A method for predicting the performance of foamed lightweight soil roadbed based on physical information data joint drive

Abstract

The present invention provides a method for predicting the performance of a foam lightweight soil roadbed based on the joint drive of physical information data, which belongs to the field of materials science. The present invention takes into account the influence of porosity and pore size. The constitutive relationship between Cauchy stress and axial tension, lateral tension, porosity and pore size is constructed by SP‑ANN. Modeling is performed after determining the range of the input variables, and the mechanical response of the foam under compression and tension is simulated to construct a data set. Two ANNs use these data and are trained. PR‑ANN is used to predict the lateral tension value through the other three inputs, and then SP‑ANN uses it as its input to predict the Cauchy stress, and the model is evaluated and used. Finally, a method for predicting the material performance of a foam lightweight soil roadbed is established. Through three input variables, engineers can obtain the material properties of the roadbed foam lightweight soil, providing a reference for the intelligent design of high-performance foam lightweight soil roadbed.

Description

Technical Field

[0001] The invention relates to the field of materials science, and in particular to a foam lightweight soil roadbed performance prediction method based on physical information data joint drive. Background Art

[0002] At present, the structural performance of foam lightweight soil roadbed is based on macroscopic material and structural loading tests. The method of predicting the performance of foam lightweight soil roadbed based solely on macroscopic data is difficult to be representative. First, macroscopic tests are small sample data, which is difficult to adapt to the existing machine learning model's demand for big data; in addition, macroscopic tests lack microscopic parameters directly related to foam lightweight soil, and thus lack performance prediction methods that combine macroscopic and microscopic characteristic test data with mechanical theory, making it difficult to obtain accurate foam lightweight soil performance.

[0003] Foamed lightweight soil is a common filler material, which is a mixture of cement, sand, foaming agent, etc. It has low density, good energy absorption performance and high compressive strength, so it is widely used in roadbed projects of infrastructure such as roads, railways, and airports.

[0004] Traditional foam lightweight soil roadbed design methods are usually based on experience and experiments, lacking intelligence and efficiency. These methods often rely on expert experience and limited test data, making it difficult to fully and accurately evaluate the performance of foam lightweight soil under different working conditions. At the same time, due to the complex and diverse composition and processing of foam lightweight soil, traditional methods often cannot cover all possible situations, resulting in instability and uncertainty in the design results.

[0005] In recent years, deep learning has gradually become an important research tool in the field of materials and engineering due to its ability to predict material properties, design new materials, and discover new material mechanisms. With the development of deep learning technology, it has become possible to intelligently design foam lightweight soil roadbed using large-scale test data and mechanical theoretical models. The deep learning model can automatically learn and extract the complex characteristics of foam lightweight soil, thereby achieving accurate prediction of its performance. Compared with traditional experience-based design methods, the intelligent prediction method of foam lightweight soil roadbed material performance considering mesoscopic structural parameters has higher accuracy and reliability, can give full play to the advantages of foam lightweight soil, and improve the stability, bearing capacity and service life of the roadbed. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for predicting the performance of a foamed lightweight soil roadbed based on the joint drive of physical information data.

[0007] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0008] A method for predicting performance of foamed lightweight soil roadbed based on physical information data joint drive, characterized by comprising the following steps:

[0009] S1. Establish data-driven intelligent constitutive equation of foam lightweight concrete considering pore structure parameters;

[0010] S2. Processing the subgrade foam lightweight soil micro-data based on random set and numerical simulation to generate training data;

[0011] S3. Use feedforward neural network to construct the roadbed foam lightweight soil constitutive model under uniaxial load and optimize the accuracy of the model;

[0012] S4. Use the optimized model to predict the performance of foam lightweight soil roadbed.

[0013] Furthermore, the constitutive equation in S1 is expressed as:

[0014]

[0015] In the formula, λ U is the axial tensile ratio of the foam lightweight soil roadbed material, λ L is the lateral tensile ratio of the foam lightweight soil roadbed material, is the initial porosity of the foamed lightweight soil in the undeformed state, and θ is the pore size of the foamed lightweight soil.

[0016] Furthermore, the specific method of generating training data in S2 is:

[0017] S21, defining structural parameters, and designing upper and lower bounds of the space based on the defined structural parameters;

[0018] S22. Structural modeling of foam lightweight soil based on the designed space;

[0019] S23. Based on the constructed structural model, multiple large deformation simulations are performed. Each time a large deformation is simulated, the strain is taken on the loading path to calculate the corresponding average Cauchy stress and average lateral stress to obtain input-output pairs of structural parameters and corresponding Cauchy stresses, and the obtained input-output pairs are stored in a data set to obtain training data.

[0020] Furthermore, the structural parameters in S21 include porosity, pore size, and axial stretching.

[0021] Furthermore, the structural modeling of the foam lightweight soil based on the designed space in S22 specifically includes the following steps:

[0022] S221, uniformly sampling a plurality of foam structures with different porosities and pore sizes from the defined structural parameters;

[0023] S222, exchanging the solid material and the gas material in the foam lightweight soil to complete the creation of the foam lightweight soil model;

[0024] S223. An xy coordinate system is established on the created foam lightweight soil model, and pores are automatically generated based on the principle that foam pores do not overlap with each other and that the foam pores satisfy Gaussian random distribution in the x and y directions, thereby completing the structural modeling of the foam lightweight soil that meets the conditions.

[0025] Furthermore, the specific method of strain calculation in S23 is:

[0026]

[0027] In the formula, U is the strain variable, is the first invariant of the isochoric left Cauchy Green deformation tensor, J is the variable measuring the volume change, C 1 and D 1 is a material constant and:

[0028]

[0029] E is Young's modulus and v is Poisson's ratio.

[0030] Furthermore, the S3 specifically includes the following steps:

[0031] S31, after the PR-ANN network training is completed, the network parameters are fixed;

[0032] S32, laterally stretching the output of the PR-ANN network, converting it into an intermediate variable between the PR-ANN network and the SP-ANN network and using it as an input of the SP-ANN network to train the SP-ANN network;

[0033] S33, after the training is completed, the weight parameters and bias of all hidden layers of SP-ANN jointly determine the specific form of the constitutive equation formula;

[0034] S34, use the mean square error as the loss function to optimize the parameters of the PR-ANN network and SP-ANN network, and select the determination coefficient R 2 The accuracy of the model prediction was evaluated, and the mean percentage error (MAPE) was used to evaluate the relative error between the predicted value and the true value.

[0035] Furthermore, the specific form of the constitutive equation formula in S33 is expressed as:

[0036]

[0037] In the formula, λ U is the axial tensile ratio of the foam lightweight soil roadbed material, is the initial porosity of the foamed lightweight soil in the undeformed state, and θ is the pore size of the foamed lightweight soil.

[0038] The present invention has the following beneficial effects:

[0039] A method for predicting the material properties of foam lightweight soil roadbed is established. Through three input variables, engineers can obtain the material properties of foam lightweight soil for roadbed, providing a reference for the intelligent design of high-performance foam lightweight soil roadbed. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic flow chart of the foam lightweight soil roadbed performance prediction method based on physical information data joint drive of the present invention. DETAILED DESCRIPTION

[0041] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0042] A foam lightweight soil roadbed performance prediction method based on physical information data joint drive, such as Figure 1 As shown, the following steps are included:

[0043] S1. Establish data-driven intelligent constitutive equation of foam lightweight concrete considering pore structure parameters;

[0044] In this embodiment, the microscopic parameters of foam lightweight soil roadbed are considered to predict its material properties. The proposed intelligent constitutive model uses Cauchy stress as the output value of the regression task, that is, the input variable is mapped to Cauchy stress. In the Cauchy elastic material, the strain tensor is defined as a function of the deformation gradient tensor F, which can be expressed by three principal tensile F is a two-point tensor that describes the deformation characteristics of the medium. It is the derivative of each component in the current configuration with respect to the corresponding component in the reference configuration. The principal stretch ratio is the eigenvalue of the deformation gradient tensor, which represents the stretching of the material in the three main directions. Under uniaxial load, λ 1 =λ U ,λ 2 =λ 3 =λ L ,λ U and λ L Respectively represent the axial and lateral tensile ratios of the foam lightweight soil roadbed material. Therefore, considering the porosity and pore size of the foam lightweight soil, the proposed constitutive equation can be expressed as:

[0045]

[0046] in is the initial porosity of the foamed lightweight soil in the undeformed state, θ represents the pore size of the foamed lightweight soil, and the nonlinear mapping of the Cauchy stress and the four input variables is implemented by an artificial neural network (SP-ANN). At the same time, in engineering applications, the porosity of the foamed lightweight soil is expressed by the relative density, and the axial tensile ratio is derived by the engineering strain (positive when stretched and negative when compressed), and the formula is as follows:

[0047]

[0048] λ U =1+ε Eng ;

[0049] ρ * is the proportion of concrete in foam concrete, ρ is the apparent density of foam lightweight concrete, ρ s is the solid density of foam lightweight concrete, ε Eng is the engineering strain of foam lightweight soil, the lateral principal tensile λ L It is calculated by the average lateral strain, rather than setting a fixed Poisson's ratio. However, in actual uniaxial mechanical testing, additional devices (such as strain gauges) are needed to measure the lateral displacement, or design engineers want to obtain the stress of a given axial displacement, so in common application scenarios, only Data of three input variables. To deal with this problem, the present invention proposes another neural network (PR-ANN) to give the lateral stretch ratio.

[0050] S2. Processing the subgrade foam lightweight soil micro-data based on random set and numerical simulation to generate training data;

[0051] In this embodiment, the following steps are specifically included:

[0052] S21, defining structural parameters, and designing upper and lower bounds of the space based on the defined structural parameters;

[0053] Since the lateral stretch is calculated by the software, it is necessary to first define the upper and lower bounds of the design space of the three input variables. The ranges of porosity, pore size, and axial stretch are shown in Table 1.

[0054] Table 1 Input variable range

[0055]

[0056] The definition process is as follows:

[0057] Define the computational domain and pore size range. Studies have shown that the pore size of foamed lightweight soil prepared by the foaming method generally ranges from 100 microns to 1 mm. The larger the pore size, the lower the uniformity of the foam. Use uniformly distributed pore sizes to represent monodisperse foams. In order to ensure that the computational domain can cover a large range of pore sizes while saving computational resources, a 2mm×2mm×2mm computational domain and a 10-micron voxel size are selected for the foam structure, so there are 200 voxels on each side, and the total computational domain covers 8 million voxels. In order to ensure the uniformity of random foams, the pore size range is set to 100μm-500μm.

[0058] The porosity range is defined. Since only a low overlap rate (overlap = 1%) is allowed for the pores, most of the random foams are non-overlapping and cannot reach the theoretically highest porosity of 64% (i.e., monodisperse dense packing). At the same time, too high a porosity will lead to anisotropy of the foam. A low porosity will produce density inhomogeneity. Based on this, in order to make the foam domain isotropic and representative, the porosity range is set to 20%-60%.

[0059] Define the range of axial stretching. The foam compression process can be divided into three stages (linear, cell wall bending, and densification). Choose a moderate compressive strain to cover the cell wall bending area. Due to the different thickness of the cell wall in random foams, when the tensile strain is large (λ U >3) The stress-strain curve drops sharply, which is due to the fracture of some pore walls. Based on the above phenomenon, the maximum stretching ratio during compression is set to λ U =0.4, the maximum stretching ratio during stretching is λ U =3.

[0060] S22. Structural modeling of foam lightweight soil based on the designed space;

[0061] Complete the structural modeling and large deformation simulation of foam lightweight soil. 500 foam structures with different porosities and pore sizes were homogenized and sampled.

[0062] First, the spherical pores in the foam are regarded as solid materials, and the original solid materials are regarded as air, so that the foam model is transformed into a particle model, and random particle structures with different porosities and pore sizes are created. The solid material and the gas material are interchanged to complete the creation of the foam lightweight soil model. The selection of appropriate calculation domain and pore size also shows a certain uniformity and isotropy for foams with larger pore sizes, which makes the proposed ANN constitutive model satisfy a certain isotropy.

[0063] Establish an xy coordinate system, and approximately regard the foam pores as spherical. The coordinates of the foam center are (x i ,yi ), i = 1, 2, 3...n, radius r i , most of the foam pores do not overlap, then it should meet the following requirements:

[0064] R i-j >r i +r j ;

[0065]

[0066] Among them, R i-j is the distance from foam pore i to j.

[0067] At the same time, the foam pore distribution meets certain randomness, and should meet certain Gaussian random distribution in the x and y directions. Python code is used for automatic generation to complete the structural modeling that meets the conditions.

[0068] S23. Based on the constructed structural model, multiple large deformation simulations are performed. Each time a large deformation is simulated, the strain is taken on the loading path to calculate the corresponding average Cauchy stress and average lateral stress to obtain input-output pairs of structural parameters and corresponding Cauchy stresses, and the obtained input-output pairs are stored in a data set to obtain training data.

[0069] First, select the matrix material and use the neo-Hookean constitutive model to calculate its deformation physical quantities. This constitutive model is similar to the linear Hooke's law. Since its parameters can be defined by the elastic modulus of the material, when the properties of the matrix material are changed, the material parameters can be directly changed. When considering slight compressibility, its strain energy function can be written as:

[0070]

[0071] in is the isochoric left Cauchy Green deformation tensor The first invariant, J = det(F), is used to measure the change in volume. 1 and D 1 is a material constant, which can be defined by the initial shear modulus and bulk modulus of the material. In this invention, in order to make the definition more intuitive, the initial Young's modulus E = 2.7 MPa and Poisson's ratio v = 0.49 are used to derive C 1 , D 1 :

[0072]

[0073] Where G is the shear modulus and K is the bulk modulus.

[0074] The structure is simulated multiple times (compression and tension), and each simulation takes the strain on the loading path to calculate the corresponding average Cauchy stress and average lateral strain. Finally, sufficient input-output pairs are obtained, namely, structural parameters and deformation states (porosity, pore size, axial tension, lateral tension) and corresponding Cauchy stresses, and all data are stored in a data set

[0075] S3. Use feedforward neural network to construct the roadbed foam lightweight soil constitutive model under uniaxial load and optimize the accuracy of the model;

[0076] In this embodiment, after generating training data, the relationship between four input variables and one output variable needs to be completed by a regression task. According to prior knowledge, its functional relationship is nonlinear. For such nonlinear and continuous value prediction, ANN usually performs better than tree-based models. Two feedforward neural networks, PR-ANN and SP-ANN, are used to construct the constitutive model of foam lightweight soil under uniaxial load.

[0077] After the PR-ANN training is completed, the network parameters are fixed and then the SP-ANN is trained. At this time, the lateral stretch is the output of the PR-ANN and becomes the intermediate variable between the two neural networks, and also the input variable of the SP-ANN. After the training is completed, the weight parameters and biases of all hidden layers of the SP-ANN jointly determine the specific form of the constitutive equation formula. By combining the two neural networks, the corresponding axial Cauchy stress can be obtained with only three input variables. Therefore, the constitutive equation can be changed to:

[0078]

[0079] In order to make ANN give predictions that are consistent with physical knowledge for axial strain outside the data set, physical experience is used to enhance the interpretability of the neural network:

[0080] Select the appropriate input form: According to the continuous medium mechanics formula J = det (F) = λ 1 λ 2 λ 3 =λ U λ L 2 , there is an obvious inverse relationship between axial stretch and lateral stretch. This means that if the axial stretch λ U As is approached to zero, the lateral stretch will tend to infinity (theoretically). Therefore, using The form replaces λ U As the input of PR-ANN.

[0081] Choose a suitable activation function: According to physical experience, when compression or stretching continues, stress should increase monotonically to a considerable value, that is, when the stretching ratio approaches zero and infinity (theoretically), the stress should tend to infinity. Common activation functions used in neural networks, such as tanh and sigmoid, are bounded functions, and their function values ​​tend to their asymptotes as the independent variable increases. Use the softplus activation function to solve this problem. It is an unbounded function, and y increases monotonically with x.

[0082] Network Configuration:

[0083] PR-ANN: 2 hidden layers, 8 nodes in each hidden layer.

[0084] SP-ANN: 4 hidden layers, 32 nodes per hidden layer.

[0085] The two networks use mean square error (MSE) as the loss function for parameter optimization. The ANN model construction and training all use the Keras library based on the Tensorflow backend.

[0086] After training, the performance of the two ANNs is evaluated on the test set, and the evaluation index selected is R 2 (coefficient of determination) and MAPE (mean percentage error). 2 It indicates the degree of fit of the model prediction, and MAPE indicates the relative error between the predicted value and the true value.

[0087] At the same time, the prediction results can be further compared with the numerical simulation and experimental results to evaluate the accuracy of the model and improve the optimization model.

[0088] S4. Use the optimized model to predict the performance of foam lightweight soil roadbed.

[0089] Since PR-ANN can accurately predict lateral stretching, the Poisson's ratio during foam deformation can be obtained through it. As an elastic constant, Poisson's ratio reflects the degree of lateral deformation of the material during stretching or compression. It is usually obtained by the ratio of the strain in the vertical loading direction to the strain in the loading direction. In the invention, the equivalent Poisson's ratio of random elastomer foam can be defined by the axial stretch ratio and the lateral stretch ratio. According to the formula λ=1+ε Eng The relationship between material strain and stretch ratio, V eff It can be defined as:

[0090]

[0091] ε L is the lateral strain of foam lightweight soil, ε U is the axial strain of foam lightweight soil.

[0092] The equivalent Poisson's ratio of foams with different porosity and pore size can be derived through two stretching ratios. Foams with higher porosity have lower equivalent Poisson's ratio because their lateral strain changes less under the same axial strain. The equivalent Poisson's ratio is independent of the pore size.

[0093] The influence of SP-ANN prediction structure parameters:

[0094] To investigate the effects of porosity and pore size on the deformation of elastomeric foams, SP-ANN was used to explore the entire training space. For each specific axial stretch, SP-ANN was used to predict the Cauchy stress values ​​for different foam structures (porosity, pore size), and the neural network was able to give a large number of predictions in a very short time. The mechanical behavior of elastomeric foams during stretching is only related to the porosity and has almost no dependence on the pore size.

[0095] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0096] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0097] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0098] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0099] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A foam lightweight soil roadbed performance prediction method based on physical information data joint drive, characterized in that: The steps include: S1. Establish data-driven intelligent constitutive equation of foam lightweight concrete considering pore structure parameters; S2. Processing the roadbed foam lightweight soil microscopic data based on random set and numerical simulation to generate training data. The specific method of generating training data in S2 is: S21, defining structural parameters, and designing upper and lower bounds of the space based on the defined structural parameters; S22. Structural modeling of foam lightweight soil based on the designed space; S23, based on the constructed structural model, multiple large deformation simulations are performed, each time the large deformation simulation is performed, the strain is taken on the loading path to calculate the corresponding average Cauchy stress and average lateral stress to obtain input-output pairs of structural parameters and corresponding Cauchy stress, and the obtained input-output pairs are stored in a data set to obtain training data; S3. Use feedforward neural network to construct the roadbed foam lightweight soil constitutive model under uniaxial load and optimize the accuracy of the model; S4. Use the optimized model to predict the performance of foam lightweight soil roadbed.

2. The foam lightweight soil roadbed performance prediction method based on physical information data joint drive according to claim 1 is characterized in that: The constitutive equation in S1 is expressed as: In the formula, λ U is the axial tensile ratio of the foam lightweight soil roadbed material, λ L is the lateral tensile ratio of the foam lightweight soil roadbed material, is the initial porosity of the foamed lightweight soil in the undeformed state, and θ is the pore size of the foamed lightweight soil.

3. The foam lightweight soil roadbed performance prediction method based on physical information data joint drive according to claim 1 is characterized in that: The structural parameters in S21 include porosity, pore size, and axial stretching.

4. The foam lightweight soil roadbed performance prediction method based on physical information data joint drive according to claim 3 is characterized in that: The structural modeling of the foam lightweight soil based on the designed space in S22 specifically includes the following steps: S221, uniformly sampling a plurality of foam structures with different porosities and pore sizes from the defined structural parameters; S222, exchanging the solid material and the gas material in the foam lightweight soil to complete the creation of the foam lightweight soil model; S223. An xy coordinate system is established on the created foam lightweight soil model, and pores are automatically generated based on the principle that foam pores do not overlap with each other and that the foam pores satisfy Gaussian random distribution in the x and y directions, thereby completing the structural modeling of the foam lightweight soil that meets the conditions.

5. The foam lightweight soil roadbed performance prediction method based on physical information data joint drive according to claim 1 is characterized in that: The specific method of strain calculation in S23 is: Where U is the strain energy function, is the first invariant of the isochoric left Cauchy Green deformation tensor, J is the variable measuring the volume change, C1 and D1 are material constants and: E is the Young’s modulus of the foam lightweight soil, and v is the Poisson’s ratio of the foam lightweight soil.

6. The method for predicting performance of foamed lightweight soil roadbed based on physical information data joint drive according to claim 1 is characterized in that: The S3 specifically includes the following steps: S31, after the PR-ANN network training is completed, the network parameters are fixed; S32, laterally stretching the output of the PR-ANN network, converting it into an intermediate variable between the PR-ANN network and the SP-ANN network and using it as an input of the SP-ANN network to train the SP-ANN network; S33, after the training is completed, the weight parameters and bias of all hidden layers of SP-ANN jointly determine the specific form of the constitutive equation formula; S34, use the mean square error as the loss function to optimize the parameters of the PR-ANN network and SP-ANN network, and select the determination coefficient R 2 The accuracy of the model prediction was evaluated, and the mean percentage error (MAPE) was used to evaluate the relative error between the predicted value and the true value.

7. The method for predicting the performance of foamed lightweight soil roadbed based on physical information data joint drive according to claim 6 is characterized in that: The specific form of the constitutive equation formula in S33 is expressed as: In the formula, σ U is the axial Cauchy stress of foam lightweight soil, λ U is the axial tensile ratio of the foam lightweight soil roadbed material, is the initial porosity of the foamed lightweight soil in the undeformed state, and θ is the pore size of the foamed lightweight soil.

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