Structural reliability analysis method and system based on radial basis function

Abstract

The invention discloses a structural reliability analysis method based on a radial basis function. The method comprises the following steps: establishing a parameterized structural model of a component; grid division is carried out on the parameterized structure model based on the geometric random variables of the component, and material attributes, loads and boundary conditions are assigned to the parameterized structure model, so that a seed finite element model of the component is obtained; obtaining a sampling value of the geometric random variable; changing the geometric shape of the parameterized structural model based on the sampling value to obtain N structural models with different geometric dimensions; converting the seed finite element model into N deterministic finite element models corresponding to the N structural models based on a radial basis function; and carrying out structural reliability analysis on the component by utilizing the N deterministic finite element models. The invention further discloses a radial basis function-based structural reliability analysis system and a computer medium.

Description

Technical Field

[0001] The present invention relates to the field of reliability analysis, and particularly to a structural reliability analysis method and system based on radial basis functions. Background Art

[0002] There are a large number of uncertain factors in engineering structures, and uncertainty is an inherent characteristic of various things in nature. The deterministic analysis models usually established in engineering analysis are obtained through various assumptions and simplifications. In fact, the material properties, geometric dimensions, loads, and boundary conditions of any real product have uncertainties, and their true values are often unobtainable. Compared with deterministic evaluation methods, structural reliability analysis can consider the uncertainties of material properties, geometric dimensions, loads, and boundary conditions. It can not only give accurate failure probability values, but also give structural improvement plans in combination with parameter sensitivity analysis. Since structural reliability analysis comprehensively considers the actual discreteness of material properties, geometric dimensions, loads, and boundary conditions, it is closer to reality than the conservative treatment of inputs in deterministic analysis.

[0003] However, there are still many difficulties in the application of structural reliability analysis in engineering design at present. The most important problem is that it is difficult to implement geometric uncertainty. Taking the finite element analysis widely used in the strength design of aeroengines as an example, it is relatively simple to consider the uncertainties of material properties, loads, and boundary conditions because it is easy to parameterize them. However, it is very difficult to establish a parametric finite element model that can reflect geometric uncertainty and realize geometric parameter-driven. The time investment required is of an order of magnitude different from that of deterministic finite element modeling. In addition, due to frequent configuration changes in the design process, rather than just geometric dimension changes, the expensive parametric finite element model is very likely to become worthless after the design configuration changes, and the time and manpower invested previously will also go to waste. Due to the inability to consider crucial geometric uncertainty, the requirements of structural reliability have so far been difficult to be implemented in engineering design.

[0004] Aiming at the deficiencies of the prior art, it is desirable to provide an improved structural reliability analysis method and system that can consider geometric uncertainty. Summary of the Invention

[0005] The following gives a brief overview of one or more aspects to provide a basic understanding of these aspects. This overview is not an exhaustive survey of all contemplated aspects, and is neither intended to identify key or decisive elements of all aspects nor to define the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed description that follows.

[0006] The present invention provides a structural reliability analysis method based on radial basis functions, including: establishing a parametric structural model of a component; performing mesh division on the parametric structural model based on the geometric random variables of the component and assigning material properties, loads, and boundary conditions thereto to obtain a seed finite element model of the component; obtaining sampling values of the geometric random variables; changing the geometric shape of the parametric structural model based on the sampling values to obtain N structural models with different geometric dimensions; transforming the seed finite element model into N deterministic finite element models corresponding to the N structural models based on radial basis functions; and performing structural reliability analysis on the component using the N deterministic finite element models.

[0007] In some embodiments, the parametric structural model can automatically change its geometric shape under the drive of geometric dimensions, and the seed finite element model cannot automatically change its geometric shape under the drive of geometric dimensions.

[0008] In some embodiments, obtaining the sampling values of the geometric random variables further includes: determining the value range of the geometric random variables of the component; generating N sample points within the value range; and obtaining the sampling values of the geometric random variables at the N sample points.

[0009] In some embodiments, transforming the seed finite element model into N deterministic finite element models corresponding to the N structural models based on radial basis functions further includes performing the following operations for each of the N structural models: extracting N surf surface nodes and N volu interior nodes of the seed finite element model; projecting the N surf surface nodes onto the structural model to obtain new coordinates of the N surf surface nodes; determining the coordinate change amounts of the N volu interior nodes when projected onto the structural model based on the radial basis functions to obtain new coordinates of the N volu interior nodes; and updating the seed finite element model based on the new coordinates of the N surf surface nodes and the new coordinates of the N volu interior nodes to obtain a deterministic finite element model corresponding to the structural model.

[0010] In some embodiments, the N surf surface nodes include corner nodes, edge nodes, and face nodes, and projecting the N surf surface nodes onto the structural model further includes: projecting the N surfA surface node is projected onto the structural model such that the new coordinates of the corner nodes are located at the corresponding corners of the structural model, the new coordinates of the edge nodes are located on the corresponding edges of the structural model, the new coordinates of the surface nodes are located on the corresponding surfaces of the structural model, and the projection direction is along the normal of the corresponding surface of the structural model.

[0011] In some embodiments, further comprising for performing structural reliability analysis on a member using N deterministic finite element models: sequentially performing finite element simulation calculations on the N deterministic finite element models to obtain corresponding structural responses; fitting a functional relationship between the geometric random variables and the structural responses to obtain a fitted function; and using the fitted function to replace the limit state function to perform structural reliability analysis.

[0012] In some embodiments, the structural response includes at least one of stress, strain, displacement, and temperature at a critical part of the member.

[0013] The present invention also provides a structural reliability analysis system based on radial basis functions, comprising: a parametric structural model unit for establishing a parametric structural model of a member; a seed finite element model unit for meshing the parametric structural model based on the geometric random variables of the member and assigning material properties, loads, and boundary conditions to obtain a seed finite element model of the member; a sampling value acquisition unit for obtaining sampling values of the geometric random variables; a geometric shape modification unit for modifying the geometric shape of the parametric structural model based on the sampling values to obtain N structural models with different geometric dimensions; a model transformation unit for transforming the seed finite element model into N deterministic finite element models corresponding to the N structural models based on radial basis functions; and a reliability analysis unit for performing structural reliability analysis on the member using the N deterministic finite element models.

[0014] In some embodiments, the parametric structural model can automatically change its geometric shape under the drive of geometric dimensions, and the seed finite element model cannot automatically change its geometric shape under the drive of geometric dimensions.

[0015] In some embodiments, the sampling value acquisition unit is further configured to: determine the value range of the geometric random variables of the member; generate N sample points within the value range; and obtain the sampling values of the geometric random variables at the N sample points.

[0016] In some embodiments, the model transformation unit is further configured to perform the following operations for each of the N structural models: extract N surf surface nodes and N volu internal nodes of the seed finite element model; project the N surf surface nodes onto the structural model to obtain the N surfthe new coordinates of the N surface nodes; determining, based on the radial basis function, the coordinate change amount of the N volu internal nodes when projected onto the structural model, so as to obtain the new coordinates of the N volu internal nodes; and updating the seeded finite element model based on the new coordinates of the N surf surface nodes and the new coordinates of the N volu internal nodes, so as to obtain a deterministic finite element model corresponding to the structural model.

[0017] In some embodiments, the N surf surface nodes include corner nodes, edge nodes, and face nodes, and the model transformation unit is further configured to: project the N surf surface nodes onto the structural model such that the new coordinates of the corner nodes are located at the corresponding corners of the structural model, the new coordinates of the edge nodes are located on the corresponding edges of the structural model, the new coordinates of the face nodes are located on the corresponding faces of the structural model, and the projection direction is along the normal of the corresponding face of the structural model.

[0018] In some embodiments, the reliability analysis unit is further configured to: sequentially perform finite element simulation calculations on N deterministic finite element models to obtain corresponding structural responses; fit the functional relationship between the geometric random variables and the structural responses to obtain a fitted function; and use the fitted function to replace the limit state function to perform structural reliability analysis.

[0019] In some embodiments, the structural response includes at least one of stress, strain, displacement, and temperature at key parts of the component.

[0020] The present invention also provides a computer-readable storage medium, which stores a computer program for structural reliability analysis based on the radial basis function, and the computer program can be executed by a processor to execute the foregoing structural reliability analysis method based on the radial basis function.

[0021] The technical solution of the present invention is based on the radial basis function to transform a parametric structural model into a deterministic finite element model, so as to replace and implement the actual functions of the parametric finite element model without establishing a parametric finite element model, effectively solving the problems of high cost and difficulty in adapting to configuration changes of the parametric finite element model containing geometric random variables, and effectively controlling the cost of structural reliability analysis. Description of the Drawings

[0022] When understanding the following detailed description in conjunction with the accompanying drawings, the features, essence, and advantages of the present invention will become more obvious. In the drawings, the same reference numerals are always correspondingly identified. It should be noted that the described drawings are only schematic and non-limiting. In the drawings, the sizes of some components may be enlarged and are not drawn to scale for illustrative purposes.

[0023] Figure 1 The flowchart of the structural reliability analysis method based on radial basis function of the present invention is shown.

[0024] Figure 2 The schematic diagram of the surface nodes of the seed finite element model of the present invention is shown.

[0025] Figure 3 The schematic diagram of the surface node projection process of the seed finite element model of the present invention is shown.

[0026] Figure 4 The schematic diagram of the compressor disk is shown.

[0027] Figure 5 The schematic diagram of the geometric random variables of the compressor disk is shown.

[0028] Figure 6 The schematic diagram of the parametric structural model of the compressor disk is shown.

[0029] Figure 7 The schematic diagram of the shape change of the parametric structural model of the compressor disk driven by geometric dimensions is shown.

[0030] Figure 8 The schematic diagram of the seed finite element model of the compressor disk is shown.

[0031] Figure 9 The schematic diagram of the deterministic finite element model of the compressor disk is shown.

[0032] Figure 10 The structural reliability analysis system based on radial basis function of the present invention is shown.

[0033] Figure 11 The device block diagram including the structural reliability analysis system based on radial basis function is shown. Detailed implementation manners

[0034] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the following further describes the present invention in detail with reference to specific embodiments and the accompanying drawings. In the following detailed description, many specific details are set forth to provide a thorough understanding of the described exemplary embodiments. However, it will be apparent to those skilled in the art that some or all of these specific details may be practiced without some or all of these specific details. In other exemplary embodiments, well-known structures are not described in detail to avoid unnecessarily obscuring the concepts of the present disclosure. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. At the same time, the various aspects described in the embodiments can be combined arbitrarily without conflict.

[0035] In the structural reliability analysis involving geometric uncertainties, it is often necessary to establish a parametric finite element model of a component to obtain the structural responses corresponding to different combinations of geometric parameters. The cost of establishing a parametric finite element model is much higher than that of a deterministic finite element model and a parametric structural model, and it cannot adapt to the frequent configuration changes in the design process. Therefore, it is difficult to implement structural reliability requirements in engineering design.

[0036] In view of this, the present invention proposes a structural reliability analysis method considering geometric uncertainties based on radial basis functions. A sequence of radial basis functions is used to connect the parametric structural model and the deterministic finite element model, and the organic combination of the "parametric structural model - radial basis function sequence - deterministic finite element model" is used to replace and implement the actual functions of the parametric finite element model, so as to solve the problem of difficult handling of geometric uncertainties in structural reliability analysis, and further improve the product design level. Compared with the parametric finite element model, the establishment of the parametric structural model is much simpler. Thus, the technical solution of the present invention can avoid establishing an expensive and inflexible parametric finite element model, and quickly obtain deterministic finite element models under different combinations of geometric parameters by modifying the node coordinates in the deterministic finite element model through radial basis function interpolation, providing a solution for low-cost solving of the problem of geometric uncertain structural reliability analysis.

[0037] Figure 1 The flowchart of the structural reliability analysis method 100 based on radial basis functions of the present invention is shown.

[0038] As Figure 1 shown, the method 100 starts at step 105. At step 105, a parametric structural model of the component is established.

[0039] For example, a parametric structural model of the component can be established through modeling software. This parametric structural model can automatically change the geometric shape under the drive of geometric dimensions. For example, the structural model (e.g., *.prt file) obtained after modeling using UG (Unigraphics) software can realize the parameterization of geometric dimensions.

[0040] At step 110, the parametric structural model is meshed and assigned material properties, loads, and boundary conditions based on the geometric random variables of the component to obtain a seed finite element model of the component.

[0041] For example, a finite element preprocessing software can be used to mesh the parametric structural model and assign material properties, loads, and boundary conditions when the geometric random variables of the component take the mean values, so as to obtain a parameterless finite element model of the component. This parameterless finite element model does not have the function of automatically changing the shape under the drive of geometric dimensions and is also referred to as the seed finite element model M in this article seed .

[0042] In step 115, a sampling value of a geometric random variable is obtained.

[0043] In some embodiments, obtaining a sampling value of a geometric random variable further includes: determining a value range of the geometric random variable of the component; generating N sample points within the value range; and obtaining sampling values of the geometric random variable at the N sample points.

[0044] Specifically, a suitable experimental design method can be selected to determine the value range of each geometric random variable of the component according to actual engineering requirements, and a series of sample points are generated within the value range of each geometric random variable, and the number of sample points is N.

[0045] In step 120, the geometric shape of the parametric structural model is changed based on the sampling value to obtain N structural models with different geometric dimensions.

[0046] For example, the sample point data generated by the experimental design can be read, and the parametric structural model obtained in step 105 is automatically updated geometrically according to the sampling values of the geometric random variables in the sample point data, so as to obtain N structural models with different geometric dimensions.

[0047] In step 125, the seed finite element model is transformed into N deterministic finite element models corresponding to the N structural models based on the radial basis function.

[0048] In some embodiments, transforming the seed finite element model into N deterministic finite element models corresponding to the N structural models based on the radial basis function further includes performing the following operations for each of the N structural models: extracting N surf surface nodes and N volu interior nodes of the seed finite element model; projecting the N surf surface nodes onto the structural model to obtain new coordinates of the N surf surface nodes; determining the coordinate change amount of the N volu interior nodes when projected onto the structural model based on the radial basis function to obtain new coordinates of the N volu interior nodes; and updating the seed finite element model based on the new coordinates of the N surf surface nodes and the new coordinates of the N volu interior nodes to obtain a deterministic finite element model corresponding to the structural model.

[0049] In some embodiments, the N surf surface nodes include corner nodes, edge nodes, and face nodes, and projecting the N surf surface nodes onto the structural model further includes: projecting the Nsurf The three-dimensional coordinates of the N surface nodes of the extracted seed finite element model are expressed as a vector as shown in Equation (1) below:

[0050] Specifically, the process of converting the seed finite element model M based on the radial basis function into N deterministic finite element models is as follows: seed The process of converting the seed finite element model M into N deterministic finite element models based on the radial basis function is as follows:

[0051] The three-dimensional coordinates of the N surface nodes of the extracted seed finite element model are expressed as a vector as shown in Equation (1) below: surf The three-dimensional coordinates of the N surface nodes of the extracted seed finite element model are expressed as a vector as shown in Equation (1) below:

[0052]

[0053] According to the different positions of each surface node on the seed finite element model, the N surface nodes can be further divided into three non-overlapping subsets, namely corner nodes, edge nodes, and face nodes. surf According to the different positions of each surface node on the seed finite element model, the N surface nodes can be further divided into three non-overlapping subsets, namely corner nodes, edge nodes, and face nodes.

[0054] Figure 2 Exemplary corner nodes, boundary points, and face nodes of the seed finite element model are shown. As an example, Figure 2 Exemplary corner nodes, boundary points, and face nodes of the seed finite element model M are shown. As an example, seed Corner node A, edge node B, and face node C of the seed finite element model M are shown. As shown in the figure, corner node A is located at a corner of the seed finite element model, edge node B is located on an edge of the seed finite element model, and face node C is located on a face of the seed finite element model.

[0055] The three-dimensional coordinates of the N internal nodes of the extracted seed finite element model are expressed as a vector as shown in Equation (2) below: volu The three-dimensional coordinates of the N internal nodes of the extracted seed finite element model are expressed as a vector as shown in Equation (2) below:

[0056]

[0057] After extracting the surface nodes and internal nodes of the seed finite element model, one structural model can be taken from the N structural models obtained in step 120 (for ease of explanation, this structural model will be referred to as M (GEOM，1) ), and the corner nodes, edge nodes, and face nodes on the surface of the seed finite element model are projected onto M (GEOM，1) respectively, and it is ensured that the projection process follows the following rules: ① The new coordinates of the corner nodes are located at the corresponding corners of M (GEOM，1) , ② The new coordinates of the edge nodes are located on the corresponding edges of M (GEOM，1) , and the corresponding edge parameters of M (GEOM，1) are aligned during the projection process, ③ The new coordinates of the face nodes are located on the corresponding faces of M (GEOM，1) , and the projection direction is along the normal of the corresponding face of M (GEOM，1)The normal direction of the corresponding surface.

[0058] Figure 3 A schematic diagram showing the projection process of the surface nodes of the seeded finite element model is presented. As shown in the figure, for the seeded finite element model M seed the corner node A is projected onto the corner node A' of M (GEOM，1) the edge node B is projected onto the edge node B' of M (GEOM，1) and the face node C is projected onto the face node C' of M (GEOM，1) It can be seen that after the surface nodes are projected onto M (GEOM，1) they remain surface nodes, and the position attributes of the nodes remain unchanged. That is, after the projection, the corner nodes remain corner nodes, the edge nodes remain edge nodes, and the face nodes remain face nodes.

[0059] After projecting the surface nodes of the seeded finite element model onto M (GEOM，1) the three-dimensional coordinates of a total of N (GEOM，1) nodes on the surface of M surf are obtained, and their vector expressions are as shown in the following formula (3):

[0060]

[0061] Calculate the displacements generated by each of the N seed nodes on the surface of the seeded finite element model M surf during the process of the model shape changing to M (GEOM，1) The vector expression is:

[0062]

[0063] Next, according to the coordinates of the N seed nodes on the surface of the seeded finite element model M surf calculate the following matrix Φ:

[0064]

[0065] In formula (5), r i = [x (s，i) y (s，i) z (s，i) T (i = 1, 2,..., N surf ) is the three-dimensional coordinate of the i-th surface node in M seed , |r j - r i | is the distance between the j-th surface node in M seed and the i-th surface node in M seed , is a radial basis function. The specific expression of the radial basis function is not unique. Preferably, the Wendland’s C2 function can be adopted, and its expression is:

[0066]

[0067] In formula (6), d is the action radius of the radial basis function, and it can be stipulated that when |r j -r i | > d,

[0068] Subsequently, solve the following equations to obtain the weight coefficient vectors W seed in N surf surface nodes in the three coordinate axis directions respectively: x 、W y 、W z :

[0069]

[0070] The respective expressions of W x 、W y 、W z are:

[0071]

[0072] Substitute the coordinates [x (v，j) y (v，j) z (v，j) of the internal nodes of the seed finite element model T (j = 1, 2,..., N volu ) into the following formula:

[0073]

[0074] Δx (v，j) 、Δy (v，j) 、Δz (v，j) can be obtained, that is, the displacement components of the jth internal node in the three coordinate axis directions.

[0075] Solve according to the following formula to obtain the new coordinates of all internal nodes of the seed finite element model in the three-dimensional coordinate system when the model shape becomes M (GEOM，1) :

[0076]

[0077] According to the new coordinates X′ surf of the N surf surface nodes obtained through formula (3), Y′ surf 、Z′ surf and the N obtained through formula (10)volu The new coordinates x′ of an internal node volu , Y′ volu , Z′ volu , update the seeded finite element model M seed in the three-dimensional coordinates of a total of (N surf +N volu ) nodes, so as to transform the seeded finite element model M seed into a deterministic finite element model M (GEOM，1) corresponding to the structural model M (FE，1) .

[0078] By repeating the above process for the other structural models (i.e., M (GEOM，1) excluded) among the N structural models (i.e., M (GEOM，k) (k = 2,..., N)) respectively, deterministic finite element models corresponding to these structural models can be obtained, and thus N deterministic finite element models (i.e., M (FE，k) (k = 1, 2,..., N)) corresponding to N sample points can be obtained.

[0079] In step 130, perform structural reliability analysis on the component using these N deterministic finite element models.

[0080] In some embodiments, performing structural reliability analysis on the component using these N deterministic finite element models further includes: sequentially performing finite element simulation calculations on these N deterministic finite element models to obtain corresponding structural responses; fitting the functional relationship between the geometric random variables and the structural responses to obtain a fitted function; and using the fitted function to replace the limit state function to perform structural reliability analysis.

[0081] Since only the node coordinates are different among the finite element models in M (FE，k) (k = 1, 2,..., N), while the number of nodes, the node numbers, and the node composition of each element are exactly the same, the material properties, the element real constants, the constraints and loads applied to the nodes can all be retained without modification. By performing finite element simulation calculations on M (FE，k) (k = 1, 2,..., N) respectively, the structural responses of M (FE，k) (k = 1, 2,..., N) can be obtained. Typical structural responses include but are not limited to stress, strain, displacement, and temperature at key parts.

[0082] Subsequently, a suitable approximation model can be selected to fit the mathematical functional relationship between each geometric random variable and the structural response, so as to obtain a fitted function.

[0083] Taking the use of the Monte Carlo method for reliability analysis as an example, in each Monte Carlo sampling, the calculation of the limit state function can use the above-mentioned fitted function, thus replacing the actual function of implementing the parametric finite element model.

[0084] As can be seen from Method 100, the present invention connects the parametric structural model and the deterministic finite element model through a radial basis function sequence, so that the geometric changes (surface deformation) occurring in the parametric structural model are conducted to the deterministic finite element model through radial basis function interpolation. The change amount of the node coordinates in the finite element model is determined according to the weighted interpolation result of the radial basis function sequence, and the structural response corresponding to different geometric parameter combinations is obtained without directly establishing a parametric finite element model, thereby controlling the analysis cost of structural reliability.

[0085] To better understand the technical solution of the present invention, the following takes the compressor disk as an example and combines Figures 4 - 9 to further explain the structural reliability analysis process of the present invention.

[0086] Figure 4 A schematic diagram of the compressor disk 400 is shown.

[0087] As shown in the figure, the compressor disk 400 is evenly distributed with 6 eccentric pressure equalizing holes 401, 402, 403, 404, 405, 406 along the circumferential direction.

[0088] The geometric random variables of the compressor disk 400 include the web thickness T 1 , the thickness T of the center hole edge 2 , the thickness T of the disk center 3 , the diameter D of the pressure equalizing hole, and the radial position R where the center of the pressure equalizing hole is located, as Figure 5 shown. The random distribution parameters of each geometric random variable are shown in Table 1 below, and each variable follows a normal distribution.

[0089] Table 1

[0090]

[0091] The limit state function for the reliability analysis of the stress at the edge of the pressure equalizing hole of the compressor disk is defined as:

[0092] g(T 1 , T 2 , T 3 , D, R) = [σ] - σ P (T 1 , T 2 , T 3 , D, R) (11)

[0093] where [σ] is the allowable stress, and σ P (T 1 , T2 , T 3 , D, R) is the stress value at point P (6 o'clock direction) on the edge of the pressure equalizing hole 401, as Figure 5 shown in

[0094] Solve for σ P (T 1 , T 2 , T 3 , D, R) requires the aid of a finite element program. Therefore, σ P (T 1 , T 2 , T 3 , D, R) is actually a parametric finite element model that includes five geometric random variables, T 1 , T 2 , T 3 , D, and R.

[0095] The establishment of a parametric finite element model driven by geometric dimensions is usually very complex. However, by using the method of the present invention, the stress value at point P (6 o'clock direction) on the edge of the pressure equalizing hole 401 can be predicted based on the sampling values of T 1 , T 2 , T 3 , D, and R without the need to establish a parametric finite element model, thereby quickly calculating the value of the limit state function and determining whether the compressor disk fails at this time. The specific calculation steps are as follows:

[0096] S1: Establish a parametric structural model of the compressor disk 400, and use the periodic symmetry of the structure to take one-sixth of the sector, that is, only retain the sector where the pressure equalizing hole 401 is located. Figure 6 shows the parametric structural model of this one-sixth sector.

[0097] The parametric structural model of the compressor disk 400 can realize automatic shape change under the drive of geometric dimensions (i.e., T 1 , T 2 , T 3 , D, and R), as Figure 7 shown.

[0098] S2: Use finite element preprocessing software to mesh the structural model of the compressor disk 400 in the mean state of T 1 , T 2 , T 3 , D, and R, and assign material properties, loads, and boundary conditions to obtain the seeded finite element model M seed , as Figure 8 shown.

[0099] S3: The experimental design method uses Latin hypercube design. According to T in Table 1 1 , T 2 , T3 For the random distribution parameters of D and R, 50 sample points are generated within the range of plus or minus 3 times the standard deviation from the mean, i.e., N = 50. It should be noted that the above method of generating sample points is merely exemplary and not restrictive. In actual implementation, those skilled in the art can generate different numbers of sample points within different value ranges according to the actual situation.

[0100] S4: According to the sampling values of T, T, T, D, and R in the 50 Latin hypercube design sample point data 1 、T 2 、T 3 、D, and R, drive the parametric structural model of the compressor disk 400 to automatically update the model geometry, obtaining N = 50 structural models with different geometric dimensions.

[0101] S5: Extract the node numbers and three-dimensional coordinates of the surface nodes of the seed finite element model M seed , the total number of which is N surf = 10770. Then, according to the different positions of the surface nodes on the seed finite element model, the N surf = 10770 surface nodes are further divided into three subsets: corner nodes, edge nodes, and face nodes. Subsequently, extract the node numbers and three-dimensional coordinates of the internal nodes of the seed finite element model, the total number of which is N volu = 33574.

[0102] S6: For each of the N = 50 structural models with different geometric dimensions obtained in S4, denoted as M (GEOM,k) (k = 1, 2,..., 50), repeat the following operations:

[0103] ① Project the corner nodes, edge nodes, and face nodes on the surface of the seed finite element model M seed onto M (GEOM,k) , obtaining the three-dimensional coordinates X (GEOM,k) ′ surf , Y s ′ urf , and Z s ′ urf of a total of N s ′ urf = 10770 nodes on the surface of M

[0104] ② Calculate the displacements ΔX seed , ΔY surf , and ΔZ (GEOM,k) generated by each of the N surf = 10770 nodes on the surface of the seed finite element model M surf during the process of the model shape changing to M surf according to Equation (4);

[0105] ③ Based on the seed finite element model Mseed Surface N surf = coordinates of 10,770 nodes, calculate matrix Φ according to Equation (5);

[0106] ④ Solve the system of equations shown in Equation (7) to obtain M seed and N in surf = weight coefficient vectors W x , W y , W z ;

[0107] ⑤ Substitute the coordinates [x (v,j) y (v,j) z (v,j) of the internal nodes of the seed finite element model into Equation (9) in sequence (j = 1, 2,..., 33,574) to obtain Δx T , Δy (v,j) , Δz (v,j) , that is, the displacement components of the j-th internal node of the seed finite element model in the three coordinate axis directions; (v,j)

[0108] ⑥ Solve for the new coordinates X′ (GEOM,k) , Y′ volu , Z′ volu , Y′ volu , Z′ volu of N

[0109] ⑦ According to the new coordinates X′ surf , Y′ surf , Z′ surf of N surf = 10,770 surface nodes and the new coordinates X′ volu , Y′ volu , Z′ volu , Z′ volu of N seed = 33,574 internal nodes, update the three-dimensional coordinates of a total of (N surf + N volu = 44,344) nodes in the seed finite element model M seed , while the material properties, element real constants, constraints and loads applied to the nodes remain unchanged, thereby converting the seed finite element model M (GEOM,k) into a deterministic finite element model M (FE,k) corresponding to the structural model M

[0110] Figure 9 The deterministic finite element models under different combinations of geometric parameters are as shown in Figure 9 . FromFigure 9 It can be seen that the radial basis function grid deformation has relatively ideal smoothness.

[0111] S7: Sequentially perform finite element simulation calculations on M (FE,k) (k = 1, 2,..., 50), and respectively obtain the stress values σ (FE,k) at point P (6 o'clock direction) on the edge of the pressure equalizing hole 401 of M (P,k) (k = 1, 2,..., 50).

[0112] S8: According to the sampling values of T 1 , T 2 , T 3 , D, R in the data of 50 Latin hypercube design sample points, and σ (P,k) (k = 1, 2,..., 50), select the Kriging method to fit the mathematical function relationship between T 1 , T 2 , T 3 , D, R and σ P (T 1 , T 2 , T 3 , D, R), and obtain the fitted Kriging approximation model / approximation function

[0113] S9: Use Monte Carlo simulation to perform multiple samplings to solve the structural reliability. In each Monte Carlo sampling, the calculation of the limit state function for the reliability analysis of the stress on the edge of the pressure equalizing hole of the compressor disk uses the Kriging approximation model established in S8 to obtain the stress value at point P (6 o'clock direction) on the edge of the pressure equalizing hole 401. When the allowable stress [σ] = 525 MPa, the calculation result of the failure probability is P f = 0.001030.

[0114] The above has shown an exemplary process for the structural reliability analysis of the compressor disk 400 with reference to Figures 4 - 9 It should be noted that the above structural reliability analysis process is only exemplary and not restrictive. In actual implementation, for different components, those skilled in the art can adopt different methods to perform structural reliability analysis on the components. For example, in specific implementation, different radial basis functions, different numbers of sample points, different fitting methods for the functional relationship between geometric random variables and structural responses, etc. can be adopted.

[0115] Figure 10 Figure 52 shows the structural reliability analysis system 1000 based on radial basis functions of the present invention.

[0116] As Figure 10As shown, the system 1000 may include a parametric structural model unit 1005, a seeded finite element model unit 1010, a sampling value acquisition unit 1015, a geometry change unit 1020, a model transformation unit 1025, and a reliability analysis unit 1030. Each of these units may be directly or indirectly connected or communicate with each other on one or more buses 1035.

[0117] In various embodiments of the present invention, the parametric structural model unit 1005 may be configured to: establish a parametric structural model of a component.

[0118] The seeded finite element model unit 1010 may be configured to: mesh the parametric structural model based on geometric random variables of the component and assign material properties, loads, and boundary conditions to obtain a seeded finite element model of the component.

[0119] The parametric structural model can automatically change its geometry driven by geometric dimensions, while the seeded finite element model cannot automatically change its geometry driven by geometric dimensions.

[0120] The sampling value acquisition unit 1015 may be configured to: obtain sampling values of geometric random variables.

[0121] In some embodiments, the sampling value acquisition unit 1015 is further configured to: determine the value range of the geometric random variables of the component; generate N sample points within the value range; and obtain the sampling values of the geometric random variables at the N sample points.

[0122] The geometry change unit 1020 may be configured to: change the geometry of the parametric structural model based on the sampling values to obtain N structural models with different geometric dimensions.

[0123] The model transformation unit 1025 may be configured to: transform the seeded finite element model into N deterministic finite element models corresponding to the N structural models based on radial basis functions.

[0124] In some embodiments, the model transformation unit 1025 is further configured to perform the following operations for each of the N structural models: extract N surf surface nodes and N volu internal nodes of the seeded finite element model; project the N surf surface nodes onto the structural model to obtain new coordinates of the N surf surface nodes; determine the coordinate change amounts of the N volu internal nodes when projected onto the structural model based on radial basis functions to obtain new coordinates of the N volu internal nodes; and based on the new coordinates of the N surf surface nodes and the Nvolu Update the seed finite element model with the new coordinates of the internal nodes to obtain a deterministic finite element model corresponding to the structural model.

[0125] In some embodiments, N surf surface nodes include corner nodes, edge nodes, and face nodes, and the model transformation unit 1025 is further configured to: project the N surf surface nodes onto the structural model such that the new coordinates of the corner nodes are located at the corresponding corners of the structural model, the new coordinates of the edge nodes are located on the corresponding edges of the structural model, the new coordinates of the face nodes are located on the corresponding faces of the structural model, and the projection direction is along the normal of the corresponding face of the structural model.

[0126] The reliability analysis unit 1030 may be configured to perform structural reliability analysis on the component using N deterministic finite element models.

[0127] In some embodiments, the reliability analysis unit 1030 is further configured to: sequentially perform finite element simulation calculations on the N deterministic finite element models to obtain corresponding structural responses; fit the functional relationship between the geometric random variables and the structural responses to obtain a fitted function; and use the fitted function to replace the limit state function to perform structural reliability analysis.

[0128] In some embodiments, the structural response includes but is not limited to at least one of stress, strain, displacement, and temperature at the critical part of the component.

[0129] It should be understood that Figure 10 only one example of the structural reliability analysis system 1000 based on radial basis functions is shown. In a specific implementation, the structural reliability analysis system based on radial basis functions of the present invention can be implemented in different ways. For example, one or more units can be added or omitted, or multiple units can be combined or integrated. For example, in some implementations, the sampling value acquisition unit 1015 and the geometric shape change unit 1020 can be combined into a single unit.

[0130] Figure 11 A block diagram of a device 1100 including a structural reliability analysis system based on radial basis functions is shown.

[0131] The device shows a general hardware environment in which the present invention can be applied according to the exemplary embodiments of the present invention.

[0132] Now will refer to Figure 11Describe the device 1100, which is an exemplary embodiment of a hardware device that can be applied to various aspects of the present invention. The device 1100 can be any machine configured to perform processing and / or computing, and can be, but is not limited to, a workstation, a server, a desktop computer, a laptop computer, a tablet computer, a personal digital assistant (PDA), a smart phone, or any combination thereof. The above system can be implemented in whole or at least in part by the device 1100 or a similar device or system.

[0133] The device 1100 may include components that can be connected to or communicate with the bus 1130 via one or more interfaces. For example, the device 1100 may include a bus 1130, a processor 1105, a memory 1110, an input device 1120, an output device 1125, and so on.

[0134] The processor 1105 can be any type of processor, and can include, but is not limited to, a general-purpose processor and / or a special-purpose processor (such as a special processing chip), a smart hardware device (such as a general-purpose processor, a DSP, a CPU, a microcontroller, an ASIC, an FPGA, a programmable logic device, discrete gate or transistor logic components, discrete hardware components, or any combination thereof). In some cases, the processor 1105 can be configured to operate the memory array using a memory controller. In other cases, the memory controller (not shown) can be integrated into the processor 1105. The processor 1105 can be responsible for managing the bus and general processing, including executing software stored in the memory. The processor 1105 can also be configured to perform various functions related to the radial basis function-based structural reliability analysis described herein. For example, the processor 1105 can be configured to: establish a parametric structural model of a member; mesh the parametric structural model based on the geometric random variables of the member and assign material properties, loads, and boundary conditions to obtain a seeded finite element model of the member; obtain sampling values of the geometric random variables; change the geometry of the parametric structural model based on the sampling values to obtain N structural models with different geometric dimensions; transform the seeded finite element model into N deterministic finite element models corresponding to the N structural models based on the radial basis function; and perform structural reliability analysis on the member using the N deterministic finite element models.

[0135] The memory 1110 can be any storage device capable of implementing data storage. The memory 1110 may include, but is not limited to, disk drives, optical storage devices, solid-state memories, floppy disks, hard disks, magnetic tapes, or any other magnetic medium, optical disks, or any other optical medium, ROM (read-only memory), RAM (random access memory), cache memory, and / or any other memory chip or cartridge, and / or any other medium from which a computer can read data, instructions, and / or code. The memory 1110 may store computer-executable software 1115 including computer-readable instructions that, when executed, cause the processor to perform various functions related to the radial basis function-based structural reliability analysis described herein.

[0136] The input device 1120 can be any type of device that can be used to input information.

[0137] The output device 1125 can be any type of device for outputting information. In one scenario, the output device 1125 can be any type of output device that can display information.

[0138] The present invention aims at the pain point of difficult handling of geometric uncertainties in structural reliability analysis. By connecting a parametric structural model and a deterministic finite element model through a radial basis function sequence, without directly establishing a parametric finite element model, the organic combination of "parametric structural model - radial basis function sequence - deterministic finite element model" is used to replace and achieve the actual functions of the parametric finite element model, and there are the following beneficial effects:

[0139] (1) It is possible to quickly obtain the structural responses corresponding to different combinations of geometric parameters without directly establishing a parametric finite element model, effectively controlling the analysis cost of the structural reliability problem containing geometric random variables;

[0140] (2) Using the organic combination of "parametric structural model - radial basis function sequence - deterministic finite element model" to replace and achieve the actual functions of the parametric finite element model solves the problems of high cost and difficulty in adapting to configuration changes of the parametric finite element model containing geometric random variables;

[0141] (3) By only updating the node coordinates while keeping the material properties, element real constants, constraints and loads applied to the nodes unchanged, it is possible to quickly and low-costly obtain finite element models with different geometric shapes;

[0142] (4) The present invention uses a weighted radial basis function sequence as the interface connection parameter between the parametric structural model and the deterministic finite element model, enabling the geometric changes (surface deformation) occurring in the parametric structural model to be conducted to the deterministic finite element model through radial basis function interpolation. This process makes no prior assumptions about the geometric shape of the part, so it is applicable to the structural reliability analysis problems with complex geometric features. Moreover, the smoothness of the radial basis function sequence interpolation can ensure that the element quality of the finite element mesh obtained after deformation is not lower than that of the seed finite element model.

[0143] The detailed description provided above in conjunction with the accompanying drawings describes examples and does not represent all examples that can be implemented or fall within the scope of the claims. The terms "example" and "exemplary" when used in this specification mean "serving as an example, instance, or illustration" and do not mean "superior to or better than other examples".

[0144] The reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment of the present invention. Thus, the use of these phrases may refer to more than just one embodiment. In addition, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0145] The foregoing description has been provided to enable any person skilled in the art to practice the various aspects described herein. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects. Thus, the claims are not intended to be limited to the aspects shown herein, but are to be accorded the full scope consistent with the language of the claims, where the recitation of a singular element is not intended to mean "one and only one" unless specifically stated otherwise, but rather "one or more". Unless specifically stated otherwise, the term "some" means one or more. Elements of the various aspects described throughout this disclosure that are presently known or later come to be known to those of ordinary skill in the art as structural and functional equivalents are hereby expressly incorporated by reference and are intended to be covered by the claims.

[0146] It should also be noted that these embodiments may be described as processes depicted as flowcharts, flow diagrams, structural diagrams, or block diagrams. Although a flowchart may describe the operations as a sequential process, many of these operations can be performed in parallel or concurrently. In addition, the order of these operations may be rearranged.

[0147] Although various embodiments have been illustrated and described, it should be understood that the embodiments are not limited to the above exact configurations and components. Various modifications, substitutions, and improvements that are obvious to those skilled in the art can be made in the arrangement, operation, and details of the devices disclosed herein without departing from the scope of the claims.

Claims

1. A method for structural reliability analysis based on radial basis functions, comprising: establishing a parametric structural model of a component; performing mesh division on the parametric structural model based on the geometric random variables of the component and assigning material properties, loads, and boundary conditions thereto to obtain a seeded finite element model of the component; obtaining sampling values of the geometric random variables; changing the geometric shape of the parametric structural model based on the sampling values to obtain N structural models with different geometric dimensions; converting the seeded finite element model into N deterministic finite element models corresponding to the N structural models based on radial basis functions; and performing structural reliability analysis on the component using the N deterministic finite element models.

2. The method according to claim 1, wherein the parametric structural model can automatically change its geometric shape under the drive of geometric dimensions, and the seeded finite element model cannot automatically change its geometric shape under the drive of geometric dimensions.

3. The method according to claim 1, wherein obtaining the sampling values of the geometric random variables further comprises: determining the value range of the geometric random variables of the component; generating N sample points within the value range; and obtaining the sampling values of the geometric random variables at the N sample points.

4. The method according to claim 1, wherein converting the seeded finite element model into N deterministic finite element models corresponding to the N structural models based on radial basis functions further comprises performing the following operations for each of the N structural models: Extract the N surf surface nodes and N volu interior nodes of the seed finite element model; Project the N surf surface nodes onto the structural model to obtain new coordinates of the N surf surface nodes; Determine the coordinate change amounts of the N volu internal nodes when projected onto the structure model to obtain the new coordinates of the N volu internal nodes; and Based on the new coordinates of the N surf surface nodes and the new coordinates of the N volu interior nodes to update the seeded finite element model to obtain a deterministic finite element model corresponding to the structural model.

5. The method according to claim 4, wherein The N surf surface nodes include corner nodes, edge nodes, and face nodes, and projecting the N surf surface nodes onto the structural model further includes: Project the N surf surface nodes onto the structure model such that the new coordinates of the corner nodes are located at the corresponding corners of the structure model, the new coordinates of the edge nodes are located on the corresponding edges of the structure model, the new coordinates of the face nodes are located on the corresponding faces of the structure model, and the projection direction is along the normal of the corresponding face of the structure model.

6. The method according to claim 1, wherein performing structural reliability analysis on the component using the N deterministic finite element models further comprises: successively performing finite element simulation calculations on the N deterministic finite element models to obtain corresponding structural responses; fitting the functional relationship between the geometric random variables and the structural responses to obtain a fitted function; and using the fitted function to replace the limit state function to perform structural reliability analysis.

7. The method according to claim 6, wherein the structural responses include at least one of stress, strain, displacement, and temperature at the key parts of the component.

8. A structural reliability analysis system based on radial basis functions, comprising: a parametric structural model unit for establishing a parametric structural model of a component; a seeded finite element model unit for performing mesh division on the parametric structural model based on the geometric random variables of the component and assigning material properties, loads, and boundary conditions thereto to obtain a seeded finite element model of the component; a sampling value acquisition unit for obtaining the sampling values of the geometric random variables; a geometric shape change unit for changing the geometric shape of the parametric structural model based on the sampling values to obtain N structural models with different geometric dimensions; A model transformation unit, configured to transform the seed finite element model into N deterministic finite element models corresponding to the N structural models based on radial basis functions; and A reliability analysis unit, configured to perform structural reliability analysis on the component by using the N deterministic finite element models.

9. The system according to claim 8, wherein the parametric structural model can automatically change its geometric shape under the drive of geometric dimensions, and the seed finite element model cannot automatically change its geometric shape under the drive of geometric dimensions.

10. The system according to claim 8, wherein the sampling value acquisition unit is further configured to: determine the value range of the geometric random variable of the component; generate N sample points within the value range; and obtain the sampling values of the geometric random variable at the N sample points.

11. The system according to claim 8, wherein the model transformation unit is further configured to perform the following operations for each of the N structural models: Extract N surface nodes and N internal nodes of the seed finite element model surf ; volu ​ Project the N surf surface nodes onto the structural model to obtain new coordinates of the N surf surface nodes; Determine the coordinate change amounts of the N volu internal nodes when projected onto the structure model to obtain the new coordinates of the N volu internal nodes; and Based on the new coordinates of the N surf surface nodes and the new coordinates of the N volu internal nodes, update the seeded finite element model to obtain a deterministic finite element model corresponding to the structural model.

12. The system according to claim 11, wherein The said N surf surface nodes include corner nodes, edge nodes, and face nodes, and the model transformation unit is further configured to: Project the N surf surface nodes onto the structure model such that the new coordinates of the corner nodes are located at the corresponding corners of the structure model, the new coordinates of the edge nodes are located on the corresponding edges of the structure model, the new coordinates of the face nodes are located on the corresponding faces of the structure model, and the projection direction is along the normal of the corresponding face of the structure model.

13. The system according to claim 8, wherein the reliability analysis unit is further configured to: perform finite element simulation calculations on the N deterministic finite element models in sequence to obtain corresponding structural responses; fit the functional relationship between the geometric random variable and the structural response to obtain a fitted function; and use the fitted function to replace the limit state function to perform structural reliability analysis.

14. The system according to claim 13, wherein the structural response includes at least one of stress, strain, displacement, and temperature of the key part of the component.

15. A computer-readable storage medium storing a computer program for structural reliability analysis based on radial basis functions, the computer program being executable by a processor to execute the method according to any one of claims 1-7.

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