CN116187140B - Dynamic ice elastic modulus prediction method - Google Patents

Dynamic ice elastic modulus prediction method Download PDF

Info

Publication number
CN116187140B
CN116187140B CN202310227454.1A CN202310227454A CN116187140B CN 116187140 B CN116187140 B CN 116187140B CN 202310227454 A CN202310227454 A CN 202310227454A CN 116187140 B CN116187140 B CN 116187140B
Authority
CN
China
Prior art keywords
pore
dynamic ice
model
finite element
pores
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202310227454.1A
Other languages
Chinese (zh)
Other versions
CN116187140A (en
Inventor
黄永杰
倪章松
易贤
薛明
陈明
张颖
潘攀
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chengdu Fluid Power Innovation Center
Original Assignee
Chengdu Fluid Power Innovation Center
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chengdu Fluid Power Innovation Center filed Critical Chengdu Fluid Power Innovation Center
Priority to CN202310227454.1A priority Critical patent/CN116187140B/en
Publication of CN116187140A publication Critical patent/CN116187140A/en
Application granted granted Critical
Publication of CN116187140B publication Critical patent/CN116187140B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

The invention relates to the field of mechanical analysis technology and ice control analysis, and particularly discloses a dynamic ice elastic modulus prediction method, which comprises the following steps: acquiring pore characteristic parameters and true porosity of the dynamic ice; determining an optimal distribution function based on the pore characteristic parameters; based on a plurality of preset previewing modeling of the number of the previewing pores, the real porosity and the like, a minimum threshold value of the number of the pores is found for a pre-designated precision level; determining at least one target finite element unit cell model from a previewing dynamic ice module corresponding to a minimum threshold value of the number of pores, inputting the elastic modulus and poisson ratio of dynamic ice without pores, dividing finite element grids, and establishing periodic boundary conditions and displacement loads; the dynamic ice structure response was calculated using the finite element method and the dynamic ice elastic modulus was calculated based on the average strain theory. According to the method, the simulation model reflecting the true distribution state of the pore diameter and the porosity in the dynamic ice is constructed, so that the dynamic ice elastic modulus is predicted efficiently.

Description

Dynamic ice elastic modulus prediction method
Technical Field
The invention relates to the fields of mechanical analysis technology and ice control analysis, in particular to a dynamic ice elastic modulus prediction method based on a finite element unit cell model.
Background
When supercooled water droplets (water droplets whose temperature is lower than the freezing point and remains in a liquid state) collide with the surface of the low-temperature substrate, freezing occurs at the collision position of the water droplets and the vicinity thereof, and dynamic ice is generated. The dynamic ice can generate pores in the freezing and growing processes due to the icing mechanism, and a very complex pore-containing microstructure with diversity is formed. The size, quantity and distribution rule of the dynamic ice pores are influenced by the temperature of supercooled water drops, the content of liquid water and the particle size. Compared with the traditional icing, the dynamic ice containing pores has remarkable difference in mechanical property and physical property. The elastic modulus is a key mechanical property of the pore-containing dynamic ice, and directly influences the design of preventing and removing ice, the detection of icing, the prediction of ice shape and the like. The elastic modulus of the dynamic ice can be obtained by using an experimental method, but the experimental period is long, the efficiency is low, and the preparation of the dynamic ice has a plurality of difficulties. Therefore, the mechanical property of the dynamic ice is predicted by numerical simulation, and the dynamic ice has important engineering value and scientific significance. However, no special method is available for dynamic ice elastic modulus numerical simulation. The invention patent number ZL201711214269.X provides a three-dimensional modeling method of a dynamic icing microstructure, which is used for expressing an icing internal microstructure in the form of a 0-1 three-dimensional matrix, wherein 0 represents icing, and 1 represents bubble pores in the icing. Then based on the assumption that the pores are spherical, the spherical coordinates of the pores are randomly generated in a uniform distribution mode, and the diameters of the pores are randomly generated in a specific distribution mode on the premise of given integral pore number, so that a model is generated in a given three-dimensional area by combining the spherical position and the pore diameter. Li Wei et al also propose a "dynamic icing pore structure three-dimensional modeling method", which, in order to study and determine the proportional relationship between the real icing size and the modeling area, analyzes the influence of the scale on the resolution and modeling, calculates the three-dimensional pore number and its pore diameter by combining the porosity and a specific pore distribution function, and a pore position random generation method, and based on this, finally establishes a method for characterizing the three-dimensional pore number microstructure in a 0-1 matrix form. However, the modeling method is applied to analysis and research of dynamic ice dynamic performance and the like and faces the following problems: 1) When the dynamic ice model is constructed, only the pore diameter distribution condition and the pore number in a specific environment are considered, so that the dynamic ice model is only suitable for dynamic ice generated in the specific environment, rounding errors exist in calculation of the pore number, and the actual conditions of the porosity and the pore diameter distribution in the dynamic ice microstructure in the corresponding environment cannot be accurately and objectively reflected, so that the simulation of the dynamic ice microstructure cannot be accurately realized, and further, the elastic modulus of the dynamic ice model constructed based on the modeling mode is predicted, and the calculation accuracy is reduced; 2) The dynamic ice model is built, the performance requirement on the computer equipment is very high, and dynamic mechanical analysis and research are further carried out on the basis, so that great challenges are provided for the performance of the computer equipment. The process of dynamic ice modeling not only requires calculation of the position (e.g., spherical coordinates) and diameter of each aperture and then generation of the corresponding aperture, but also requires extensive calculations based on the model, such as meshing, finite element solution, etc., in the process of dynamic mechanical analysis. On the premise of ensuring certain precision, a large number of pores are required to be constructed, the number of pores is large, the geometric size of the model is large, and as mentioned above, the method can provide great challenges for the performance requirements of computer equipment, and dynamic mechanical performance analysis and research are required to be carried out on the basis again. However, for many businesses or research units that have been equipped with relatively low performance computer devices (e.g., many years ago), or for some remote research units (e.g., south pole research sites, etc.), modeling using this approach may occupy much of the CPU and memory of the computer device, and may not even be affordable, let alone performing dynamic ice mechanics research analysis work on a modeling basis. However, to perform modeling based on the modeling method and further perform dynamics analysis research, it is necessary to purchase high-performance computer equipment again, which greatly increases the cost of scientific research for enterprises or scientific research institutions already equipped with large amounts of computer equipment, and it is impractical to purchase high-performance computer equipment in a short period of time for some places such as south-pole scientific research. Therefore, how to enable rapid dynamic mechanical analysis research on relatively low-performance or limited-computing-power computer devices is a current urgent problem to be solved.
Disclosure of Invention
The present invention aims to provide a method for predicting the elastic modulus of dynamic ice, which partially solves or alleviates at least one of the problems in the prior art, and can more efficiently predict the elastic modulus of dynamic ice without sacrificing accuracy.
In order to solve the technical problems, the invention adopts the following technical scheme:
the invention aims to provide a dynamic ice elastic modulus prediction method, which comprises the following steps: acquiring pore characteristic parameters and true porosity of the dynamic ice; the pore characteristic parameters include: the number of pore samples, the sample pore diameter size, and the frequency of the sample pore diameters of different sizes; determining an optimal distribution function for characterizing a true distribution state of pore diameters in the dynamic ice based on the pore characteristic parameters; calculating the geometric dimension of a finite element unit model corresponding to each of the number of the pre-cast pores based on a plurality of pre-cast pores, the real porosity and the optimal distribution function, and performing pre-cast modeling in a space range defined by the geometric dimension to construct a finite element unit model with the pore diameter conforming to the optimal distribution function and the porosity conforming to the real condition, so as to obtain a pre-cast dynamic ice module corresponding to each of the number of the pre-cast pores; the previewing dynamic ice module comprises a plurality of finite element unit cell models; calculating the porosity error of each previewing dynamic ice module, and judging whether the accuracy of the previewing dynamic ice module reaches an accuracy grade appointed in advance based on the current equipment performance based on the porosity error; if the specified precision grade is reached, obtaining at least one target pore number, and determining a minimum pore number threshold value corresponding to the specified precision grade from the at least one target pore number; taking any finite element unit model in the previewing dynamic ice module corresponding to the minimum threshold value of the pore number or one finite element unit model with the minimum absolute value of the difference between the porosity and the real porosity as a target finite element unit model corresponding to the appointed precision grade; the finite element unit cell model comprises a three-dimensional model or a two-dimensional model; inputting the elastic modulus and poisson ratio of dynamic ice without pores aiming at the target finite element unit cell model, dividing finite element grids, and establishing periodic boundary conditions and a displacement loading mode; the dynamic ice structure response was calculated using the finite element method and the dynamic ice elastic modulus was calculated based on the average strain theory.
In some embodiments of the present invention, if the accuracy of the pre-modeling dynamic ice module does not reach the specified accuracy level, the number of pre-modeling pores is adjusted based on a preset adjustment reference, or the number of pre-modeling pores defined by a user is obtained, then the geometric dimension of the corresponding finite element unit cell model is recalculated, and pre-modeling is performed, and the process is repeated until the target finite element unit cell model corresponding to the specified accuracy level is obtained.
In some embodiments of the invention, the method further comprises the steps of: and randomly selecting a plurality of finite element unit cell models from the previewing dynamic ice module corresponding to the minimum pore number threshold to calculate for a plurality of times to obtain a plurality of elastic moduli, and outputting an average value of the plurality of elastic moduli as a final elastic modulus of the dynamic ice.
In some embodiments of the invention, the method further comprises the steps of: and calculating absolute values of differences between porosities of all finite element unit cell models in the previewing dynamic ice module corresponding to the minimum threshold value of the number of the porosities and the true porosities, sequencing the calculated absolute values in a sequence from small to large, then selecting a plurality of finite element unit cell models which are sequenced in front for multiple times to calculate to obtain a plurality of elastic moduli, and outputting an average value of the plurality of elastic moduli as a final elastic modulus of the dynamic ice.
In some embodiments of the present invention, the step of determining an optimal distribution function for characterizing a distribution state of pore diameters in the dynamic ice based on the obtained pore characteristic parameters specifically includes the steps of: respectively carrying out parameter estimation on a plurality of preset distribution functions by adopting a maximum likelihood method, and fitting each distribution function; respectively calculating the fitting goodness-of-fit parameters between the fitting data of each distribution function and the pore characteristic parameters; and taking the distribution function corresponding to the smallest fitting goodness parameter as the optimal distribution function for representing the true distribution state of the pore diameter in the dynamic ice.
In some embodiments of the invention, the goodness-of-fit parameter is the sum of squares error between the fit data and pore diameter in the pore characterization parameterWherein d i N, which is the obtained measurement value of the pore diameter of the ith sample of the dynamic ice di For the number of pore samples taken, +.>And (3) fitting the obtained i-th sample pore diameter fitting value based on the distribution function.
In some embodiments of the present invention, the step of performing a pre-modeling within a space defined by the geometric dimensions to construct a finite element unit cell model with a pore diameter conforming to the optimal distribution function, specifically includes the steps of: generating spherical coordinates O of each pore in the three-dimensional model in a uniform random form within a space range defined by the geometric dimensions j，3d (X j ，Y j ，Z j ) The method comprises the steps of carrying out a first treatment on the surface of the Determining a corresponding pore diameter d of the pore at each spherical center coordinate in the three-dimensional model based on a random form of the optimal distribution function j，3d Obtaining the three-dimensional model; wherein j=1, 2 … N, X j ，Y j ，Z j And the coordinates of the sphere center of the jth pore on the X axis, the Y axis and the Z axis in the three-dimensional coordinate system where the three-dimensional model is located are respectively obtained.
In some embodiments of the present invention, the calculation formula of the geometric dimension of the three-dimensional model is:the calculation formula of the geometric dimension of the two-dimensional model is as follows:wherein N is k A k-th number of preformed pores among the preset number of preformed poresThe side length of the two-dimensional model is; l (L) 3d A side length of the three-dimensional model; lambda is the true porosity of the dynamic ice; f (F) -1 (1) The value of the inverse function of the optimal distribution function at the position 1; f' (x) is a probability density function of the optimal distribution function; x is the pore diameter.
In some embodiments of the invention, the space defined by the geometry is: [ L 3d -F -1 (1)]×[L 3d -F -1 (1)]×[L 3d -F -1 (1)]Alternatively, [ L ] 3d -δ*F -1 (1)]×[L 3d -δ*F -1 (1)]×[L 3d -δ*F -1 (1)]The method comprises the steps of carrying out a first treatment on the surface of the Wherein, delta takes a value of 0.7 or 0.8.
Since the coordinates of the centers of the pores will be randomly generated, in order to avoid that each pore near the edge is cut to affect the accuracy of the subsequent meshing and finite element solving, the spatial range in which each pore is generated is defined within the spatial range defined by the above-mentioned geometric dimensions based on the specified value delta.
In some embodiments of the present invention, the step of performing a pre-modeling within a space defined by the geometric dimensions to construct a finite element unit cell model with a pore diameter conforming to the optimal distribution function, specifically includes the steps of: generating spherical coordinates O of each pore in the two-dimensional model in a uniform random form within a space range defined by the geometric dimensions j，2d (X j ，Y j ) The method comprises the steps of carrying out a first treatment on the surface of the Determining a corresponding pore diameter d of the pore at each spherical center coordinate in the two-dimensional model based on a random form of the optimal distribution function j，2d Obtaining the two-dimensional model; wherein j=1, 2 … N, X j ，Y j And the coordinates of the sphere center of the jth hole on the X axis and the Y axis in the two-dimensional coordinate system where the two-dimensional model is located are respectively shown.
In some embodiments of the invention, the space defined by the geometry is: [ L 2d -F -1 (1)]×[L 2d -F -1 (1)]The method comprises the steps of carrying out a first treatment on the surface of the Alternatively, [ L ] 2d -δ*F -1 (1)]×[L 2d -δ*F -1 (1)]The method comprises the steps of carrying out a first treatment on the surface of the Wherein, the delta takes the value of 0.7 or 0.8.
In some embodiments of the present invention, the step of performing a pre-modeling within a space defined by the geometric dimensions to construct a finite element unit cell model having a pore diameter corresponding to the optimal distribution function, further comprises the steps of: judging whether the generated multiple pores are intersected, if so, regenerating the spherical coordinates and pore diameters of the multiple pores, and judging whether the multiple pores are intersected again until all the generated pores are disjoint.
The beneficial effects are that: it is well known that the size of the number of pores in the modeling process directly affects the size of the geometric dimension of the model and the speed of modeling, and also affects the speed and the time consumed for meshing and finite element solving in the subsequent elastic modulus analysis process. Therefore, on the premise of not sacrificing the precision (namely meeting or reaching the precision required by a user), a dynamic ice model with smaller pore number and smaller geometric dimension is constructed, so that the requirement on the performance of computer equipment is reduced, and the modeling speed and the dynamic mechanical analysis speed are accelerated to a certain extent. Based on the method, on the basis of not specifying geometric dimensions and not specifying the number of pores, the method provided by the invention can be used for quickly constructing the dynamic ice model conforming to the specified precision grade without sacrificing precision, and can be used for greatly reducing the time and the calculated amount consumed by the elastic modulus analysis (particularly, the dynamic ice model can be any finite element unit model in the pre-modeling dynamic ice model, or one finite element unit model with the minimum absolute value of the difference between the porosity and the actual porosity in the pre-modeling dynamic ice model), on the premise of not sacrificing precision, namely, the method can be used for quickly constructing the dynamic ice model conforming to the specified precision grade without occupying too much CPU, reserving enough CPU and memory for the subsequent elastic modulus analysis, and simultaneously greatly reducing the time and the calculated amount consumed by the elastic modulus analysis (because the reduction of the geometric dimensions of the model, the corresponding time and the calculated amount required by the finite element unit equation are also reduced), so that the elastic modulus analysis can be effectively carried out on the premise of not consuming a large amount of computers. In addition, as the user designates the precision grade according to the current equipment performance in advance, then finds the minimum threshold value of the pore number corresponding to the precision grade in a pre-modeling mode, then finds the target finite element unit cell model in the pre-modeling dynamic ice module corresponding to the minimum threshold value of the pore number, and then carries out elastic modulus analysis on the target finite element unit cell model, namely on the premise of limited conditions, an optimal research strategy (such as a modeling mode and an elastic modulus prediction mode with relatively small calculated amount) is found for dynamic ice elastic modulus research and analysis as soon as possible, so that the working efficiency is greatly improved; and meanwhile, the user can reasonably allocate resources in advance according to the performance of each device. The invention avoids the defects that the pore diameter distribution function is single and the true porosity cannot be accurately simulated in the prior art by searching the optimal distribution function close to the dynamic ice pore diameter distribution in a plurality of distribution functions. In the elastic modulus prediction, the geometric dimension of the target finite element unit cell model is obtained by calculation according to the real porosity and the minimum pore number threshold value of the dynamic ice in advance, and then the generation space of the center position of the pore is set according to the appointed value, so that the generated pore is prevented from being cut off by the edge of the model, the pore distribution characteristics can be accurately simulated, the real porosity of the dynamic ice (the pore distribution characteristics and the porosity have obvious influence on the elastic modulus calculation) can be accurately reflected, namely, the accuracy of pore diameter distribution is improved, the accurate simulation of the real porosity is realized, the microstructure of the dynamic ice is truly and objectively reflected, and the calculation of the elastic modulus of the dynamic ice is more accurate and efficient. On the other hand, based on the dynamic ice elastic modulus prediction method, not only can a two-dimensional model of dynamic ice be constructed to predict the elastic modulus, but also a three-dimensional model of dynamic ice can be constructed to predict the elastic modulus, so that a user can further select to construct a corresponding model according to different application scenes, and then the elastic modulus is predicted. For example, the performance of the current hardware equipment is not high, a two-dimensional model of the dynamic ice can be correspondingly obtained based on the modeling method of the invention, and then the elastic modulus can be calculated on a two-dimensional scale, and if the performance of the current hardware equipment is high, a three-dimensional model of the dynamic ice can be correspondingly constructed based on the modeling method of the invention, and then the elastic modulus can be calculated on a three-dimensional scale. The invention has more universality and universality, also provides the possibility of selection for users, and is more flexible.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. Like elements or portions are generally identified by like reference numerals throughout the several figures. In the drawings, elements or portions thereof are not necessarily drawn to scale. It will be apparent to those of ordinary skill in the art that the drawings in the following description are of some embodiments of the invention and that other drawings may be derived from these drawings without inventive faculty.
FIG. 1 is a flow chart of a dynamic ice elastic modulus prediction method according to an exemplary embodiment of the present invention;
FIG. 2 is a flowchart of step S12 in a dynamic ice elastic modulus prediction method according to an exemplary embodiment of the present invention;
FIG. 3a is a flowchart of step S13 in a dynamic ice elastic modulus prediction method according to an exemplary embodiment of the present invention;
FIG. 3b is a flowchart of step S13 in a dynamic ice elasticity module prediction method according to yet another exemplary embodiment of the present invention;
FIG. 4a is a schematic diagram of loading with X-direction displacement in periodic boundary conditions of a finite element single cell three-dimensional model;
FIG. 4b is a schematic diagram of loading with X-direction displacement in periodic boundary conditions of a two-dimensional model of finite element single;
FIG. 5a is a view of a dynamic ice profile image obtained under a microscope;
FIG. 5b is a graph of pore diameter statistics and frequency histogram obtained by image analysis of the cross-sectional morphology image of FIG. 5 a;
FIG. 6a is a schematic fit of a predetermined plurality of distribution functions to the histogram of pore diameter frequency shown in FIG. 5 b;
FIG. 6b is a schematic diagram showing the results of calculating the goodness-of-fit parameter corresponding to the various distribution functions shown in FIG. 6 a;
FIG. 7 is a schematic diagram of a constructed dynamic ice three-dimensional finite element single cell model;
FIGS. 8a and 8b are schematic diagrams of dynamic ice three-dimensional finite element single cell model meshing;
FIG. 9a is a dynamic ice three-dimensional finite element single cell model displacement cloud;
FIG. 9b is a stress cloud diagram of a dynamic ice three-dimensional finite element single cell model;
FIG. 10 is a schematic diagram of a dynamic ice two-dimensional finite element single cell model;
FIG. 11 is a schematic diagram of a dynamic ice two-dimensional finite element single cell model network partition;
FIGS. 12a and 12b are dynamic ice two-dimensional finite element single cell model displacement cloud and stress cloud, respectively;
FIG. 13a is a graph of statistical results reflecting the mean and standard deviation of porosities for 100 three-dimensional models of dynamic ice microstructures with a pore size of 10;
FIG. 13b is a graph of statistical results reflecting the mean and standard deviation of porosities for 100 three-dimensional models of dynamic ice microstructures with a pore number of 50;
FIG. 13c is a graph of statistical results reflecting the mean and standard deviation of the porosities of 100 dynamic ice microstructure three-dimensional models with a pore number of 100;
FIG. 13d is a graph of statistical results reflecting the mean and standard deviation of the porosities of 100 dynamic ice microstructure three-dimensional models with a pore number of 150;
FIG. 13e is a graph of statistical results reflecting the mean and standard deviation of the porosities of 100 dynamic ice microstructure three-dimensional models with 300 porosities;
FIG. 14a is a graph of statistical results reflecting the mean and standard deviation of porosities for 100 two-dimensional models of dynamic ice microstructures with a pore number of 10;
FIG. 14b is a graph of statistical results reflecting the mean and standard deviation of porosities for 100 two-dimensional models of dynamic ice microstructures with a pore number of 50;
FIG. 14c is a graph of statistical results reflecting the mean and standard deviation of the porosities of 100 dynamic ice microstructure two-dimensional models with a pore number of 100;
FIG. 14d is a graph of statistical results reflecting the mean and standard deviation of the porosities of 100 dynamic ice microstructure two-dimensional models with a pore number of 150;
FIG. 14e is a graph of statistical results reflecting the mean and standard deviation of the porosities of 100 dynamic ice microstructure two-dimensional models with 300 porosities;
FIG. 15 is a graph showing the average value statistics of porosities of a three-dimensional model and a two-dimensional model under different pore number conditions.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. In this document, suffixes such as "module", "component", or "unit" used to represent elements are used only for facilitating the description of the present invention, and have no particular meaning in themselves. Thus, "module," "component," or "unit" may be used in combination. The terms "upper," "lower," "inner," "outer," "front," "rear," "one end," "the other end," and the like herein refer to an orientation or positional relationship based on that shown in the drawings, merely for convenience of description and to simplify the description, and do not denote or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus should not be construed as limiting the invention. Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. As used in this specification, the term "about equal to" refers to a value obtained by rounding. The terms "mounted," "configured to," "connected," and the like, herein, are to be construed broadly as, for example, "connected," whether fixedly, detachably, or integrally connected, unless otherwise specifically defined and limited; the two components can be mechanically connected, can be directly connected or can be indirectly connected through an intermediate medium, and can be communicated with each other. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art. Herein, "and/or" includes any and all combinations of one or more of the associated listed items. Herein, "plurality" means two or more, i.e., it includes two, three, four, five, etc. "true" or "near true" or "mirror. True" herein refers to a true case that approximates the microstructure within the dynamic ice, e.g., a true case where the distribution between pores in the model constructed herein is more closely related to the distribution of pore diameters of the dynamic ice, and the porosity of the model constructed herein is the same as (or has almost negligible error as) the true porosity of the dynamic ice. It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element. In this specification, certain embodiments may be disclosed in a format that is within a certain range. It should be appreciated that such a description of "within a certain range" is merely for convenience and brevity and should not be construed as a inflexible limitation on the disclosed ranges. Accordingly, the description of a range should be considered to have specifically disclosed all possible sub-ranges and individual numerical values within that range. The above rule applies regardless of the breadth of the range.
Pore diameter sample data: herein, "pore diameter sample data" includes each sample pore diameter d in real dynamic ice corresponding to the dynamic ice model currently to be constructed i The pore characteristics of the dynamic ice can be obtained based on the statistics of the pore diameter sample data, including the number of pore samples (typically the number of pore samples n of dynamic ice di Typically greater than 400), sample pore diameter size, and frequency of occurrence of various sample pore diameters (i.e., sample pore diameters of different sizes) in the dynamic ice, which represents a true distribution of pore diameters in the dynamic ice. For example, the cross-sectional morphology of the real dynamic ice is obtained by a microscope (as shown in fig. 5 a), then image analysis is performed according to the cross-sectional morphology obtained by the microscope, so as to obtain the pore diameter statistical data (i.e. the pore diameter size in the dynamic ice) and the frequency histogram (i.e. the frequency f of each occurrence of the pore diameters of samples with different sizes in the dynamic ice), and the real porosity of the dynamic ice can also be obtained.
Porosity: herein, "porosity" refers to the ratio of pores in the microstructure of the dynamic ice. For example, the ratio of the total volume of all pores in the microstructure of the dynamic ice to the volume of the dynamic ice obtained by image analysis of the profile of the dynamic ice; or the ratio of the total area of all apertures in the cross section to the cross section area; for another example, if a three-dimensional model of dynamic ice is constructed, the porosity refers to the ratio of the volume of all pores in the three-dimensional model to the volume of the three-dimensional model, i.e., the pore volume ratio in the three-dimensional model; if a two-dimensional model (e.g., a cross-section) of dynamic ice is constructed, the porosity refers to the ratio of the area of all pores in the two-dimensional model to the area of the two-dimensional model, i.e., the pore area ratio in the two-dimensional model.
Optimum distribution function: the "optimal distribution function" herein refers to a distribution function that is most capable of reflecting or closest to the true distribution state of pore diameters in dynamic ice.
Error between the porosity of the finite element single cell model and the true porosity of the dynamic ice: refers to the ratio of the absolute value of the difference between the average value of the model porosity and the true porosity obtained by modeling for a plurality of times and the true porosity under the same modeling input condition. For example, calculating to obtain the geometric dimension of the corresponding finite element unit cell model based on the same number of the preformed pores, the real porosity and the optimal distribution function, then performing the preformed modeling for a plurality of times based on the geometric dimension to obtain a plurality of finite element unit cell models (i.e. the preformed dynamic ice modules corresponding to the same number of the preformed pores), and then calculating the ratio of the absolute value of the difference between the average value of the porosities of the finite element unit cell models and the real porosity to the real porosity, namely the calculated error.
Precision grade: herein, "precision grade" refers to grading based on the error between the porosity of the constructed dynamic ice model and the true porosity of the dynamic ice. For example, the error between the porosity of the dynamic ice model and the true porosity of the dynamic ice (after rounding) is less than or equal to 1%, and then the first precision grade is divided; if the error (after rounding) is not less than 1% and not more than 2%, the second precision grade is classified. Specifically, the precision level may be adjusted according to the actual application scenario, which is not limited herein.
Pore number minimum threshold: the "minimum threshold of the number of pores" herein refers to the minimum value of the number of pores required to construct a dynamic ice model of a specified level of accuracy. On the premise of not specifying the geometric dimension of the dynamic ice model, the corresponding pore number cannot be determined, when the pore number is increased, the porosity of the dynamic ice model is closer to the real porosity of the dynamic ice, namely the error between the two is smaller, and for the same precision grade, when the pore number reaches a certain critical value, even if the pore number is increased, the error change between the porosity of the dynamic ice model and the real porosity of the dynamic ice is not large, so that the critical value is the minimum pore number required for constructing the dynamic ice model conforming to the corresponding precision grade. For example, based on any given pore number 10, the number of pores is increased by a preset increment unit for modeling, and when the pore number is 50, the error between the porosity and the true porosity of the constructed dynamic ice model is within 1%, and when the pore number is increased to 100, 150, 200, 300, the error between the porosity and the true porosity of the constructed dynamic ice model is still within 1%, that is, when the pore number reaches 50, even if the pore number is increased again, the error between the porosity and the true porosity of the dynamic ice model is not changed greatly, so 50 is the minimum threshold value of the found pore number.
Example 1-dynamic ice elastic modulus prediction method: referring to fig. 1, a flowchart of a dynamic ice elastic modulus prediction method according to an exemplary embodiment of the present invention, specifically, the method includes the steps of: s11, acquiring the pore characteristic parameters and the actual porosity of the dynamic ice. In some embodiments, the pore characterization parameters include: the sample pore diameter size of each pore in the dynamic ice, the frequency of sample pore diameters of different sizes, and the number of pore samples. In some embodiments, the dynamic ice may be prepared in advance through a wind tunnel icing test, or the dynamic ice in a real icing environment may be obtained, then, a profile of the dynamic ice may be obtained by using a microscope, as shown in fig. 5a (a scale bar in a white line length representation is 1mm in the drawing), and then, an image processing is performed on a profile image obtained by using the microscope, so as to obtain each pore characteristic parameter of the dynamic ice, as shown in fig. 5b (in the drawing, an ordinate f is a frequency of occurrence of the same diameter, and an abscissa is a pore diameter, and is in mm).
And S12, determining an optimal distribution function for representing the true distribution state of the pore diameter in the dynamic ice from a plurality of preset distribution functions based on the pore characteristic parameters obtained in the step S11. Specifically, referring to fig. 2, in some embodiments, the step S12 specifically includes the steps of:
S121, respectively carrying out parameter estimation on a plurality of preset distribution functions by adopting a maximum likelihood method, and fitting each distribution function. In some embodiments, the predetermined plurality of distribution functions includes: t distribution function, normal distribution function, gamma distribution function, beta distribution function, rayleigh distribution function, weibull distribution function, cauchy distribution function, and the like.
S122, calculating the fitting goodness-of-fit parameters between the fitting data of each distribution function and the acquired pore characteristic parameters respectively. In some embodiments, the goodness-of-fit parameter is the sum of the square error between the sample pore diameter in the pore characterization parameter and the fit dataWherein d i For the obtained measurement of the ith sample pore diameter of the dynamic ice, n di For the number of pore samples taken, +.>For the fitting value of the ith pore diameter obtained by fitting based on the distribution function, that is, the sum of square errors between the fitting data of each distribution function (that is, the fitting value of the pore diameter) and the sample pore measurement value in the pore characteristic parameter of the dynamic ice is calculated in this step S122. In some embodiments, "root mean square error", "average error" and "as the goodness-of-fit parameter may also be used to filter the optimal distribution function.
And S123, taking the distribution function corresponding to the minimum fitting goodness parameter calculated in the step S122 as the optimal distribution function for representing the true distribution state of the pore diameter in the dynamic ice. In some embodiments, the goodness-of-fit parameters between the respective distribution functions calculated in step S122 and the pore characteristic parameters may be ordered (e.g., in order from large to small, or from small to large), and then the distribution function corresponding to the smallest goodness-of-fit parameter may be selected as the optimal distribution function F (x) for characterizing the true distribution state of pore diameters in the dynamic ice.
And S13, calculating the geometric dimension of the finite element unit model corresponding to each pre-modeling pore number based on a plurality of pre-modeling pore numbers preset, the real porosity in the step S11 and the optimal distribution function in the step S12, and performing pre-modeling in a space range defined by the geometric dimension to obtain a pre-modeling dynamic ice module corresponding to each pre-modeling pore number. In some embodiments, the number of preformed pores is preset, but the number of pores is not randomly specified, but is preset in consideration of the approximate desired geometric dimensions of the finite element single cell model, the precision level specified by the user, and the true porosity of the dynamic ice. In some embodiments, different finite element single cell models, e.g., three-dimensional models or two-dimensional models, may be built in advance according to different requirements. Referring to fig. 3, in some embodiments, the step S13 specifically includes the steps of: s131, determining the geometric dimension of each corresponding finite element unit cell model of the number of the pre-modeling pores based on the preset number of the pre-modeling pores, the real porosity obtained in the step S11 and the preset geometric dimension mathematical model of the finite element unit cell model.
S132, generating spherical center coordinates of each pore in the finite element single cell model in a uniform and random mode in a space range defined by the geometric dimension calculated in the step S131 according to the number of each previewing pore. In some embodiments, if the pre-modeling builds a three-dimensional model, the mathematical model of the geometry of the pre-modeling dynamic ice model is calculated as:correspondingly, if the two-dimensional model is constructed by the pre-modeling, the mathematical model for calculating the geometric dimension of the pre-modeling dynamic ice model is as follows: />Wherein L is 2d Is the side length of the two-dimensional model, L 3d Is the side length of the three-dimensional model; n (N) k A k-th number of pre-determined pores; lambda is the true porosity of the dynamic ice; f (F) -1 (1) The value of the inverse function of the optimal distribution function at the position 1; f' (x) is the probability density function of the optimal distribution function F (x), x being the pore diameter. In some embodiments, if the previewing is constructed as a three-dimensional model, the spatial range defined by the calculated geometry is: [ L 3d -F -1 (1)]×[L 3d -F -1 (1)]×[L 3d -F -1 (1)](3). And the spherical center coordinates of the pores are generated in a uniform and random form within the space range to be O j，3d (X j ，Y j ，Z j )，j＝1，2…N i ，X j ，Y j ，Z j Respectively the j-th pore sphere center is positioned on the X axis, the Y axis and the Z axis in the three-dimensional coordinate system where the three-dimensional model is positioned The scale (i.e., the probability that the coordinates of the center of the pore sphere are randomly generated at any point is equal within the spatial range defined by the geometry). Accordingly, if a two-dimensional model is constructed, the space defined by the geometric dimensions is: [ L 2d -F -1 (1)]×[L 2d -F -1 (1)](4) And generating the spherical center coordinate of the pore as O in a uniform random form in the space range j，2d (X j ，Y j )，j＝1，2…N i ，X j ，Y j The coordinates of the sphere center of the jth aperture on the X axis and the Y axis in the two-dimensional coordinate system where the two-dimensional model is located are respectively (i.e. the probability that the coordinates of the sphere center of the aperture are randomly generated at any point is equal in the space range defined by the geometric dimensions). Further, in other embodiments, in order to obtain a higher quality finite element mesh, the prediction accuracy of the subsequent elastic modulus is prevented from being affected by the aperture in the three-dimensional model being cut by the surface (or the boundary surface) of the three-dimensional model, and the spatial range of the aperture is set based on the geometric dimension calculated in step S131, specifically, the spatial range is: [ L 3d -δ*F -1 (1)]×[L 3d -δ*F -1 (1)]×[L 3d -δ*F -1 (1)](5) Wherein, delta is a specified value, and the value is 0.7 or 0.8. Correspondingly, if a two-dimensional model is constructed, in order to obtain a higher-quality finite element mesh, the problem that the prediction accuracy of the subsequent elastic modulus is affected by the fact that the pores in the two-dimensional model are cut by the edges of the two-dimensional model is avoided, and the spatial range of the pores is set based on the geometric dimension calculated in the step S131, specifically, the spatial range is as follows: [ L 2d -δ*F -1 (1)]×[L 2d -δ*F -1 (1)](6) Wherein, delta is a specified value/constant, and the value is 0.7 or 0.8. Since the pores themselves have no elastic modulus and the difference between the elastic modulus of the pores and the elastic modulus of the ice layer is too large, i.e. the elastic modulus of the pores is far from the elastic modulus of the ice layer by a large order of magnitude, the pores are defined inside non-boundary surfaces (e.g. six surfaces of a three-dimensional model or four edges of a two-dimensional model) during modeling in order to avoid distortion at boundaries during the calculation of the finite elements of the whole model during subsequent elastic modulus predictionThe continuity of the boundary conditions (i.e., no voids are present on the boundary surface such that the voids are not cut) is left, thereby improving the uniformity and stability of subsequent elastic modulus calculations based on the model.
S133, determining the corresponding pore diameter of the pore at each spherical center coordinate in the simulation model (namely the finite element unit cell model) based on the random form of the optimal distribution function, and finally obtaining the simulation model, namely the finite element unit cell model corresponding to the number of the preformed pores. In some embodiments, if the previewing builds a three-dimensional model, the corresponding pore diameter d of each pore in the simulation model is determined based on a random form of the optimal distribution function j，3d (namely, the specific value of the diameter of each pore in the model is randomly generated according to a probability density function F' (x) conforming to a previously determined optimal distribution function F (x)), and finally the three-dimensional simulation model corresponding to the number of the pre-modeling pores is obtained. If a two-dimensional model is constructed, correspondingly, determining the corresponding pore diameter d of each pore in the simulation model based on the random form of the optimal distribution function j，2d Finally, a two-dimensional simulation model corresponding to the number of the pre-modeling pores is obtained. In the embodiment, the geometric dimension of the model is reversely deduced based on the real porosity of the dynamic ice and the number of the preformed pores, and each pore is generated in the geometric dimension based on the optimal distribution function which accords with the real distribution of the profile of the dynamic ice, so that a simulation model which is close to the real condition and the real porosity of the pore diameter distribution in the dynamic ice can be obtained, and further the dynamic ice mechanical property measurement is more accurate based on the simulation model; meanwhile, the minimum threshold value of the number of pores required for constructing the precision grade according to the precision grade supported by the current performance of the existing computer equipment can be found, so that a dynamic ice model is quickly constructed and dynamic ice mechanical property measurement is carried out with low cost on the premise of not sacrificing the precision grade.
And S134, repeatedly executing the steps S132-S133 for a plurality of times to obtain the previewing dynamic ice module corresponding to the number of each previewing pore. In some embodiments, for the number of preview apertures N 1 Performing multiple previewing modeling according to the steps to obtain a group of previewing dynamicsAn ice module; for the number N of the previewing pores 2 And performing multiple previewing modeling according to the steps to obtain a second group of previewing dynamic ice modules. The real pore distribution in the dynamic ice may have the condition of pore intersection, so the generated corresponding simulation model also has the condition of pore intersection, and when the dynamic ice mechanical property measurement is performed based on the simulation model, the pore intersection may affect the network quality, and even may cause calculation distortion, thereby affecting the accuracy and calculation efficiency of the mechanical property measurement to a certain extent. Thus, in other embodiments, for some application scenarios with higher requirements on accuracy and computational efficiency, to obtain a higher quality finite element mesh, see fig. 3b, after each generation of a finite element single cell model, the method further comprises the steps of: and S135, judging whether the generated multiple pores are intersected, and if so, repeating the steps S132 to S133 until all the pores in the finite element single cell model generated at present are not intersected in the step S135. In some embodiments, intersecting means that the center-of-sphere distance of two pores is less than the sum of their respective pore radii, so that, specifically, each time a pore is created, it can be determined whether it intersects with other pores that have been created; if so, regenerating the pore, judging whether the pore is intersected with the existing pore again, and repeating the steps until the pore is not intersected with the existing pore, and generating the next pore according to the same principle. For example, the spatial coordinates O of the center of the first aperture are randomly generated 1，3d (X 1 ，Y 1 ，Z 1 ) And randomly generating the diameter d of the first pore according to the pore diameter optimal distribution function 1，3d The method comprises the steps of carrying out a first treatment on the surface of the Subsequently randomly generating the spatial coordinates O of the sphere center of the second aperture 2，3d (X 2 ，Y 2 ，Z 2 ) Then the diameter d of the second pore is generated randomly according to the pore diameter optimal distribution function 2，3d The method comprises the steps of carrying out a first treatment on the surface of the Then judging whether the two pores are intersected, namely judging whether the distance between the spherical center of the first pore and the spherical center of the second pore is smaller than the sum of the radius of the first pore and the radius of the second pore, if so, judging that the two pores are intersected, regenerating the space coordinate and the pore diameter of the second pore, and intersecting againJudging until the judgment is disjoint; then generating a third pore sphere center coordinate 0 according to the same principle 3，3d (X 3 ，Y 3 ，Z 3 ) Pore diameter d 3，3d And judging whether the first pore and the second pore respectively intersect with each other, and repeating the steps until all the pores are formed. Note that when the j+1th pore center coordinates O are generated j+1，3d (X j+1 ，Y j+1 ，Z j+1 ) Pore diameter d j+1，3d When the method is used, whether the i+1th pore is intersected with any generated pore or not is judged, namely, whether the distances between the sphere centers of the 1 st pore, the 2 nd pore and the 3 rd pore and the sphere center of the j+1th pore are smaller than the sum of corresponding radiuses is calculated in sequence, if the distances are not met, the coordinates of the sphere center of the j+1th pore and the pore diameter are regenerated until the conditions are met (namely, the j+1th pore is not intersected with any generated pore), the j+2th pore meeting the conditions is regenerated, and the method is repeated until all the pores are generated. In this embodiment, since the measurement of the mechanical properties of the dynamic ice is considered to be performed subsequently, the simulation model with disjointed pores is constructed in the above manner, and although the consistency with the real pore situation of the dynamic ice is sacrificed to a certain extent, the calculation distortion can be effectively avoided, so that the mesh division quality of the subsequent model is improved, the calculation efficiency of the mechanical properties of the subsequent dynamic ice is also improved, that is, a balance is obtained between the consistency with the real pore situation of the dynamic ice, the calculation precision and the calculation speed.
And S14, calculating the porosity error of each previewing dynamic ice module, judging whether the corresponding previewing dynamic ice module accords with the designated precision grade based on the porosity error, if so, executing the step S15, otherwise, executing the step S16. In some embodiments, in order to reduce the error, therefore, for each number of pre-performed pores, a set of pre-performed dynamic ice models is obtained by performing a number of pre-performed modeling, i.e., a plurality of dynamic ice models are constructed based on each number of pre-performed pores, then the porosity error (i.e., the ratio of the absolute value of the difference between the average value of the porosities of all the finite element unit cell models in the set of dynamic ice models and the true porosity) of each set of dynamic ice models is calculated, and then it is determined whether it meets the precision level set by the user in advance based on the current computer device performance. For example, the user designates the precision grade as 1 (i.e. the error is less than or equal to 0.01) according to the performance of the current equipment, and accordingly, when the respective porosity error of each group of dynamic ice modules is obtained, whether the group meets the designated precision grade can be judged.
S15, obtaining at least one target pore number, determining a minimum pore number threshold value corresponding to the specified precision grade from the target pore number, taking a finite element unit cell model with the minimum absolute value of the difference between the porosity and the true porosity in the previewing dynamic ice module corresponding to the minimum pore number threshold value as a target finite element unit cell model corresponding to the specified precision grade, and executing the step S21. In some embodiments, since the number of previewing apertures is preset, there are multiple groups, e.g., N, of the multiple groups of previewing dynamic ice modules that may be configured to meet the user-specified level of accuracy 3 ，N 4 Wherein the minimum number of preformed pores N 3 The minimum threshold value of the pore number corresponding to the specified precision grade is obtained, and modeling is carried out for a plurality of times according to the number of each preformed pore during the preformed modeling, so that each group of preformed dynamic ice modules is provided with a plurality of finite element unit models, and therefore, in order to further reduce the calculation amount of the subsequent elastic modulus, the minimum one of absolute values of differences between the porosity and the actual pore is selected as the target finite element unit model so as to carry out the subsequent elastic modulus prediction. Of course, in other embodiments, a finite element single cell model may be randomly selected therefrom as the target finite element single cell model.
S16, adjusting the number of the previewing pores based on a preset adjustment reference, and executing the step S13. In some embodiments, the adjustment reference (or adjustment increment) is increased by 50 apertures each time, and of course, may be user-defined; or, after the user directly defines the corresponding number of the preview pores, step S13 is executed. Further, different adjustment references may be set in advance according to different precision levels, and as the precision level increases, the adjustment reference increases. For example, for a first level of precision (i.e., the highest level of precision), the corresponding adjustment basis is 50 increments at a time, and for a second level of precision, the corresponding adjustment basis is 10 increments at a time. In some embodiments, the closer the porosity of the constructed dynamic ice model approaches to the real porosity of the dynamic ice, that is, the smaller the error between the two, the more the constructed dynamic ice model can represent the porosity condition in the real dynamic ice, thereby providing possibility for more accurate analysis and research of the subsequent dynamic ice mechanics. Therefore, the gradation of the porosity accuracy is performed in advance based on the error. For example, less than or equal to 0.01 is a first level of accuracy; less than or equal to 0.02 is the second level of accuracy, and so on. Typically, the error that can be received in the art is around 0.04. Of course, the modeling method in the prediction method of the present invention is adopted in advance to perform multiple pre-modeling, for example, dynamic ice models under different pre-modeling pore numbers are built for real porosities, and the error between the porosity of each dynamic ice model corresponding to the pore numbers (for example, 100-150 models are built for each pore number, and the average value of the porosity is obtained) and the porosity of the real dynamic ice is calculated, and according to the error, which of the pre-modeling pore numbers reaching the specified precision level is determined, then the minimum pore number is found, that is, the minimum threshold of the pore number required for building the dynamic ice model of the specified precision level is obtained, that is, all the finite element models (i.e., the pre-modeling dynamic ice models) in the pre-modeling dynamic ice models corresponding to the minimum threshold of the pore number are in accordance with the specified precision level, so that one target finite element model can be directly selected from the pre-modeling dynamic ice models corresponding to the minimum threshold of the pore number to perform elastic modulus prediction, and further, the computer equipment with limited calculation performance can perform modeling accurately and rapidly, and the elastic modulus can be analyzed. In some embodiments, each precision level is matched with a respective minimum threshold of the number of apertures, for example, 50 for a first precision level and 10 for a second precision level (of course, consistent with the nature of the first precision level and also consistent with the second precision level).
S21, inputting the elastic modulus and the Poisson' S ratio of the dynamic ice without pores aiming at the target finite element unit cell model (a three-dimensional model or a two-dimensional model) determined in the step S15, dividing finite element grids, and establishing periodic boundary conditions and displacement loads. Referring to fig. 5a, in some embodiments, if the target finite element unit cell model is a three-dimensional model, the periodic boundary conditions of the dynamic ice three-dimensional unit cell model are set as follows: taking X-direction displacement loading as an example, there are:
X front face -X Rear face ＝ΔL1(7)，X Upper, left side -X Lower, right side ＝0(8)，Y Upper, front, left -Y Lower, rear, right ＝0(9)，Z Front, upper, left -Z Rear, lower, right =0 (10). Wherein X is Front face The displacement of the front node of the unit cell model along the X direction; x is X Rear face Is the displacement of the rear node of the unit cell model along the X direction; Δl1 is the displacement load applied to the front and rear facing nodes of the unit cell model in the X direction; x is X Upper, left side The displacement of the upper and left nodes of the unit cell model along the X direction; y is Y Upper, front, left The displacement of the upper, front and left nodes of the unit cell model along the Y direction; y is Y Lower, rear, right Is the displacement of the lower, rear and right nodes of the unit cell model along the Y direction; z is Z Front, upper, left The front, upper and left nodes of the unit cell model are displaced along the Z direction; z is Z Rear, lower, right Is the displacement of the rear, lower and right nodes of the unit cell model in the Z direction. Referring to fig. 4b, in some embodiments, if the target finite element unit cell model is a two-dimensional model, the periodic boundary conditions of the dynamic ice two-dimensional unit cell model are correspondingly degraded as follows: taking X-direction displacement loading as an example, there are: x is X Front edge -X Rear edge ＝ΔL1 (11)，X Upper edge -X Lower edge ＝0 (12)，Y Upper edge, front edge -Y Lower edge, rear edge =0 (13), where X Front edge Displacement of a front edge node of the unit cell model along the X direction; x is X Rear edge The displacement of the rear node of the unit cell model along the X direction; Δl1 is a displacement load applied to corresponding nodes of the front and rear sides of the unit cell model along the X direction; x is X Upper edge Bit along X direction for upper edge node of unit cell modelMoving; x is X Lower edge The displacement of the lower node of the unit cell model along the X direction; y is Y Upper edge, front edge The displacement of the upper edge and the front edge nodes of the unit cell model along the Y direction; y is Y Lower edge, rear edge Is the displacement of the lower and rear nodes of the unit cell model along the Y direction.
S22, calculating dynamic ice structure response by using a finite element method. In some embodiments, stress, strain and displacement responses of each node of the dynamic ice (i.e., each node in the dynamic ice finite element single cell model) are obtained by using finite element software and a finite element first principles method.
S23, calculating the dynamic ice elastic modulus based on the average strain theory. In some embodiments, according to average strain theory, when the intrinsic strain is uniform (inclusion of intrinsic strain) or when the external load is uniform (inclusion of inhomogeneities), the elastic field inside the inclusion is also uniform. The integral expression is as follows:
for a three-dimensional model, its modulus of elasticity is solved by:
for a two-dimensional model, its modulus of elasticity is solved by:
where v denotes the spatial extent of the calculated substance (e.g., the spatial extent defined by the geometry of the simulation model), X denotes a point of spatial location within the spatial extent v (e.g., the coordinates in the three-dimensional model are (X) 1 ，Y 1 ，Z 1 ) Is a point of (2); alternatively, the coordinates in the two-dimensional model are (X 1 ，Y 1 ) Epsilon (x) refers to the strain at spatial location x, and the integral of the strain at each point across the spatial extent of the substance is the overall strain of the substance; />Average strain for the dynamic ice simulation model; σ (x) refers to the stress at spatial position x; />Is the average stress of the dynamic ice model; e (E) i An elastic modulus in the i direction (i is X, Y, Z direction); stress is Stress; axial strain is uniaxial strain;
∑Front surface nodal forces in，i-Direction the resultant force in the i direction of all nodes on the displacement load loading surface of the finite element model is Front surface area, and the area of the displacement loading surface of the three-dimensional finite element model is the area; ΔL is the displacement variation of the finite element model, L 3d Characteristic side length of the three-dimensional finite element model; l (L) 2d The characteristic side length of the two-dimensional limited model is; sigma Front edge nodal forces in，i-Direction The resultant force of the line for the two-dimensional finite element model displacement loading edge is Front edge length, which is the length of the two-dimensional finite element model displacement loading edge.
In order to make the calculation result more in line with the statistical significance, further, a plurality of finite element unit cell models can be randomly selected from the previewing dynamic ice module corresponding to the minimum pore number threshold as target finite element unit cell models, and then S21-S23 are executed to obtain a plurality of E based on each selected finite element unit cell model x 、E y 、E z Calculating the value, and finally measuring the average value of the elastic modulus to beOr calculating absolute values of differences between each finite element unit cell model and the actual porosity in the language dynamic ice module corresponding to the minimum threshold of the pore number, sorting the calculated absolute values in order from small to large, selecting the first few bits of the calculated absolute values as target finite element unit cell models, and executing S12-S23 on the basis of each selected finite element unit cell model to obtain a plurality of E x 、E y 、E z Calculated value, final modulus of elasticityTaking the average value as
Example 2: a dynamic ice elastic modulus prediction method. The dynamic ice modeling method and the elastic modulus prediction method of the present invention will be described in detail with reference to specific examples and drawings.
(1) Referring to fig. 5a, a dynamic ice profile image (a circular or oval black spot is a pore in the figure) is obtained through a microscope, and image analysis is performed on the profile image to obtain pore diameter statistical data, a frequency histogram (as shown in fig. 5 b) and true porosity of the dynamic ice. (2) Based on the raw data of pore diameter frequency and python data processing, for example, fitting a preset selected distribution function such as norm, t, laplace, rayleigh, beta, cauchy, exponpow, gamma, mielke, burr, and calculating a fitting goodness parameter, the calculation result is shown in fig. 6a (as can be seen from fig. 6a, the gamma distribution function is closest to the pore diameter distribution of the dynamic ice), and, for the current pore diameter statistical data, the square error sum between the fitted data of each distribution function shown in fig. 6a and the pore diameter measurement value of the dynamic ice is ordered in order from small to large, see fig. 6b, so, based on fig. 6a and 6b, the pore diameter optimal distribution F (x) of the dynamic ice is a gamma distribution function. (3) the number of the preset plurality of preformed pores is respectively as follows: 10. 50, 100, 150, 300, the geometry of its corresponding finite element single cell model is calculated for each number of preformed pores, in combination with the true porosity of the dynamic ice and the optimal distribution function. For example, taking the number of preformed pores as 50 as an example, the actual porosity lambda is obtained 3d :0.0512 the side length of the three-dimensional model obtained by inputting the geometric mathematical model of the three-dimensional model and calculating is as follows:then, using the three-dimensional unit cell model side length L 3d The number of the preformed pores 50 and the optimal distribution F (x) of the pore diameters are used for preprocessing abaqus python to generate a three-dimensional single cell model corresponding to the number of the preformed pores 50, as shown in figure 7, and the sphere isDynamic ice pore. (4) And (3) repeating the pre-modeling for a plurality of times based on the space range defined by the geometric dimension calculated in the step (3), so as to obtain the pre-modeling dynamic ice module corresponding to each number of pre-modeling pores. For example, by using the three-dimensional modeling method, the working conditions with preset pore numbers of 10, 50, 100, 150 and 300 are respectively pre-modeled, and 100 models are built for each group of working conditions in consideration of randomness of model generation, namely, each pre-modeling dynamic ice module corresponding to the number of pre-modeling pores comprises 100 finite element unit models. (5) Statistically analyzing the pore errors of each group of the previewing dynamic ice modules in the step (4), judging whether the pore errors reach the precision grade appointed by a user in advance based on the current equipment performance, if so, obtaining at least one target pore quantity, and obtaining a minimum threshold value of the pore quantity required for meeting the appointed precision grade from the target pore quantity; otherwise, the geometric dimension is recalculated again after the preset pore number is adjusted, and the pre-modeling is performed until the minimum threshold value of the pore number is found. For example, the accuracy level specified by the user according to the current equipment performance is 1, and the average values of the porosities of the previewing dynamic ice modules corresponding to the previewing porosities of 10, 50, 100, 150 and 300 are respectively: 0.0483, 0.0506, 0.0511, 0.0514, 0.0510, see fig. 13 a-13 e; the corresponding errors are respectively as follows: 0.0483-0.0512/0.0512 ≡0.057; 0.0506-0.0512/0.0512 ≡0.012; 0.0511-0.0512/0.0512 ≡0.002; 0.0514-0.0512/0.0512 ≡0.004; 0.0510-0.0512/0.0512.apprxeq.0.004. From the above, the number of the previewed pores satisfying the preset precision level 1 (i.e. the error is less than or equal to 0.01) is a plurality of: 50. 100, 150, 300; and 50 is the minimum threshold value of the number of pores meeting the precision level, and then randomly selecting one finite element unit model from the corresponding pre-modeling dynamic ice modules (namely 100 finite element unit models obtained by pre-modeling) as a target finite element unit model (or selecting one with the minimum absolute value of the difference between one porosity and the actual porosity from the 100 finite element unit models as the target finite element unit model). (6) For the target finite element single cell model, inputting the elastic modulus E=5.5 GPa and Poisson ratio v=0.35 of the dynamic ice without pores, dividing a finite element grid, and according to a formula (7) - (10) establishing periodic boundary conditions and displacement loading modes, and obtaining dynamic ice three-dimensional finite element single cell model grid division as shown in fig. 8a (which is a schematic diagram of the three-dimensional finite element single cell model based on fig. 7, and the pores and grids thereof are singly shown) and fig. 8b (which is a schematic diagram of displacement loading along the X direction based on the three-dimensional finite element single cell model of fig. 7). (7) calculating dynamic ice structure response using finite element method. And the stress, strain and displacement response of each node of the dynamic ice are obtained by utilizing finite element software and a finite element basic principle method. Specifically, the calculation result is shown in fig. 9a, which is a dynamic ice three-dimensional finite element unit cell model displacement cloud chart; FIG. 9b is a stress cloud of dynamic ice three-dimensional finite element single cell model. (8) Based on the average strain theory and formulas (15) - (16), the dynamic ice elastic modulus was calculated. In this example, 5 models were calculated and the average modulus of elasticity was 5.16GPa as shown in Table 1 below.
TABLE 1 calculation results of elastic modulus of dynamic Ice three-dimensional finite element unit cell model
Because the mechanical property measurement of the dynamic ice is considered, and the influence of the porosity on the mechanical property is larger, the finite element unit cell model constructed based on the real porosity of the dynamic ice and the minimum threshold value of the pore number corresponding to the corresponding precision grade is the geometric model closest to the real condition of the pore in the dynamic ice. And no matter how the geometric dimension of the geometric model is finally obtained, the porosity of the model is always consistent with the true porosity of the dynamic ice, so that the mechanical property can be measured more accurately based on the model. The consistency of the porosity and the dynamic ice Kong Zhenshi porosity (because the result obtained by calculating according to the specified geometric dimension is not only rounded but also subjected to certain compensation) cannot be ensured by the traditional method, so that the model obtained by the traditional method cannot accurately reflect the real situation and the real porosity of the dynamic ice inner porosity distribution.
Example 3: a dynamic ice elastic modulus prediction method. The method in this embodiment includes steps (1) - (3) in embodiment 2 above, except that a two-dimensional model is constructed in this embodiment. For example, taking the number of preformed pores as 50, according to the true porosity obtained: 0.0512 and a preset two-dimensional model geometric dimension mathematical model are calculated to obtain the side length of the two-dimensional model as follows:
correspondingly, according to the side length L of the two-dimensional unit cell model 2d The two-dimensional unit cell model is generated by the number of the preformed pores 50 and the optimal distribution F (x) of the pore diameters, and is shown in figure 10, and the spheres are dynamic ice pores.
(4) And (3) repeating the pre-modeling for a plurality of times based on the space range defined by the geometric dimension calculated in the step (3), so as to obtain the pre-modeling dynamic ice module corresponding to each number of the pre-modeling pores. For example, by using the two-dimensional modeling method, the working conditions with preset pore numbers of 10, 50, 100, 150 and 300 are respectively pre-modeled, and 100 models are built for each group of working conditions in consideration of randomness of model generation, namely, each pre-modeling dynamic ice module corresponding to the number of pre-modeling pores comprises 100 finite element unit models.
(5) Statistically analyzing the pore errors of each group of the previewing dynamic ice modules in the step (4), judging whether the pore errors reach the precision grade appointed by a user in advance based on the current equipment performance, if so, obtaining at least one target pore quantity, and obtaining a minimum threshold value of the pore quantity required for meeting the appointed precision grade from the target pore quantity; otherwise, the geometric dimension is recalculated again after the preset pore number is adjusted, and the pre-modeling is performed until the minimum threshold value of the pore number is found. For example, the accuracy level specified by the user according to the current equipment performance is 1, and the average values of the porosities of the previewing dynamic ice modules corresponding to the previewing porosities of 10, 50, 100, 150 and 300 are respectively: 0.0480, 0.0516, 0.0514, 0.0510, 0.0516, see fig. 14 a-14 e; the corresponding errors are respectively as follows: 0.0480-0.0512/0.0512 is approximately equal to 0.063; 0.0516-0.0512/0.0512 ≡0.008; 0.0514-0.0512/0.0512 ≡0.004; 0.0510-0.0512/0.0512 is approximately equal to 0.004; 0.0516-0.0512/0.0512 ≡0.008. From the above, the number of the previewed pores satisfying the preset precision level of 1 (i.e. the error is less than 0.01) is a plurality of: 50. 100, 150, 300; and 50 is the minimum threshold value of the pore number meeting the precision grade, and then one finite element unit cell model is selected from the corresponding pre-modeling dynamic ice modules (namely 100 finite element unit cell models obtained by pre-modeling) as a target finite element unit cell model.
(6) And (3) inputting the elastic modulus E=5.5 GPa and the Poisson ratio v=0.35 of the dynamic ice without the pore for the target unit cell finite element model, dividing a finite element grid, and establishing a periodic boundary condition and a displacement loading mode according to formulas (11) - (13). The dynamic ice two-dimensional finite element single cell model meshing is shown in fig. 11.
(7) Dynamic ice structure response was calculated using the finite element method. And the stress, strain and displacement response of each node of the dynamic ice are obtained by utilizing finite element software and a finite element basic principle method. The calculation results are shown in fig. 12a and 12 b.
(8) Based on the average strain theory and formulas (15), (16), the dynamic ice elastic modulus is calculated. In this example, 5 models were calculated and the final elastic modulus mean value4.84GPa, as shown in Table 2 below.
TABLE 2 calculation results of elastic modulus of dynamic ice two-dimensional finite element unit cell model
The invention provides a calculation prediction method for establishing a finite element unit cell model based on the combination of mesomechanics and mathematical statistics, because the accurate prediction of dynamic ice elastic modulus is considered, a minimum threshold value of the number of pores meeting a preset precision level is found through a pre-modeling, then a target finite element unit cell model is found from a pre-modeling dynamic ice module corresponding to the minimum threshold value of the number of pores, and the geometric dimension of the model is reversely pushed based on the real porosity of dynamic ice in the process to establish the pre-modeling dynamic ice model, so that the elastic modulus of dynamic ice containing pores can be obtained efficiently, and the accuracy is higher; on the other hand, based on the fitting goodness parameter, the optimal distribution function which accords with the real distribution of the pore morphology of the dynamic ice section (namely, the real pore diameter distribution) is screened out, so that a simulation model which reflects the real distribution state of the pore diameter and the real porosity in the dynamic ice can be constructed, the geometrical characteristics of the pore distribution of the dynamic ice can be reflected more comprehensively and objectively, the elastic modulus is predicted based on the simulation model, and the refinement degree and the accuracy of a calculation result are further improved; moreover, the method is also suitable for predicting the elastic modulus of the dynamic ice under the conditions of different pore diameter sizes, distribution rules and space occupation ratios, and has higher universality and flexibility.
In order to verify that when the modeling method of the embodiment generates a dynamic ice model containing pores, on the premise of not sacrificing the precision of the porosity (for example, the true dynamic ice porosity is 0.0512, the average value of the porosities obtained by 100 times of modeling tests by adopting the existing modeling method and 100 times of tests by adopting the modeling method of the invention reaches 0.0506, namely, the method accords with the specified precision level 1), the number of the pores to be built is less, the size of the built model is smaller, the modeling speed and convenience are higher, and the requirement on the performance of computer equipment is greatly reduced. And performing pre-modeling on working conditions with the number of pre-modeling pores of 10, 50, 100, 150 and 300 respectively by using the real porosity of the real dynamic ice of 0.0512 and using the three-dimensional modeling method and the two-dimensional modeling method, establishing 100 models for each group of working conditions in consideration of the randomness of model generation, and statistically analyzing the average value of the porosity of the model after each group of working conditions are established.
Referring to fig. 13 a-13 e, three-dimensional model porosity generation results for the number of preformed pores 10, 50, 100, 150, 300, respectively: when the number of the preformed pores is 10, the porosity of 100 three-dimensional models is between [ 0.022,0.075 ], and the average value of the porosities is 0.0483; the standard deviation of the porosity is 0.0271; when the number of the preformed pores is 50, the porosity of 100 three-dimensional models is between [ 0.039,0.064 ], and the average value of the porosities is 0.0506; the standard deviation of the porosity is 0.0122; when the number of the preformed pores is 100, the porosity of 100 three-dimensional models is between [ 0.041,0.061 ], and the average value of the porosities is 0.0511; the standard deviation of the porosity is 0.0101; when the number of the preformed pores is 150, the porosity of 100 three-dimensional models is between [ 0.045,0.058 ], and the average value of the porosities is 0.0514; the standard deviation of the porosity is 0.0071; when the number of the preformed pores is 300, the porosity of 100 three-dimensional models is between [ 0.045,0.055 ], and the average value of the porosities is 0.0510; the standard deviation of the porosity was 0.0051.
Fig. 14 a-14 e are graphs showing the results of two-dimensional model porosity generation for different pore numbers, respectively: when the number of the preformed pores is 10, the porosity of 100 two-dimensional models is between [ 0.034,0.064 ], and the average value of the porosities is 0.0480; the standard deviation of the porosity is 0.0147; when the number of the preformed pores is 50, the porosity of 100 two-dimensional models is between [ 0.044,0.06 ], and the average value of the porosity is 0.0516; the standard deviation of the porosity is 0.0076; when the number of the preformed pores is 100, the porosity of 100 two-dimensional models is between [ 0.048,0.058 ], and the average value of the porosity is 0.0514; the standard deviation of the porosity is 0.0052; when the number of the preformed pores is 150, the porosity of 100 two-dimensional models is between [ 0.048,0.055 ], and the average value of the porosities is 0.0510; the standard deviation of the porosity is 0.0042; when the number of the preformed pores is 300, the porosity of 100 two-dimensional models is between [ 0.049,0.055 ], and the average value of the porosities is 0.0516; the standard deviation of the porosity was 0.0031.
From the above statistics, as the number of preformed pores increases from 10 to 300, the average value of the porosity of the three-dimensional model/two-dimensional model approaches the preset porosity (0.0512) more and more, and the standard deviation of the porosity is lower and lower, which indicates that the accuracy of the porosity of the model increases with the increase of the number of pores.
As can be seen by combining the average values of the porosities of the three-dimensional model under the working conditions of different number of the preformed porosities in fig. 13 a-13 e, when the number of the preformed porosities of the model reaches 50 or more, the matching degree of the average value of the porosities of the model and the true porosity 0.0512 is higher; when the number of the preformed pores of the model reaches 50 or more, the matching degree of the average porosity value of the two-dimensional model and the true porosity 0.0512 is higher.
However, in the practical application process, not the larger the number of pores, the better the smaller the number of pores is required to be constructed on the basis of guaranteeing the same precision grade in consideration of the condition that the performance of computer equipment is lower, so that in order to be capable of modeling on the computer equipment with lower performance, the corresponding CPU and memory operation capability is reserved for the subsequent dynamic mechanical analysis research (such as the work of carrying out grid division, finite element solving and the like on the basis of a model and needing a large amount of calculation capability), and the range of the corresponding pore number is preferably 50-300 when a dynamic ice model with a specified precision grade is constructed according to the porosity. Of course, the above-mentioned method of modeling in advance may be adopted, and multiple modeling experiments may be performed in advance based on the actual porosity of the dynamic ice and different amounts of the pre-modeling pores, so that the minimum threshold (and/or the maximum threshold) of the number of pores required for each precision level may be determined.
On the other hand, in order to prove the convenience of the modeling method of the present embodiment compared with the existing modeling method, by counting the time required for model construction under the working conditions of different number of preformed pores (as shown in the following table one), the modeling time decreases with decreasing number of preformed pores, that is, the modeling time and the number of pores have a positively correlated functional relationship: when the number of the pre-modeling pores is 50, the modeling time T1 is about 1/40 of the time T2 required for the number of pores 1000, that is, the modeling time is reduced by a multiple, and even if the model of 50 to 300 pores is constructed, the total time required for constructing the model of 1000 pores is much smaller (approximately 1/5), that is, even if the model is constructed by the pre-modeling, the time required for constructing the model of 1000 pores is smaller than that required for directly constructing the model of 1000 pores, so that even if the minimum threshold value of the number of pores is found by presetting the number of the pre-modeling pores becomes possible.
TABLE 3 time required for model construction under different conditions of preformed pore number
However, in the existing modeling method, when 1000 pore sizes are required to be constructed, the average value of the porosities approaches the set porosity 0.0512. Therefore, to achieve the porosity of the same level of accuracy, the number of pores of the dynamic ice model to be constructed by the modeling method of the invention is greatly reduced, and the geometric dimension of the generated dynamic ice model is greatly reduced, which not only greatly reduces the modeling time, but also reduces the performance requirements on computer equipment.
1) The modeling method of the invention provides possibility for realizing analysis and research of dynamic ice mechanical properties with higher speed, lower cost and without sacrificing accuracy. Firstly, in actual work, the pores are built one by one, and a large number of three-dimensional models/two-dimensional models are built for dynamic ice mechanical property analysis research, so that when a large number of models are to be built for dynamic ice mechanical property analysis, great challenges are presented to the performance of computer equipment. Second, for some businesses or research units that are already equipped with relatively low performance computer devices, or for some remote areas of the research unit (e.g., south pole research sites, etc.), the cost of replacing high performance computer devices is prohibitive. As another example, for some businesses that are only everyday text offices, the performance requirements for computer devices are not high, and therefore, it is not necessary to purchase high performance configured computer devices. In view of this, how to realize modeling on relatively low performance computer equipment more quickly and conveniently without sacrificing accuracy, so as to realize low-cost dynamic mechanical performance analysis and research, is a problem to be solved in the current technology. Compared with the existing modeling method, the modeling method provided by the invention has the advantages that the number of the pores required to be constructed is greatly reduced on the basis of achieving the porosity with the same precision, so that the modeling is realized on computer equipment with relatively low performance more quickly and conveniently without sacrificing the precision, and the possibility is provided for realizing the analysis and research of the dynamic ice mechanical properties with low cost.
2) The dynamic ice mechanical property calculation is carried out based on the three-dimensional model/two-dimensional model of the dynamic ice microstructure constructed by the invention, so that the efficiency is greatly improved. The dynamic mechanical property analysis is carried out, the dynamic ice microstructure model is required to be subjected to grid division, and the geometric size of the model definitely determines the cost and time of network division on the basis of a certain single grid size. As described above, to achieve the same level of accuracy, the number of pores of the target finite element single cell model finally determined by the method of the present invention is much smaller than the number of pores required to be constructed in the existing modeling method, and therefore, the geometry of the generated corresponding dynamic ice microstructure model is also much smaller than that of the microstructure model constructed in the existing modeling method. Accordingly, the time and the time T3 required for finite element network division based on the dynamic ice microstructure model constructed by the method are far smaller than the time T4 required for finite element network division based on the dynamic ice microstructure model constructed by the existing modeling method. Specifically, since the finite element model mesh division time and the model geometry are positively correlated, if the dynamic ice model geometry is small, a decrease in the model mesh division is necessarily caused. Generally, the grid division time and the model geometric dimension are in a positive correlation, so when the number of the model pores is 50 and the number of the model pores of the original method is 1000 (i.e. 1/20), the finite element grid division time T3 after modeling is reduced to 1/20 of the original time T4. Further, after the finite element network is divided, the dynamic ice mechanical property calculation time T5 based on the finite element unit cell model is reduced to 1/20 of the time T6 required by the mechanical property after the grid division of the model constructed by the existing modeling method. From this, it can be seen that the time can be saved by carrying out dynamic ice mechanical property analysis and research based on the method of the invention: overall time saving = modeling time saving times x model grid time saving times subsequent dynamic ice mechanical property calculation time times = 1/40 x 1/20 = 1/8000. Therefore, the time is saved remarkably, the running performance requirement on a computer is greatly reduced, the benefit of carrying out low-cost dynamic ice mechanical property calculation on a large number of subsequent dynamic ice mechanical properties is remarkable, and the development and design of scientific research analysis efficiency, supporting icing and preventing and removing ice technology are greatly facilitated.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element. From the above description of the embodiments, it will be clear to those skilled in the art that the above-described embodiment method may be implemented by means of software plus a necessary general hardware platform, but of course may also be implemented by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product stored in a storage medium (e.g. ROM/RAM, magnetic disk, optical disk) comprising several instructions for causing a computer terminal (which may be a mobile phone, a computer, a server, or a network device, etc.) to perform the method according to the embodiments of the present invention. The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are to be protected by the present invention.

Claims (9)

1. The dynamic ice elastic modulus prediction method is characterized by comprising the following steps:
acquiring pore characteristic parameters and true porosity of the dynamic ice; the pore characteristic parameters include: the number of pore samples, the sample pore diameter size, and the frequency of the sample pore diameters of different sizes;
determining an optimal distribution function for representing the true distribution state of the pore diameters in the dynamic ice based on the pore characteristic parameters;
calculating the geometric dimension of a finite element unit model corresponding to each pre-cast pore number based on a plurality of pre-cast pore numbers, the real porosity and the optimal distribution function, and performing pre-cast modeling in a space range defined by the geometric dimension to construct the finite element unit model with the pore diameter conforming to the optimal distribution function, so as to obtain a pre-cast dynamic ice module corresponding to each pre-cast pore number; the finite element unit cell model comprises a three-dimensional model or a two-dimensional model;
calculating the porosity error of each previewing dynamic ice module, and judging whether the accuracy of the previewing dynamic ice module reaches an accuracy grade appointed in advance based on the current equipment performance based on the porosity error; if the target pore number is reached, obtaining at least one target pore number, and determining a minimum pore number threshold from the at least one target pore number;
Taking any finite element unit model in the previewing dynamic ice module corresponding to the minimum threshold value of the pore number or one finite element unit model with the minimum absolute value of the difference between the porosity and the real porosity as a target finite element unit model corresponding to the appointed precision grade;
inputting the elastic modulus and poisson ratio of dynamic ice without pores aiming at the target finite element unit cell model, dividing finite element grids, and establishing periodic boundary conditions and a displacement loading mode;
calculating dynamic ice structure response by using a finite element method, and calculating dynamic ice elastic modulus based on an average strain theory;
the step of constructing a finite element unit cell model with pore diameters conforming to the optimal distribution function by performing pre-modeling in a space range defined by the geometric dimension specifically comprises the steps of:
generating the spherical center coordinates of each pore in the three-dimensional model in a uniform and random form or generating the spherical center coordinates of each pore in the two-dimensional model in a uniform and random form in a spatial range defined by the geometric dimensions;
and determining the corresponding pore diameter of the pore at each spherical center coordinate in the three-dimensional model or the two-dimensional model based on the random form of the optimal distribution function, so as to obtain the three-dimensional model or the two-dimensional model.
2. The method for predicting dynamic ice elastic modulus according to claim 1, further comprising the steps of:
if the accuracy of the pre-modeling dynamic ice module does not reach the specified accuracy level, adjusting the number of pre-modeling pores based on a preset adjusting reference, or acquiring the number of pre-modeling pores customized by a user, then re-calculating the geometric dimension of the corresponding finite element unit cell model, and performing pre-modeling, and repeating the steps until the target finite element unit cell model corresponding to the specified accuracy level is obtained;
and/or the number of the groups of groups,
the step of determining an optimal distribution function for representing the true distribution state of pore diameters in the dynamic ice based on the pore characteristic parameters specifically comprises the following steps: respectively carrying out parameter estimation on a plurality of preset distribution functions by adopting a maximum likelihood method, and fitting each distribution function; respectively calculating the fitting goodness-of-fit parameters between the fitting data of each distribution function and the pore characteristic parameters; and taking the distribution function corresponding to the smallest fitting goodness parameter as the optimal distribution function for representing the true distribution state of the pore diameter in the dynamic ice.
3. A method according to claim 2, wherein the goodness-of-fit parameter is the sum of squares error between the fit data and the sample pore diameter in the pore characterization parameter d i N, which is the obtained measurement value of the pore diameter of the ith sample of the dynamic ice di For the number of pore samples taken, +.>And (3) fitting the obtained i-th sample pore diameter fitting value based on the distribution function.
4. The method for predicting dynamic ice elastic modulus according to claim 1, further comprising the steps of:
randomly selecting a plurality of finite element unit cell models from the previewing dynamic ice module corresponding to the minimum pore number threshold to calculate for a plurality of times to obtain a plurality of elastic moduli, and outputting an average value of the plurality of elastic moduli as a final elastic modulus of the dynamic ice; or alternatively, the process may be performed,
calculating absolute values of differences between porosities of all finite element unit cell models in the previewing dynamic ice module corresponding to the minimum threshold value of the number of the porosities and the true porosities, sequencing the absolute values according to a sequence from small to large, then selecting a plurality of finite element unit cell models which are sequenced at the front for multiple times to calculate, obtaining a plurality of elastic models, and outputting an average value of the elastic moduli as a final elastic modulus of the dynamic ice.
5. The method for predicting dynamic ice elastic modulus according to claim 1, wherein the calculation formula of the geometric dimension of the three-dimensional model is: Wherein N is k A k-th number of pre-modeling pores among a preset plurality of pre-modeling pore numbers; l (L) 3d A side length of the three-dimensional model; lambda is the true porosity, F -1 (1) The value of the inverse function of the optimal distribution function at the position 1 is taken; f (F) ′ (x) A probability density function that is the optimal distribution function; x is the pore diameter.
6. The method of claim 5, wherein the geometric dimension defines a spatial range of:
[L 3d -F -1 (1)]×[L 3d -F -1 (1)]×[L 3d -F -1 (1)]the method comprises the steps of carrying out a first treatment on the surface of the Or alternatively, the process may be performed,
[L 3d -δ*F -1 (1)]×[L 3d -δ*F -1 (1)]×[L 3d -δ*F -1 (1)]the method comprises the steps of carrying out a first treatment on the surface of the Wherein, delta takes a value of 0.7 or 0.8.
7. The method for predicting dynamic ice elastic modulus according to claim 1, wherein the calculation formula of the geometric dimension of the two-dimensional model is:wherein N is k A k-th number of pre-modeling pores among a preset plurality of pre-modeling pore numbers; l (L) 2d A side length of the two-dimensional model; lambda is the true porosity, F -1 (1) The value of the inverse function of the optimal distribution function at the position 1 is taken; f (F) ′ (x) A probability density function that is the optimal distribution function; x is the pore diameter.
8. The method of claim 7, wherein the geometric dimension defines a spatial range of: [ L 2d -F -1 (1)]×[L 2d -F -1 (1)]Alternatively, the first and second substrates may be coated,
[L 2d -δ*F -1 (1)]×[L 2d -δ*F -1 (1)]the method comprises the steps of carrying out a first treatment on the surface of the Wherein, the delta takes the value of 0.7 or 0.8.
9. A dynamic ice elastic modulus prediction method according to any one of claims 4 to 8, wherein the step of constructing a finite element unit cell model having pore diameters conforming to the optimum distribution function by performing a pre-modeling within a spatial range defined by the geometric dimensions, further comprises the step of: judging whether a plurality of generated pores in a space range defined by the geometric dimension are intersected, if so, regenerating the spherical center coordinates and the pore diameters of the plurality of pores, and judging whether the regenerated plurality of pores are intersected again until all the pores in the space range defined by the geometric dimension are not intersected.
CN202310227454.1A 2023-03-09 2023-03-09 Dynamic ice elastic modulus prediction method Active CN116187140B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310227454.1A CN116187140B (en) 2023-03-09 2023-03-09 Dynamic ice elastic modulus prediction method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310227454.1A CN116187140B (en) 2023-03-09 2023-03-09 Dynamic ice elastic modulus prediction method

Publications (2)

Publication Number Publication Date
CN116187140A CN116187140A (en) 2023-05-30
CN116187140B true CN116187140B (en) 2023-10-13

Family

ID=86434478

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310227454.1A Active CN116187140B (en) 2023-03-09 2023-03-09 Dynamic ice elastic modulus prediction method

Country Status (1)

Country Link
CN (1) CN116187140B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107833275A (en) * 2017-11-28 2018-03-23 中国空气动力研究与发展中心计算空气动力研究所 A kind of dynamic ice microstructure three-dimensional modeling method
CN113268897A (en) * 2021-01-05 2021-08-17 北京航空航天大学 Multi-scale modeling and simulation method based on random pore reconstruction
CN114676560A (en) * 2022-03-07 2022-06-28 中国空气动力研究与发展中心低速空气动力研究所 Cloud and mist parameter calculation and ice shape prediction method and medium based on optical fiber icing detection
CN114858849A (en) * 2022-07-11 2022-08-05 中国空气动力研究与发展中心低速空气动力研究所 Method for obtaining thermal conductivity coefficient of dynamic ice

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2804021A1 (en) * 2009-12-16 2014-11-19 Bp Exploration Operating Company Limited Method for measuring wettability
SG11201600486VA (en) * 2013-08-30 2016-02-26 Landmark Graphics Corp Method, system, and optimization technique to improve oil reservoir recovery in the water-alternating-gas injection process by using downhole control valves (wag-cv)
US20210187604A1 (en) * 2014-02-21 2021-06-24 Terves, Llc Degradable and/or Deformable Diverters and Seals
KR20220003013A (en) * 2019-05-01 2022-01-07 더 트러스티즈 오브 프린스턴 유니버시티 Bacteria in 3D porous media

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107833275A (en) * 2017-11-28 2018-03-23 中国空气动力研究与发展中心计算空气动力研究所 A kind of dynamic ice microstructure three-dimensional modeling method
CN113268897A (en) * 2021-01-05 2021-08-17 北京航空航天大学 Multi-scale modeling and simulation method based on random pore reconstruction
CN114676560A (en) * 2022-03-07 2022-06-28 中国空气动力研究与发展中心低速空气动力研究所 Cloud and mist parameter calculation and ice shape prediction method and medium based on optical fiber icing detection
CN114858849A (en) * 2022-07-11 2022-08-05 中国空气动力研究与发展中心低速空气动力研究所 Method for obtaining thermal conductivity coefficient of dynamic ice

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
偏航条件下覆冰风力机气动特性研究;王强，等;《工程热物理学报》;第918-928页 *

Also Published As

Publication number Publication date
CN116187140A (en) 2023-05-30

Similar Documents

Publication Publication Date Title
CN110275148B (en) Sea clutter amplitude distribution parameter estimation method and system
CN108304679A (en) A kind of adaptive reliability analysis method
CN111563589A (en) Quantification method and device of neural network model
CN110992432B (en) Depth neural network-based minimum variance gradient quantization compression and image processing method
CN111428918B (en) Soil pollution range prediction method and system for heavy metal attenuation pollution source
CN111967183A (en) Method and system for calculating line loss of distribution network area
CN116050007A (en) Complex equipment optimization design method based on hybrid self-adaptive sampling agent model
CN116187140B (en) Dynamic ice elastic modulus prediction method
CN115237878A (en) Process database construction method and medium based on additive manufacturing
CN111783351B (en) Non-probability credible set quantification method for uncertainty parameters of structural system
CN116306127B (en) Dynamic ice microstructure modeling method
CN112949944A (en) Underground water level intelligent prediction method and system based on space-time characteristics
CN107357714B (en) Fault analysis method and device based on monitoring platform
CN117273109A (en) Quantum neuron-based hybrid neural network construction method and device
CN116523640A (en) Financial information management system based on scheduling feedback algorithm
CN115392441A (en) Method, apparatus, device and medium for on-chip adaptation of quantized neural network model
Frieden et al. Power laws of complex systems from extreme physical information
CN112016956B (en) Ore grade estimation method and device based on BP neural network
CN112307670A (en) Design method of pressurized water reactor core parameter prediction model based on bagging integrated neural network
CN113688498B (en) Method for determining trusted interval response of aircraft structure
Du et al. Fuzzy description of topological relations II: computation methods and examples
CN112731545B (en) Ocean irregular net measurement data adjustment method
CN117634323B (en) Ship propeller optimal design method based on proxy model
Yang et al. Grey Confidence Interval Estimation of Small Samples Based on Numerical Characteristics.
Bărbulescu et al. Modeling the annual precipitation evolution in the region of Dobrudja

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant