CN116432538A - Multi-physical-field simulation method and system based on residual dense network - Google Patents
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Abstract
The invention discloses a multi-physical field simulation method and system based on a residual dense network, wherein the method comprises the following steps: acquiring a low grid density physical field data set and a high grid density physical field data set; constructing a physical field mapping neural network model based on super-resolution fitting; and training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by taking the high-grid density physical field data set as a training index, and performing a multi-physical field simulation experiment based on the trained super-resolution fitting physical field mapping neural network model. The system comprises: the system comprises an acquisition module, a construction module, a training module and an application module. According to the invention, the high grid density sample can be generated by constructing the super-resolution fitting physical field mapping neural network model, so that the efficiency of multi-physical field simulation analysis is improved. The multi-physical-field simulation method and system based on the residual dense network can be widely applied to the technical field of multi-physical-field simulation.
Description
Technical Field
The invention relates to the technical field of multi-physical-field simulation, in particular to a multi-physical-field simulation method and system based on a residual dense network.
Background
Numerical computing, and in particular Finite Element Analysis (FEA), has wide application in scientific research, particularly in the mechanical field, such as structural performance assessment and topology optimization. Finite element analysis is effectively a computer technique that discretizes a continuous physical system into a number of small parts and solves these small parts in combination. The grid density determines the discretization finesse of the continuous system, so it is an important factor in FEA, and at the same time, it also affects the computational resources required to solve the linear equation set. This results in the inherent contradiction of finite element analysis between improving spatial resolution and improving computational efficiency;
in order to solve the problem of low computational efficiency of finite elements at high grid densities, two solutions have emerged in recent years: the method is characterized in that the AMR algorithm uses grids with different thicknesses according to the importance of different areas, so that better solutions are obtained by using fewer grids, however, the AMR algorithm still needs to update parameters for multiple iterations to determine which areas need finer grids and improve numerical precision, the trade-off still exists between spatial resolution and computing efficiency, the AMR algorithm cannot fundamentally solve the conflict between improving the spatial resolution of finite elements and improving the computing efficiency, the physical field can be predicted once by using a machine learning-based method, multiple iteration updating is avoided, input physical conditions are converted into output physical fields by using a data driving framework, the previous work has applied the method to the fields of medicine and hydrodynamics, and good effects are obtained, compared with the traditional finite element method, the model computing efficiency based on machine learning is improved by 1-2 orders of magnitude, and the research progress shows that the machine learning has great potential in solving the space resolution and the computing efficiency, but the existing physical field prediction technology based on the machine learning cannot directly utilize the neural network to learn the contradiction of the physical field contained in the multiple physical fields, so that the computing efficiency is low in the map.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a multi-physical-field simulation method and system based on a residual dense network, which can be used for generating high-grid density samples by introducing residual dense blocks to construct a super-resolution fitting physical-field mapping neural network model, so that the efficiency of multi-physical-field simulation analysis is improved.
The first technical scheme adopted by the invention is as follows: a multi-physical field simulation method based on a residual dense network comprises the following steps:
acquiring a low grid density physical field data set and a high grid density physical field data set, wherein the low grid density physical field data set is a low grid density physical field image, and the high grid density physical field data set is a high grid density physical field image;
introducing a global residual error structure and a cascade residual error dense block structure, and constructing a physical field mapping neural network model based on super-resolution fitting;
training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by taking the high-grid density physical field data set as a training index to obtain a trained super-resolution fitting physical field mapping neural network model;
and performing a multi-physical-field simulation experiment based on the trained super-resolution fitting physical-field mapping neural network model.
Further, the step of acquiring the low grid density physical field data set and the high grid density physical field data set specifically includes:
acquiring isotropic linear elastic materials;
applying prescribed constraint treatment to the left boundary of the isotropic linear elastic material, and then performing heating treatment to construct a physical field of the isotropic linear elastic material with multiple field coupling of a thermal field and a stress field;
and combining constitutive equations of plane strain problems, and performing simulation calculation on the homopolar linear elastic material physical field through finite element analysis software to obtain a low-grid-density physical field data set and a high-grid-density physical field data set.
Further, constitutive equations of the plane strain problem include geometric equations, equilibrium equations, generalized hooke's law equations, and thermal strain equations, wherein:
the expression of the geometric equation is:
the expression of the equilibrium equation is:
α ij,j +g i ＝0
the generalized hooke's law equation is expressed as:
the expression of the thermal strain equation is:
ε yh ＝γ(T)(T-T 0 )
in the above, delta i Represents x i On the shaftIs a displacement of alpha ij And epsilon ij Respectively represent x i X on surface j Stress and strain in direction g i Represents x i The volumetric force component in the direction, E represents Young's modulus, delta represents Poisson's ratio, gamma represents the thermal expansion coefficient of the material, T represents the current temperature of the material, T 0 Indicating the ambient temperature.
Further, the constructed structure based on the super-resolution fitting physical field mapping neural network model comprises a first convolution layer, a global residual error structure, a second convolution layer, a plurality of residual error dense blocks, a third convolution layer, a sub-pixel convolution layer and a fourth convolution layer, wherein the residual error dense blocks are in cascade connection, and each residual error dense block comprises a convolution layer, a nonlinear mapping layer and a serial layer.
Further, the step of training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by using the high-grid density physical field data set as a training index to obtain a trained super-resolution fitting physical field mapping neural network model specifically comprises the following steps:
inputting a low-grid density physical field data set into the super-resolution fitting physical field mapping neural network model for training to obtain a training result;
taking the high grid density physical field data set as a training index, introducing an average absolute error function as a loss function, and comparing the difference value between the training result and the training index through the MRSE index;
and automatically adjusting parameters of the super-resolution fitting physical field mapping neural network model according to the difference value, and carrying out back propagation to continuously and iteratively update weight parameters of the network model until the difference value is smaller than a preset threshold value, and outputting the trained super-resolution fitting physical field mapping neural network model.
Further, the step of inputting the low grid density physical field data set to the super-resolution fitting physical field mapping neural network model for training to obtain a training result specifically includes:
inputting a low grid density physical field data set into the super-resolution fitting physical field mapping neural network model;
performing feature extraction processing on the input low-grid-density physical field data set based on the first convolution layer, a bypass structure in the global residual structure and the second convolution layer to obtain shallow features of the low-grid-density physical field;
performing feature extraction processing on the input low-grid density physical field data set based on a plurality of residual error dense blocks to obtain deep features of the low-grid density physical field;
splicing the deep features of the low grid density physical field output by the residual error dense blocks to obtain the deep features of the spliced low grid density physical field;
the dimension of the deep features of the spliced low-grid-density physical field is reduced based on the third convolution layer, and the deep features of the low-grid-density physical field with reduced dimension are obtained;
carrying out fusion processing on the shallow features of the low-grid density physical field and the deep features of the low-grid density physical field after the dimensionality reduction to obtain fusion features of the low-grid density physical field;
and (3) carrying out up-sampling processing on the fusion characteristics of the low-grid-density physical field based on the sub-pixel convolution layer and the fourth convolution layer, rearranging the fusion characteristics of the low-grid-density physical field, and outputting a training result.
Further, the step of performing feature extraction processing on the input low grid density physical field data set based on the plurality of residual error density blocks to obtain deep features of the low grid density physical field specifically includes:
the convolution layer based on the residual error dense block is used for extracting deep features;
based on a nonlinear mapping layer of the residual error dense block, mapping the characteristics to a nonlinear space by using a ReLU function, and enhancing the nonlinear representation capability of the model;
and the serial layer based on the residual error dense blocks is used for connecting the output of each dense layer in each residual error dense block in series, namely the output of the convolution layer of the residual error dense block and the output of the nonlinear mapping layer of the residual error dense block.
The second technical scheme adopted by the invention is as follows: a multi-physical field simulation system based on a residual dense network, comprising:
the acquisition module is used for acquiring a low grid density physical field data set and a high grid density physical field data set, wherein the low grid density physical field data set is a low grid density physical field image, and the high grid density physical field data set is a high grid density physical field image;
the building module is used for introducing a global residual error structure and a cascade residual error dense block structure and building a physical field mapping neural network model based on super-resolution fitting;
the training module is used for training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by taking the high-grid density physical field data set as a training index to obtain a trained super-resolution fitting physical field mapping neural network model;
and the application module is used for carrying out a multi-physical-field simulation experiment based on the trained super-resolution fitting physical-field mapping neural network model.
The method and the system have the beneficial effects that: the invention generates a low-grid density physical field data set and a high-grid density physical field data set through traditional commercial software, constructs a residual dense network, namely a super-resolution fitting physical field mapping neural network model, which is suitable for fitting multiple physical fields, and comprises a shallow convolution structure, a global residual structure, a cascade residual dense block structure and a sub-pixel convolution layer structure.
Drawings
FIG. 1 is a flow chart of steps of a multi-physical field simulation method based on a residual dense network of the present invention;
FIG. 2 is a block diagram of a multi-physical field simulation system based on a residual dense network of the present invention;
FIG. 3 is a schematic representation of a model of planar thermal stress of a linearly isotropic material in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of the structure of a super-resolution fitting physical field mapping neural network model constructed by the invention;
FIG. 5 is a graph of simulated calculation test results of thermal stress distribution of several groups of physical fields according to a specific embodiment of the invention;
FIG. 6 is a graph showing the distribution of the relative pressure error between the maximum thermal stress value of each sample prediction and the maximum thermal stress value of the reference label.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
Referring to fig. 1, the present invention provides a multi-physical field simulation method based on a residual dense network, the method comprising the steps of:
s1, acquiring a low grid density physical field data set and a high grid density physical field data set, wherein the low grid density physical field data set is a low grid density physical field image, and the high grid density physical field data set is a high grid density physical field image;
specifically, referring to fig. 3, for a plane square isotropic linear elastic material, a certain thermal load and boundary conditions are applied, the plane square isotropic linear elastic material is treated as a plane thermal stress problem, a thermal load of 100 ℃ is applied to the left boundary of the structure, a fixed constraint is applied to the left boundary, the material is heated and deformed by a heat source, the left boundary is subjected to the fixed constraint and cannot expand freely, so that thermal stress is generated, the situation is that a thermal field and a stress field are coupled in multiple fields, meanwhile, three other boundaries conduct convective heat transfer, the convective heat transfer coefficient changes within a certain range, the corresponding plane thermal stress distribution also changes, the constitutive equation of the plane strain problem consists of a geometric equation, a balance equation and a physical equation, namely a generalized hooke law, meanwhile, the thermal-structural coupling also considers the thermal strain equation, and therefore, the expression of the constitutive equation of the plane strain problem is specifically shown as follows:
α ij,j +g i ＝0
ε th ＝γ(T)(T-T 0 )
in the above, delta i Represents x i Displacement on the shaft, alpha ij And epsilon ij Respectively represent x i X on surface j Stress and strain in direction g i Represents x i The volumetric force component in the direction, E represents Young's modulus, delta represents Poisson's ratio, gamma represents the thermal expansion coefficient of the material, T represents the current temperature of the material, T 0 Representing ambient temperature;
the commercial finite element analysis software COMSOL used in the invention automatically calls a solver according to initial physical conditions, and carries out simulation calculation according to constitutive equation of plane strain problem, thereby generating a data set required by training. The neural network model inputs stress field results of 16×16 grid density and uses the stress field results of 64×64 grid density as tag data, and in addition, in the experiment, the invention randomly rotates all samples in the training process so as to increase the diversity of thermal load and boundary conditions and improve the prediction capability of the model for processing more input conditions.
S2, introducing a global residual error structure and a cascade residual error dense block structure, and constructing a physical field mapping neural network model based on super-resolution fitting;
s3, training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by taking the high-grid density physical field data set as a training index to obtain a trained super-resolution fitting physical field mapping neural network model;
specifically, as shown in fig. 4, the invention uses two convolution layers C1 and C2 to extract shallow features of an input stress field image, and introduces a global residual error learning structure after C1 for similarity of low and high grid density stress fields, so that a network can concentrate on high-frequency information of the stress fields, thereby obtaining a better learning effect;
after shallow features are extracted, deep feature extraction is performed by using eight Residual Dense Blocks (RDBs), each RDB contains 8 dense layer structures consisting of a convolution layer and a ReLU layer, wherein the convolution layer is used for extracting deep features, and the ReLU layer is used for improving nonlinear mapping capability. The input and output results of each dense layer are fused to make full use of the low frequency and high frequency information extracted by each layer. Extracting deep features of a low grid density stress field by cascading a plurality of RDBs, then connecting and inputting feature graphs extracted from each RDB to C3, wherein the features extracted from each RDB can be further comprehensively used due to cascading, a convolution layer C3 is provided with a filter with a convolution kernel of 1 multiplied by 1, and the dimension of the feature graphs is reduced by introducing the filter, so that the network training difficulty is reduced;
up-sampling is carried out by adopting a sub-pixel convolution layer SP, and the scale of the feature images is increased by rearranging a plurality of feature images to obtain stress field images with increased grid density, wherein in the invention, each convolution layer is provided with 64 filters, and the convolution kernel size of all the filters is 3 multiplied by 3 except that the filter in C3 is 1 multiplied by 1;
selecting Mean Absolute Error (MAE) as loss function of model for training, and predicting result of model
I.e. training results and reference truth values +.>
That is, the high grid density physical field data set is represented by an image, the resolution of the image is 16×16 and 64×64 respectively according to different grid density scale factors, before MAE is calculated, the image is replaced by +.>
And->
Conversion to one-dimensional vector>
Denoted as->
Denoted as->
The expression of MAE is:
in the above formula, n represents the number of pixels of the image.
And S4, performing a multi-physical field simulation experiment based on the trained super-resolution fitting physical field mapping neural network model.
Specifically, the residual dense network oriented to multiple physical fields is realized by Pytorch, training and testing are carried out on a NVIDIAGeForce RTX 3090GPU, and under the condition that the grid density scale factor is 4, the residual dense network oriented to multiple physical fields is compared with the traditional FEM, so that the superiority of the method is proved;
in experiments, our multi-physical field oriented residual dense network is trained and evaluated using the whole data set, the training data size is 400, the test data size is 100, fig. 5 shows several test results under 4 times grid density scale factor, and the left-to-right images are the input low grid density thermal stress field, the high grid density thermal stress field as a tag, and the high grid density thermal stress field generated by the model in sequence. For most plane strain problems, we mainly pay attention to the maximum stress and the position thereof to judge whether damage occurs in a certain place, so the invention tests the prediction performance of the model on the maximum stress, and the invention measures the relative error between the reference real thermal stress distribution diagram generated by the traditional FEM and the maximum thermal stress value in the prediction thermal stress distribution diagram generated by the model according to the MRSE index, namely the maximum corresponding stress error function, as shown in fig. 6, the MRSE value of most test samples is about 2%, namely the prediction result is considered to be within the range of the acceptable thermal stress field prediction error, and the expression of the MRSE is as follows:
in the above-mentioned method, the step of,
the reference real thermal stress distribution generated by the traditional FEM and the predicted thermal stress distribution generated by the model trained by the invention are respectively;
in order to verify the acceleration efficiency of the invention, the calculation efficiency between the method of the invention and the traditional FEM is tested, and the traditional FEM takes 3.89 seconds to calculate a low grid density sample; in the case of a mesh density scale factor of 4, our model requires on average 0.013s per sample of one high mesh density generated; the method of the invention combines the traditional FEM to generate the thermal stress field at the same grid density at a speed which is 1.16 times faster than that of the FEM, and only when the grid density scale factor is 4, the traditional FEM calculation efficiency is exponentially reduced after the scale factor is increased, but the calculation efficiency of the invention is not obviously changed, and in this case, the acceleration effect of the invention is greatly improved, and all finite element calculations are completed by commercial finite element analysis software COMSOL (NVIDIA GeForce GTX 3070Laptop GPU).
Referring to fig. 2, a multi-physical field simulation system based on a residual dense network, comprising:
the acquisition module is used for acquiring a low grid density physical field data set and a high grid density physical field data set, wherein the low grid density physical field data set is a low grid density physical field image, and the high grid density physical field data set is a high grid density physical field image;
the building module is used for introducing a global residual error structure and a cascade residual error dense block structure and building a physical field mapping neural network model based on super-resolution fitting;
the training module is used for training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by taking the high-grid density physical field data set as a training index to obtain a trained super-resolution fitting physical field mapping neural network model;
and the application module is used for carrying out a multi-physical-field simulation experiment based on the trained super-resolution fitting physical-field mapping neural network model.
In summary, the invention has the characteristics of high precision and high efficiency, can be applied to engineering examples such as simulation of thermal deformation of a CPU radiator, simulation of thermal stress distribution during heat treatment of a metal plate, and the like, provides a digital simulation means for deployment of actual engineering, and reduces research, development, test and production costs.
The content in the method embodiment is applicable to the system embodiment, the functions specifically realized by the system embodiment are the same as those of the method embodiment, and the achieved beneficial effects are the same as those of the method embodiment.
While the preferred embodiment of the present invention has been described in detail, the invention is not limited to the embodiment, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the invention, and these modifications and substitutions are intended to be included in the scope of the present invention as defined in the appended claims.
Claims (8)
1. The multi-physical-field simulation method based on the residual dense network is characterized by comprising the following steps of:
acquiring a low grid density physical field data set and a high grid density physical field data set, wherein the low grid density physical field data set is a low grid density physical field image, and the high grid density physical field data set is a high grid density physical field image;
introducing a global residual error structure and a cascade residual error dense block structure, and constructing a physical field mapping neural network model based on super-resolution fitting;
training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by taking the high-grid density physical field data set as a training index to obtain a trained super-resolution fitting physical field mapping neural network model;
and performing a multi-physical-field simulation experiment based on the trained super-resolution fitting physical-field mapping neural network model.
2. The method for multi-physical field simulation based on the residual dense network according to claim 1, wherein the step of acquiring the low grid density physical field data set and the high grid density physical field data set specifically comprises the following steps:
acquiring isotropic linear elastic materials;
applying prescribed constraint treatment to the left boundary of the isotropic linear elastic material, and then performing heating treatment to construct a physical field of the isotropic linear elastic material with multiple field coupling of a thermal field and a stress field;
and combining constitutive equations of plane strain problems, and performing simulation calculation on the homopolar linear elastic material physical field through finite element analysis software to obtain a low-grid-density physical field data set and a high-grid-density physical field data set.
3. The multi-physical field simulation method based on the residual dense network according to claim 2, wherein constitutive equations of the plane strain problem comprise geometric equations, balance equations, generalized hooke's law equations and thermal strain equations, wherein:
the expression of the geometric equation is:
the expression of the equilibrium equation is:
α ij,j +g i ＝0
the generalized hooke's law equation is expressed as:
the expression of the thermal strain equation is:
ε th ＝γ(T)(T-T 0 )
in the above, delta i Represents x i Displacement on the shaft, alpha ij And epsilon ij Respectively represent x i X on surface j Stress and strain in direction g i Represents x i The volumetric force component in the direction, E represents Young's modulus, delta represents Poisson's ratio, gamma represents the thermal expansion coefficient of the material, T represents the current temperature of the material, T 0 Indicating the ambient temperature.
4. The multi-physical field simulation method based on the residual dense network according to claim 3, wherein the constructed structure based on the super-resolution fitting physical field mapping neural network model comprises a first convolution layer, a global residual structure, a second convolution layer, a plurality of residual dense blocks, a third convolution layer, a sub-pixel convolution layer and a fourth convolution layer, wherein cascade connection is arranged among the plurality of residual dense blocks, and the residual dense blocks comprise convolution layers, nonlinear mapping layers and serial layers.
5. The multi-physical-field simulation method based on the residual dense network according to claim 4, wherein the step of training the super-resolution fitting physical-field mapping neural network model based on the low-grid density physical-field data set by using the high-grid density physical-field data set as a training index to obtain a trained super-resolution fitting physical-field mapping neural network model specifically comprises the following steps:
inputting a low-grid density physical field data set into the super-resolution fitting physical field mapping neural network model for training to obtain a training result;
taking the high grid density physical field data set as a training index, introducing an average absolute error function as a loss function, and comparing the difference value between the training result and the training index through the MRSE index;
and automatically adjusting parameters of the super-resolution fitting physical field mapping neural network model according to the difference value, and carrying out back propagation to continuously and iteratively update weight parameters of the network model until the difference value is smaller than a preset threshold value, and outputting the trained super-resolution fitting physical field mapping neural network model.
6. The multi-physical field simulation method based on the residual dense network according to claim 5, wherein the step of inputting the low grid density physical field data set into the super-resolution fitting physical field mapping neural network model for training to obtain a training result specifically comprises the following steps:
inputting a low grid density physical field data set into the super-resolution fitting physical field mapping neural network model;
performing feature extraction processing on the input low-grid-density physical field data set based on the first convolution layer, a bypass structure in the global residual structure and the second convolution layer to obtain shallow features of the low-grid-density physical field;
performing feature extraction processing on the input low-grid density physical field data set based on a plurality of residual error dense blocks to obtain deep features of the low-grid density physical field;
splicing the deep features of the low grid density physical field output by the residual error dense blocks to obtain the deep features of the spliced low grid density physical field;
the dimension of the deep features of the spliced low-grid-density physical field is reduced based on the third convolution layer, and the deep features of the low-grid-density physical field with reduced dimension are obtained;
carrying out fusion processing on the shallow features of the low-grid density physical field and the deep features of the low-grid density physical field after the dimensionality reduction to obtain fusion features of the low-grid density physical field;
and (3) carrying out up-sampling processing on the fusion characteristics of the low-grid-density physical field based on the sub-pixel convolution layer and the fourth convolution layer, rearranging the fusion characteristics of the low-grid-density physical field, and outputting a training result.
7. The multi-physical-field simulation method based on the residual dense network according to claim 6, wherein the step of performing feature extraction processing on the input low-grid-density physical-field data set based on the plurality of residual dense blocks to obtain deep features of the low-grid-density physical field specifically comprises the following steps:
the convolution layer based on the residual error dense block is used for extracting deep features;
based on a nonlinear mapping layer of the residual error dense block, mapping the characteristics to a nonlinear space by using a ReLU function, and enhancing the nonlinear representation capability of the model;
and the serial layer based on the residual error dense blocks is used for connecting the output of each dense layer in each residual error dense block in series, namely the output of the convolution layer of the residual error dense block and the output of the nonlinear mapping layer of the residual error dense block.
8. The multi-physical field simulation system based on the residual dense network is characterized by comprising the following modules:
the acquisition module is used for acquiring a low grid density physical field data set and a high grid density physical field data set, wherein the low grid density physical field data set is a low grid density physical field image, and the high grid density physical field data set is a high grid density physical field image;
the building module is used for introducing a global residual error structure and a cascade residual error dense block structure and building a physical field mapping neural network model based on super-resolution fitting;
the training module is used for training the super-resolution fitting physical field mapping neural network model based on the low-grid density physical field data set by taking the high-grid density physical field data set as a training index to obtain a trained super-resolution fitting physical field mapping neural network model;
and the application module is used for carrying out a multi-physical-field simulation experiment based on the trained super-resolution fitting physical-field mapping neural network model.
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