CN112652069A - Particle swarm algorithm-based tetrahedral subdivision grid optimization method and system - Google Patents
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Abstract
A tetrahedron subdivision grid optimization method and system based on particle swarm optimization are disclosed. The method can comprise the following steps: step 1: acquiring basic data of a three-dimensional block model of a target area, and constructing an initial tetrahedral model; step 2: determining a tetrahedron to be optimized of the initial tetrahedron model, and adding the tetrahedron to be optimized into a queue Q to be optimized; and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization; and 4, step 4: and performing particle swarm optimization aiming at four vertexes of each tetrahedron to be optimized to obtain an optimized tetrahedron model. The method aims at optimizing the average quality of tetrahedrons around the vertex, so that the tetrahedrons have good geometric shapes, the condition that the tetrahedrons are too long, narrow and flat is avoided, the quality of the tetrahedron subdivision is improved, the requirement of a three-dimensional finite element forward modeling algorithm is met, the modeling efficiency is high, the purpose of rapid attribute modeling can be achieved, and the practicability is high.
Description
Technical Field
The invention relates to the field of three-dimensional forward attribute modeling, in particular to a tetrahedron subdivision grid optimization method and system based on a particle swarm algorithm.
Background
The seismic forward modeling technology is widely applied to acquisition, processing and interpretation of seismic exploration, and plays an important role in design optimization of an observation system, processing parameter extraction and verification of an interpretation scheme. The interpolation optimization based on the Delaunay subdivision can not only improve the network quality, but also encrypt the original mesh, because the tetrahedral mesh for forward modeling must meet the size limit, and the accuracy of the large forward modeling of the tetrahedron cannot be guaranteed, the mesh optimization by the interpolation method can ensure that the mesh size is not larger than the requirement of forward computation. On the other hand, the tetrahedral mesh size required by forward calculation cannot be too small, because the mesh is small, the seismic wave propagation time in the mesh is small, and when the mesh is smaller than the forward calculation time interval, the forward calculation result is unstable, so it is not desirable to optimize the tetrahedron by using the unrestricted vertex insertion of the Delaunay interpolation, and the insertion optimization should be stopped when the tetrahedral size is closest to the minimum mesh size. The Delaunay interpolation optimization cannot accomplish the optimization of all tetrahedrons due to the minimum size constraint. Therefore, there is a need to develop a method and a system for tetrahedron mesh generation optimization based on particle swarm optimization.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention provides a particle swarm algorithm-based tetrahedron subdivision mesh optimization method and system, which aim at optimizing the average quality of tetrahedrons around a vertex, so that the tetrahedron has good geometric form, the condition that the tetrahedron is too long, narrow and flat is avoided, the quality of tetrahedron subdivision is improved, the requirement of a three-dimensional finite element forward modeling algorithm is met, the modeling efficiency is high, the purpose of rapid attribute modeling can be achieved, and the practicability is high.
According to one aspect of the invention, a tetrahedron subdivision grid optimization method based on a particle swarm algorithm is provided. The method may include: step 1: acquiring basic data of a three-dimensional block model of a target area, and constructing an initial tetrahedral model by a three-dimensional Delaunay interpolation method; step 2: determining a tetrahedron to be optimized of the initial tetrahedron model, and adding the tetrahedron to be optimized into a queue Q to be optimized; and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization; and 4, step 4: and performing particle swarm optimization aiming at four vertexes of each tetrahedron to be optimized to obtain an optimized tetrahedron model.
Preferably, the tetrahedron to be optimized of the initial tetrahedral model is determined as: and taking the ratio of the spatial external sphere radius of the tetrahedron to the length of the shortest side of the tetrahedron as a target parameter, wherein the tetrahedron of which the target parameter does not meet the set requirement is the tetrahedron to be optimized.
Preferably, step 2 is preceded by: performing Delaunay subdivision insert optimization for the initial tetrahedral model.
Preferably, the particle swarm optimization for the four vertices of each tetrahedron to be optimized comprises: and sequentially moving four vertexes of each tetrahedron to be optimized, and reducing the average length-to-height ratio of the tetrahedrons adjacent to the vertexes.
Preferably, the average aspect ratio is calculated by equation (1):
wherein A is the average aspect ratio, N is the total number of adjacent tetrahedrons at the vertex, and LiIs the longest side length of the ith adjoining tetrahedron, HiIs the minimum height of the ith adjoining tetrahedron.
According to another aspect of the present invention, a tetrahedron mesh generation optimization system based on particle swarm optimization is provided, which is characterized in that the system comprises: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: step 1: acquiring basic data of a three-dimensional block model of a target area, and constructing an initial tetrahedral model by a three-dimensional Delaunay interpolation method; step 2: determining a tetrahedron to be optimized of the initial tetrahedron model, and adding the tetrahedron to be optimized into a queue Q to be optimized; and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization; and 4, step 4: and performing particle swarm optimization aiming at four vertexes of each tetrahedron to be optimized to obtain an optimized tetrahedron model.
Preferably, the tetrahedron to be optimized of the initial tetrahedral model is determined as: and taking the ratio of the spatial external sphere radius of the tetrahedron to the length of the shortest side of the tetrahedron as a target parameter, wherein the tetrahedron of which the target parameter does not meet the set requirement is the tetrahedron to be optimized.
Preferably, step 2 is preceded by: performing Delaunay subdivision insert optimization for the initial tetrahedral model.
Preferably, the particle swarm optimization for the four vertices of each tetrahedron to be optimized comprises: and sequentially moving four vertexes of each tetrahedron to be optimized, and reducing the average length-to-height ratio of the tetrahedrons adjacent to the vertexes.
Preferably, the average aspect ratio is calculated by equation (1):
wherein A is the average aspect ratio, N is the total number of adjacent tetrahedrons at the vertex, and LiIs the longest side length of the ith adjoining tetrahedron, HiIs the minimum height of the ith adjoining tetrahedron.
The beneficial effects are that:
(1) the method combines the principle of a particle swarm optimization algorithm with a three-dimensional interactive modeling technology, and solves the optimization problem of a closed block tetrahedral subdivision algorithm in three-dimensional interactive modeling software;
(2) the method aims at optimizing the average quality of tetrahedrons around the vertex, and moves the tetrahedron vertex with quality problem, so that the moved tetrahedron has good geometric form, the condition that the tetrahedron is too long, narrow and flat is avoided, the quality of tetrahedron subdivision is improved, and the requirement of a three-dimensional finite element forward modeling algorithm is met.
The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
Fig. 1 shows a flow chart of the steps of the tetrahedral mesh generation optimization method based on the particle swarm optimization according to the present invention.
Fig. 2a and 2b show schematic diagrams of a triangulation of an initial tetrahedral model and a triangulation of an optimized tetrahedral model, respectively, according to one embodiment of the invention.
Fig. 3a, fig. 3b, and fig. 3c respectively show a comparison of the three-dimensional model before the particle swarm optimization of the actual work area, the optimization model with the target parameter of 1.8, and the optimization model with the target parameter of 1.4, according to an embodiment of the present invention.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Fig. 1 shows a flow chart of the steps of the tetrahedral mesh generation optimization method based on the particle swarm optimization according to the present invention.
In this embodiment, the tetrahedral mesh generation optimization method based on the particle swarm optimization according to the present invention may include: step 1: acquiring basic data of a three-dimensional block model of a target area, and constructing an initial tetrahedral model by a three-dimensional Delaunay interpolation method; step 2: determining a tetrahedron to be optimized of the initial tetrahedron model, and adding the tetrahedron to be optimized into a queue Q to be optimized; and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization; and 4, step 4: and performing particle swarm optimization aiming at four vertexes of each tetrahedron to be optimized to obtain an optimized tetrahedron model.
In one example, the tetrahedron to be optimized for the initial tetrahedral model is determined as: and taking the ratio of the external sphere radius of the tetrahedron space to the length of the shortest side of the tetrahedron as a target parameter, wherein the tetrahedron of which the target parameter does not meet the set requirement is the tetrahedron to be optimized.
In one example, step 2 is preceded by: and performing Delaunay subdivision insertion optimization aiming at the initial tetrahedral model.
In one example, performing particle swarm optimization for the four vertices of each tetrahedron to be optimized comprises: and sequentially moving four vertexes of each tetrahedron to be optimized, and reducing the average length-to-height ratio of the tetrahedrons adjacent to the vertexes.
In one example, the average aspect ratio is calculated by equation (1):
wherein A is the average aspect ratio, N is the total number of adjacent tetrahedrons at the vertex, and LiIs the longest side length of the ith adjoining tetrahedron, HiIs the minimum height of the ith adjoining tetrahedron.
Specifically, the particle swarm optimization algorithm is an evolutionary computing technology and is derived from the behavior research of bird swarm predation. The basic idea of the particle swarm optimization algorithm is as follows: the optimal solution is found through cooperation and information sharing among individuals in the group. The tetrahedron subdivision grid optimization method based on the particle swarm optimization can comprise the following steps:
step 1: the basic data of a three-dimensional block model of a target area are obtained, an initial tetrahedral model is constructed through a three-dimensional Delaunay interpolation method, and then the initial tetrahedral model is subjected to Delaunay subdivision interpolation optimization, so that the network quality can be improved, and meanwhile, the original grid can be encrypted, because the tetrahedral grid for forward modeling must meet the size limitation, and the accuracy of forward modeling cannot be guaranteed because the tetrahedron is too large, the grid size can be ensured to be not larger than the requirement of forward modeling calculation through the interpolation method optimization;
step 2: taking the ratio of the external sphere radius of the tetrahedron space to the length of the shortest side of the tetrahedron as a target parameter, adding the tetrahedron of which the target parameter does not meet the setting requirement, namely the tetrahedron to be optimized, into a queue Q to be optimized, wherein the optimal range of the target parameter is less than or equal to 1.8 and greater than 1, if the target parameter is greater than 1.8, the tetrahedron becomes very long and narrow, the quality of the tetrahedron cannot meet the forward performance requirement, and the requirements can be set by technicians in the field according to specific conditions;
and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization;
and 4, step 4: and performing particle swarm optimization on the four vertexes of each tetrahedron to be optimized, sequentially moving the four vertexes of each tetrahedron to be optimized, calculating the average length-to-height ratio through a formula (1), reducing the average length-to-height ratio of the tetrahedron adjacent to the vertexes, and obtaining the optimized tetrahedron model.
The method aims at optimizing the average quality of tetrahedrons around the vertex, so that the tetrahedrons have good geometric forms, the condition that the tetrahedrons are too long, narrow and flat is avoided, the quality of the tetrahedron subdivision is improved, the requirement of a three-dimensional finite element forward modeling algorithm is met, the modeling efficiency is high, the purpose of rapid attribute modeling can be achieved, and the practicability is high.
Application example
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
The tetrahedron subdivision grid optimization method based on the particle swarm optimization comprises the following steps:
step 1: the basic data of a three-dimensional block model of a target area are obtained, an initial tetrahedral model is constructed through a three-dimensional Delaunay interpolation method, and then the initial tetrahedral model is subjected to Delaunay subdivision interpolation optimization, so that the network quality can be improved, and meanwhile, the original grid can be encrypted, because the tetrahedral grid for forward modeling must meet the size limitation, and the accuracy of forward modeling cannot be guaranteed because the tetrahedron is too large, the grid size can be ensured to be not larger than the requirement of forward modeling calculation through the interpolation method optimization;
step 2: taking the ratio of the external sphere radius of the tetrahedron space to the length of the shortest side of the tetrahedron as a target parameter, wherein the tetrahedron of which the target parameter does not meet the set requirement is the tetrahedron to be optimized, and adding the tetrahedron to the queue Q to be optimized;
and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization;
and 4, step 4: and performing particle swarm optimization on the four vertexes of each tetrahedron to be optimized, sequentially moving the four vertexes of each tetrahedron to be optimized, calculating the average length-to-height ratio through a formula (1), reducing the average length-to-height ratio of the tetrahedron adjacent to the vertexes, and obtaining the optimized tetrahedron model.
Fig. 2a and 2b show schematic diagrams of a triangulation of an initial tetrahedral model and a triangulation of an optimized tetrahedral model, respectively, according to one embodiment of the invention.
Fig. 3a, fig. 3b, and fig. 3c respectively show a comparison of the three-dimensional model before the particle swarm optimization of the actual work area, the optimization model with the target parameter of 1.8, and the optimization model with the target parameter of 1.4, according to an embodiment of the present invention. It can be seen that as the target parameter is reduced, the quality of the tetrahedron becomes better and better, and the amount of calculation becomes larger and larger.
In conclusion, the method aims at optimizing the average quality of the tetrahedron around the vertex, so that the tetrahedron has good geometric shape, the condition that the tetrahedron is too long, narrow and flat is avoided, the quality of the tetrahedron subdivision is improved, the requirement of a three-dimensional finite element forward modeling algorithm is met, the modeling efficiency is high, the purpose of rapid attribute modeling can be achieved, and the practicability is high.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
According to an embodiment of the present invention, there is provided a tetrahedral subdivision grid optimization system based on a particle swarm optimization, the system comprising: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: step 1: acquiring basic data of a three-dimensional block model of a target area, and constructing an initial tetrahedral model by a three-dimensional Delaunay interpolation method; step 2: determining a tetrahedron to be optimized of the initial tetrahedron model, and adding the tetrahedron to be optimized into a queue Q to be optimized; and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization; and 4, step 4: and performing particle swarm optimization aiming at four vertexes of each tetrahedron to be optimized to obtain an optimized tetrahedron model.
In one example, the tetrahedron to be optimized for the initial tetrahedral model is determined as: and taking the ratio of the external sphere radius of the tetrahedron space to the length of the shortest side of the tetrahedron as a target parameter, wherein the tetrahedron of which the target parameter does not meet the set requirement is the tetrahedron to be optimized.
In one example, step 2 is preceded by: and performing Delaunay subdivision insertion optimization aiming at the initial tetrahedral model.
In one example, performing particle swarm optimization for the four vertices of each tetrahedron to be optimized comprises: and sequentially moving four vertexes of each tetrahedron to be optimized, and reducing the average length-to-height ratio of the tetrahedrons adjacent to the vertexes.
In one example, the average aspect ratio is calculated by equation (1):
wherein A is the average aspect ratio, N is the total number of adjacent tetrahedrons at the vertex, and LiIs the longest side length of the ith adjoining tetrahedron, HiIs the minimum height of the ith adjoining tetrahedron.
The system aims at optimizing the average quality of tetrahedrons around the vertex, so that the tetrahedrons have good geometric forms, the condition that the tetrahedrons are too long, narrow and flat is avoided, the quality of the tetrahedron subdivision is improved, the requirement of a three-dimensional finite element forward modeling algorithm is met, the modeling efficiency is high, the purpose of rapid attribute modeling can be achieved, and the practicability is high.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (10)
1. A tetrahedron subdivision grid optimization method based on particle swarm optimization is characterized by comprising the following steps:
step 1: acquiring basic data of a three-dimensional block model of a target area, and constructing an initial tetrahedral model by a three-dimensional Delaunay interpolation method;
step 2: determining a tetrahedron to be optimized of the initial tetrahedron model, and adding the tetrahedron to be optimized into a queue Q to be optimized;
and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization;
and 4, step 4: and performing particle swarm optimization aiming at four vertexes of each tetrahedron to be optimized to obtain an optimized tetrahedron model.
2. The tetrahedron subdivision grid optimization method based on the particle swarm optimization algorithm according to claim 1, wherein the tetrahedron to be optimized of the initial tetrahedral model is determined as follows:
and taking the ratio of the spatial external sphere radius of the tetrahedron to the length of the shortest side of the tetrahedron as a target parameter, wherein the tetrahedron of which the target parameter does not meet the set requirement is the tetrahedron to be optimized.
3. The tetrahedron subdivision grid optimization method based on the particle swarm optimization algorithm according to claim 1, wherein step 2 is preceded by:
performing Delaunay subdivision insert optimization for the initial tetrahedral model.
4. The tetrahedron subdivision mesh optimization method based on the particle swarm optimization algorithm according to claim 1, wherein the particle swarm optimization for the four vertices of each tetrahedron to be optimized includes:
and sequentially moving four vertexes of each tetrahedron to be optimized, and reducing the average length-to-height ratio of the tetrahedrons adjacent to the vertexes.
5. The tetrahedron subdivision grid optimization method based on particle swarm optimization according to claim 1, wherein the average aspect ratio is calculated by formula (1):
wherein A is the average aspect ratio, N is the total number of adjacent tetrahedrons at the vertex, and LiOf the ith adjacent tetrahedronLongest side length, HiIs the minimum height of the ith adjoining tetrahedron.
6. A tetrahedron subdivision grid optimization system based on particle swarm optimization is characterized by comprising the following components:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
step 1: acquiring basic data of a three-dimensional block model of a target area, and constructing an initial tetrahedral model by a three-dimensional Delaunay interpolation method;
step 2: determining a tetrahedron to be optimized of the initial tetrahedron model, and adding the tetrahedron to be optimized into a queue Q to be optimized;
and step 3: judging whether a tetrahedron to be optimized exists in the Q, if so, entering the step 4, and if not, ending the optimization;
and 4, step 4: and performing particle swarm optimization aiming at four vertexes of each tetrahedron to be optimized to obtain an optimized tetrahedron model.
7. The particle swarm algorithm-based tetrahedron subdivision grid optimization system of claim 6, wherein the tetrahedron to be optimized of the initial tetrahedral model is determined as:
and taking the ratio of the spatial external sphere radius of the tetrahedron to the length of the shortest side of the tetrahedron as a target parameter, wherein the tetrahedron of which the target parameter does not meet the set requirement is the tetrahedron to be optimized.
8. The tetrahedron subdivision grid optimization system based on the particle swarm optimization algorithm according to claim 6, wherein step 2 is preceded by:
performing Delaunay subdivision insert optimization for the initial tetrahedral model.
9. The tetrahedron subdivision mesh optimization system based on the particle swarm optimization algorithm of claim 6, wherein performing the particle swarm optimization for the four vertices of each tetrahedron to be optimized comprises:
and sequentially moving four vertexes of each tetrahedron to be optimized, and reducing the average length-to-height ratio of the tetrahedrons adjacent to the vertexes.
10. The tetrahedron subdivision grid optimization system based on the particle swarm optimization algorithm of claim 9, wherein the average aspect ratio is calculated by equation (1):
wherein A is the average aspect ratio, N is the total number of adjacent tetrahedrons at the vertex, and LiIs the longest side length of the ith adjoining tetrahedron, HiIs the minimum height of the ith adjoining tetrahedron.
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