steps S4.3 to S4.5 until the number of iterations reaches the set number of iterations, and obtain the Pareto optimal solution set.

[0055] S4.7. After the parameters are set, run it in Matlab and get the optimization process and the distribution of Parto optimal solution set as follows Figure 4 As shown. The small dotted circle frame on the Pareto frontier indicates the design point. After determining the non-dominant Pareto frontier, the TOPSIS method is used to obtain the optimal solution in the Pareto optimal solution set. The central idea of ​​this method is to first determine the positive ideal solution (optimal solution) and negative ideal solution (worst solution) of each indicator, and then calculate the Euclidean distance between each solution and the positive ideal solution and the negative ideal solution, thereby obtaining the degree of proximity between each solution and the optimal solution as a criterion for evaluating the quality of the solution: , in, is the closeness between the ith solution and the worst solution, is the closeness between the ith solution and the optimal solution, is the score of the ith solution. and The expression is as follows: , , Where m is the total number of targets, Indicates The solution is The position on the scale, and are the most positive and negative ideal solutions among all solutions. and They can be expressed by the following formulas: ,

[0056] After optimizing the sample data, the corresponding Pareto optimal solution s u and W EA 733.470 kPa / g and 217.147 kJ / m 3 The results show that the solution obtained by the method provided by the present invention can simultaneously achieve the goal of increasing s u and W EA The dual objectives of can obtain the optimal combination of design parameters.

[0057] In order to provide additional evidence for the effectiveness of the proposed optimization method for predicting the mechanical properties of foamed concrete considering economy (CNN-BiGRU), five models, including long short-term memory network (LSTM), gated recurrent unit (GRU), convolutional gated long short-term memory network (CNN-LSTM), convolutional neural network gated recurrent unit attention mechanism (CNN-GRU-Attention), and convolutional gated recurrent unit (CNN-GRU), are used to predict σ u and W EA And compare the results with the prediction results of the method (CNN-BiGRU) provided by the present invention.

[0058] The prediction effect of each model on the training set and test set is as follows:

[0059] The CNN-BiGRU prediction model has higher prediction accuracy than the other four traditional models. s u and W EA When the training set The values ​​are 0.970 and 0.984 respectively. The values ​​are 0.961 and 0.971 respectively. The CNN-BiGRU model has the highest prediction accuracy, while the LSTM model has the lowest prediction accuracy. This is because GRU integrates the output gate and the forget gate together to form an update gate, which makes it less expensive to build them and runs faster, and has excellent performance in dealing with the problem of foam concrete performance prediction. The BiGRU model has higher accuracy than GRU and CNN-GRU-Attention because in the BiGRU model, each GRU unit has an update gate and a reset gate to control the flow of information.

[0060] The update gate determines whether the current state is updated by the input at the current moment, while the reset gate determines how to combine the past state with the current input. Through these gating mechanisms, the BiGRU model can adaptively learn the long-term dependencies in time series data and the mutual influence between multiple variables. In addition, by comparing the algorithm results, it can be seen that CNN-BiGRU has better prediction results than BiGRU, the final values ​​of different errors are lower, and the prediction results are more accurate. This is because the CNN-BiGRU model combines the advantages of BiGRU's ability to capture long-term dependencies in time series data with the CNN model's ability to extract features from data in the spatial dimension. It shows higher accuracy in dealing with nonlinear problems in predicting the performance of foam concrete. In short, the CNN-BiGRU model proposed in this paper has better performance in data prediction tasks, and compared with traditional neural network models, it can still achieve higher prediction accuracy under small data samples.

[0061] Although the preferred embodiments of the present invention 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 invention.

[0062] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for optimizing the prediction model of mechanical properties of foamed concrete considering economy, characterized in that: The method comprises: Step 1: Establish a finite element matrix void structure model of foam concrete; Step 2: Generate data set: Use various working conditions as input parameters, apply them to the foam concrete finite element matrix void structure model, and output the unit mass compressive strength under different working conditions. σ u and energy absorption value W EA , and obtain the unit mass compressive strength under different working conditions σ u and energy absorption value W EA As output parameters, the input parameters and output parameters under each same working condition are a set of samples; each set of working condition combination includes density, elastic modulus, Poisson's ratio, shear dilation angle, friction coefficient, loading rate and porosity; part of the samples in the data set are used as training data sets, and the other part of the samples are used as test data sets; Step 3: Use CNN-BiGRU combined neural network to establish a foam concrete performance prediction model; Step 4: Use a multi-objective optimization method to optimize the parameters of the foam concrete performance prediction model to obtain an optimized foam concrete mechanical properties prediction model.

2. The method for optimizing the prediction model of mechanical properties of foamed concrete taking into account economy according to claim 1, characterized in that: Step 1: Use the following steps to establish the finite element matrix void structure model of foam concrete: S1.1, continuously photograph the foam concrete specimens by X-ray computed tomography to obtain a set of pore structure images; S1.2, performing bilinear interpolation processing on the pore structure image, reducing the image size, and representing the reduced set of pore structure images with a three-dimensional stacking matrix; S1.3, set the grayscale threshold, perform binarization on each grayscale value in the three-dimensional stacking matrix, reset the grayscale value of pixels greater than the grayscale threshold to the maximum value, indicating cement paste, reset the grayscale value of pixels less than or equal to the grayscale threshold to 0, indicating pore structure, and obtain a binary stacking matrix image file; S1.4, generate solid parts, divide the solid parts into networks, write the divided mesh model files into the INPUT file, and complete the modeling of the initial dense concrete model; S1.5, reconstructing the foam concrete model using the binary stacked matrix image file and the initial dense concrete model; S1.

6. Define the contact relationship between each unit in the dense concrete model, where the normal contact relationship between the units is hard contact, and the tangential contact relationship is controlled by the friction coefficient.

3. The method for optimizing the prediction model of mechanical properties of foamed concrete considering economy according to claim 1, characterized in that: Step 2: Generate data set, including the following process: Using ABAQUS system, adopting control variable method to take different working conditions as input parameters of finite element matrix void structure model of foam concrete, extracting ODB file results, and obtaining unit mass compressive strength under different working conditions σ u and energy absorption value W EA As output parameters, the input parameters and output parameters under each identical working condition are a set of samples.

4. The method for optimizing the prediction model of mechanical properties of foamed concrete taking into account economy according to claim 3 is characterized in that: The foamed concrete performance prediction model described in step 3 includes an input layer, a CNN layer, a BiGRU layer and a fully connected layer. The processing process of the foamed concrete performance prediction model includes the following steps: S3.1, input the input parameters from the input layer; S3.2, CNN layer extracts dynamic coupling characteristics from input parameters; S3.3, BiGRU layer models the dynamic changes of dynamic coupling characteristics and captures the unit mass compressive strength σ u and energy absorption value W EA The temporal compliance relationship of S3.

4. Compressive strength per unit mass σ u and energy absorption value W EA The temporal compliance relationship of is output through the fully connected layer to obtain the final prediction result.

5. The method for optimizing the prediction model of mechanical properties of foamed concrete taking into account economy according to claim 4, characterized in that: The CNN layer described in step S3.1 includes 1 convolution layer and a pooling layer.

6. The method for optimizing the prediction model of mechanical properties of foamed concrete considering economy according to claim 5, characterized in that: The number of convolution kernels in the convolution layer is 32, the convolution kernel size is 1×1, and the activation function is ReLU; in the pooling layer, the pool size is 1; the feature sequence output by the CNN layer passes through the Dropout layer as the input of the second BiGRU layer, and finally outputs the predicted sequence through the Dense layer; the Dropout layer parameter is set to 0.2, and the number of neurons in the second BiGRU layer is set to (64, 128); among them, the model parameters BiGRU hidden layer activation function is set to ReLU, the Dropout layer parameter is 0.2, the Dense fully connected layer activation function is linear, the learning rate is 0.001, epochs=1000, batch_size=500, the loss function is MAE, and the optimizer is adam.

7. The method for optimizing the prediction model of mechanical properties of foamed concrete considering economy according to claim 1, characterized in that: Step 4 includes the following process: S4.

1. Use the input parameters as input variables to establish the first objective function And the second objective function : ， Among them, the first objective function The purpose is to maximize the compressive strength per unit mass σ u , the second objective function The purpose is to maximize the energy absorption value W EA , represents the input parameters to be optimized, x1,x2,x3,x4,x5,x 6, x7], x1,x2,x3,x4,x5,x 6, x7] is the set of input parameters, the first objective function And the second objective function The constraints are: ； S4.

2. Determine an initial population of size N, obtain a first-generation offspring population of size N after selection, crossover, and mutation operations, merge the two populations, and obtain a population of size 2N; S4.3, non-dominated sorting 2N-scale population, determine the non-dominated level of individuals, and retain individuals in descending order of dominance level until the set of offspring in the next generation is larger than the size of the initial population, and record the non-dominated level L at this time; S4.

4. Use crowding distance to sort the individuals in the L layer, select relatively sparse points, and avoid local maximum and minimum values. The calculation formula of crowding distance CD is: ， in, M is the total number of individuals in the same layer, is the distance between the ith individual and its neighbors in order of m dimensions, is the crowding distance between the i-th individuals; S4.

5. After selecting the next generation parent population, a new offspring population is obtained after selection, crossover and mutation operations; S4.6, looping steps S4.3 to S4.5 until the number of iterations reaches the set number of iterations, obtaining the Pareto optimal solution set; S4.

7. Use the TOPSIS method to obtain the optimal solution in the Pareto optimal solution set.

8. The method for optimizing the prediction model of mechanical properties of foamed concrete considering economy according to claim 7, characterized in that: The crossover probability and mutation probability are set to 0.6 and 0.05 respectively, the initial population size is 100, and the maximum evolutionary generation and stop generation are 100.

9. The method for optimizing the prediction model of mechanical properties of foamed concrete considering economy according to claim 7, characterized in that: Step S4.7 includes the following process: Determine the maximum unit mass compressive strength σ u And maximize the energy absorption value W EA and input parameters The positive ideal solution and negative ideal solution of the optimal solution set are then obtained, and the Euclidean distance between each solution in the optimal solution set and the positive ideal solution and the negative ideal solution is then calculated. The degree of closeness between each solution and the optimal solution is thus obtained, and the solution closest to the optimal solution is taken as the optimal solution.

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