Random field modeling method for quantifying initial defects of spherical shell structure

Abstract

The invention discloses a random field modeling method for quantifying an initial defect of a spherical shell structure. The method comprises the following steps: determining simulated spherical shell data corresponding to a target spherical shell; the simulated spherical shell data comprises spherical shell geometric information and spherical shell material information; determining a target correlation function and representative discrete points corresponding to a target spherical shell based on spherical shell geometric information and the spherical shell material information; determining a correlation coefficient matrix based on the target correlation function and the representative discrete points; performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field; and performing random field transformation on the standard random field based on a random field transformation formula to obtain a target random field corresponding to the target spherical shell. According to the method, the target correlation function and the representative discrete points are determined according to the simulated spherical shell data, the geodesic distance is introduced into the target correlation function, the spherical shell random field is established based on the eigenvalue decomposition method, the intrinsic correlation of the initial defect of the spherical shell can be accurately quantified, and then the accuracy of spherical shell performance analysis can be improved.

Description

Technical Field

[0001] The invention relates to the technical field of structural engineering, and in particular to a random field modeling method for quantifying initial defects of a spherical shell structure. Background Art

[0002] Spherical shell structures are widely used in the fields of construction, aerospace, industry, etc. due to their reasonable stress-bearing performance. However, in actual engineering, spherical shells inevitably have various initial defects, such as geometric defects and material defects, which will significantly reduce the overall bearing capacity, stability, fatigue life, etc. of the spherical shell structure.

[0003] Since the distribution of the initial defects of the spherical shell structure is random, it is usually characterized as a random field on the spherical shell. Many random field simulation methods have been developed in the prior art, but these methods are only applicable to Euclidean space, such as planes, cubes, etc., and are not applicable to curved surface structures such as spherical shells; using the methods in the prior art to generate random fields on the spherical shell, it is impossible to characterize the actual correlation between any two points of the spherical shell, and thus it is impossible to accurately quantify the initial defects of the spherical shell, which affects the performance analysis and evaluation of the spherical shell. Summary of the invention

[0004] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to improve the quantification accuracy of the initial defects of the spherical shell.

[0005] In order to solve at least one of the above-mentioned technical problems, the present invention discloses a random field modeling method for quantifying initial defects of a spherical shell structure.

[0006] According to a first aspect of the present disclosure, a random field modeling method for quantifying initial defects of a spherical shell structure is provided, comprising:

[0007] Determining simulated spherical shell data for constructing a target spherical shell; the simulated spherical shell data includes spherical shell geometry information, spherical shell material information, and spherical shell defect information;

[0008] Based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information, determining a target correlation function and a representative discrete point corresponding to the spherical shell defect information;

[0009] Determine a correlation coefficient matrix corresponding to the spherical shell defect information based on the target correlation function, the representative discrete points and the spherical shell defect information;

[0010] Performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field;

[0011] Based on the random field transformation formula, the standard random field is transformed to obtain the target random field corresponding to the spherical shell defect information.

[0012] In some possible embodiments, determining the target correlation function and the representative discrete points corresponding to the spherical shell defect information based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information includes:

[0013] Based on the spherical shell geometry information and the spherical shell material information, modeling processing is performed to obtain the target spherical shell;

[0014] The target spherical shell is meshed to obtain the representative discrete points.

[0015] In some possible embodiments, determining the target correlation function and the representative discrete points corresponding to the target spherical shell based on the spherical shell geometry information, the spherical shell material information, and the spherical shell defect information includes:

[0016] Based on the spherical shell defect information, a target length parameter corresponding to the target spherical shell is obtained; the target length parameter represents the range information corresponding to the target random field;

[0017] Calculating target distance parameters based on the spherical shell geometry information;

[0018] The target correlation function is constructed based on the target length parameter and the target distance parameter.

[0019] In some possible embodiments, determining a correlation coefficient matrix based on the target correlation function, the representative discrete points, and the spherical shell defect information includes:

[0020] Performing probability distribution type judgment on the spherical shell defect information to obtain a type judgment result;

[0021] When the type judgment result indicates that the spherical shell defect information corresponds to a normal distribution, based on the target correlation function, sequentially calculating a first correlation coefficient between any two representative discrete points among the plurality of representative discrete points;

[0022] The correlation coefficient matrix is ​​constructed based on the first correlation coefficients corresponding to the multiple representative discrete points.

[0023] In some possible embodiments, the method further includes:

[0024] In the case where the type judgment result indicates that the spherical shell defect information corresponds to a logarithmic normal distribution, determining a correlation coefficient calculation formula based on the target correlation function;

[0025] Based on the correlation coefficient calculation formula, sequentially calculating a second correlation coefficient between any two representative discrete points among the plurality of representative discrete points;

[0026] The correlation coefficient matrix is ​​constructed based on the second correlation coefficients corresponding to the multiple representative discrete points.

[0027] In some possible embodiments, performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field includes:

[0028] Performing eigenvalue decomposition on the correlation coefficient matrix to obtain an eigenvalue matrix and an eigenvector matrix corresponding to the correlation coefficient matrix;

[0029] Determining a target number of random variables based on a reconstruction threshold calculation formula and a reconstruction threshold parameter; the target number of random variables is less than the number of representative discrete points;

[0030] Determine a target eigenvalue matrix, a target eigenvector matrix, and a target random vector parameter based on the target number of random variables, the eigenvalue matrix, and the eigenvector matrix;

[0031] The standard random field is constructed based on the target eigenvalue matrix, the target eigenvector matrix and the target random vector parameters.

[0032] In some possible embodiments, performing random field transformation on the standard random field based on a random field transformation formula to obtain a target random field corresponding to the target spherical shell includes:

[0033] Obtain the mean and standard deviation corresponding to the spherical shell defect information;

[0034] The mean, the standard deviation and the standard random field are input into the random field transformation formula to obtain the target random field.

[0035] According to a second aspect of the present disclosure, a random field modeling device for quantifying initial defects of a spherical shell structure is provided, the device comprising:

[0036] A simulation information acquisition module, used to acquire simulated spherical shell data for constructing a target spherical shell; the simulated spherical shell data includes spherical shell geometry information, spherical shell material information and spherical shell defect information;

[0037] A spherical shell parameter determination module, used to determine a target correlation function and a representative discrete point corresponding to the spherical shell defect information based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information;

[0038] A correlation coefficient matrix determination module, used to determine the correlation coefficient matrix corresponding to the spherical shell defect information based on the target correlation function, the representative discrete points and the spherical shell defect information;

[0039] An eigenvalue decomposition module, used for performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field;

[0040] The random field determination module is used to perform random field transformation on the standard random field based on the random field transformation formula to obtain the target random field corresponding to the spherical shell defect information.

[0041] According to a third aspect of the present disclosure, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction and at least one program, and the at least one instruction and the at least one program are loaded and executed by the processor to implement the random field modeling method for quantifying the initial defects of a spherical shell structure as described above.

[0042] According to a fourth aspect of the present disclosure, a computer storage medium is provided, in which at least one instruction and at least one program are stored, and the at least one instruction and the at least one program are loaded and executed by a processor to implement the random field modeling method for quantifying the initial defects of a spherical shell structure as described above.

[0043] The implementation of the present invention has the following beneficial effects:

[0044] In the present invention, a target correlation function and representative discrete points are determined according to simulated spherical shell data corresponding to the target spherical shell, wherein the target distance parameters involved in the target correlation function are determined based on the specific simulated spherical shell data, and a correlation coefficient matrix is ​​determined according to the target correlation function and the representative discrete points, and then the correlation coefficient matrix is ​​subjected to eigenvalue decomposition, which can accurately quantify the intrinsic correlation of the initial defects of the target spherical shell; at the same time, for different initial probability distribution types, different random field transformation formulas are used, which can ensure the correlation and matching degree between the random field and the spherical shell defects, thereby improving the accuracy of the quantification of the initial defects of the spherical shell, and then improving the reliability of the spherical shell performance analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0046] Figure 1 A schematic diagram of a flow chart corresponding to the random field modeling method provided in an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of a corresponding process for determining representative discrete points provided in an embodiment of the present invention;

[0048] Figure 3A schematic diagram of a corresponding process for determining a target-related function provided in an embodiment of the present invention;

[0049] Figure 4 A schematic diagram of a first process flow corresponding to determining a correlation coefficient matrix provided in an embodiment of the present invention;

[0050] Figure 5 A schematic diagram of a second process flow corresponding to determining a correlation coefficient matrix provided in an embodiment of the present invention;

[0051] Figure 6 A schematic diagram of a corresponding process for determining a standard random field provided in an embodiment of the present invention;

[0052] Figure 7 A schematic diagram of a corresponding process for determining a target random field provided by an embodiment of the present invention;

[0053] Figure 8 A first schematic diagram of a spherical shell normal distribution random field provided by a specific embodiment of the present invention;

[0054] Fig. 9 A second schematic diagram of a spherical shell normal distribution random field provided by a specific embodiment of the present invention;

[0055] Fig.10 A third schematic diagram of a spherical shell normal distribution random field provided by a specific embodiment of the present invention;

[0056] Fig.11 A first schematic diagram of a spherical shell log-normal distribution random field provided by a specific embodiment of the present invention;

[0057] Fig.12 A second schematic diagram of a spherical shell log-normal distribution random field provided by a specific embodiment of the present invention;

[0058] Fig.13 A third schematic diagram of a spherical shell log-normal distribution random field provided by a specific embodiment of the present invention;

[0059] Fig.14 A schematic diagram of the structure corresponding to the random field modeling device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of this specification to clearly and completely describe the technical solutions in the embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a method, system, product, or server that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these methods, products, or devices.

[0062] Various exemplary embodiments, features and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0063] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0064] The term "and / or" herein is only a description of the association relationship of the associated objects, indicating that there may be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the term "at least one" herein represents any combination of at least two of any one or more of a plurality of. For example, including at least one of A, B, and C can represent including any one or more elements selected from the set consisting of A, B, and C.

[0065] In addition, in order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the subject matter of the present disclosure.

[0066] Figure 1 The flowchart corresponding to the random field modeling method provided in the embodiment of the present invention is shown in FIG. 1 . The execution subject can be any terminal or electronic device that can implement the random field modeling method for quantifying the initial defects of the spherical shell structure, such as a computer, a server, an embedded system, a smart phone, a tablet computer or a server cluster, and any other device that has computing power and can implement the random field modeling method. In a specific embodiment, Figure 1 As shown, a random field modeling method for quantifying the initial defects of a spherical shell structure includes:

[0067] Step S101: determining simulated spherical shell data for constructing a target spherical shell; the simulated spherical shell data includes spherical shell geometry information, spherical shell material information, and spherical shell defect information;

[0068] In a specific embodiment, the simulated spherical shell data may include spherical shell geometry information and spherical shell material information, and may also include spherical shell defect information; wherein the spherical shell geometry information may at least include the spherical shell radius r and the spherical shell thickness t; the spherical shell material information may include spherical shell material information and the spherical shell elastic modulus E; the spherical shell defect information may be initial defect information, and is determined before constructing the target spherical shell, and may be determined by numerical simulation, statistical analysis, and the like.

[0069] Step S102: determining a target correlation function and a representative discrete point corresponding to the target spherical shell based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information;

[0070] In a specific embodiment, a target spherical shell may be first constructed according to the spherical shell geometry information and the spherical shell material information, and then the corresponding target correlation function and representative discrete points may be obtained based on the target spherical shell.

[0071] Can be combined separately Figure 2 and Figure 3 Explain how to determine the target correlation function and represent discrete points; specifically, Figure 2 The target related function provided in the embodiment of the present invention determines the corresponding flow chart; Figure 2 As shown, for determining the representative discrete points, step S102 may include:

[0072] Step S201: performing modeling processing based on the spherical shell geometry information and the spherical shell material information to obtain the target spherical shell;

[0073] Specifically, the target spherical shell can be constructed by combining the spherical shell radius, spherical shell thickness, spherical shell material information and spherical shell elastic modulus through ABAQUS finite element software.

[0074] Step S202: meshing the target spherical shell to obtain the representative discrete points.

[0075] Furthermore, after obtaining the target spherical shell, the target spherical shell can be meshed, the target spherical shell can be divided into triangular meshes, and the nodes or integral points of each mesh unit are determined as representative discrete points of the target spherical shell; wherein the representative discrete points can be expressed as: P i (x i ,y i ,z i ),i=1,2,…,n, where n represents the number of discrete points.

[0076] Specifically, the target spherical shell is meshed and divided into a plurality of geometric units. The vertex of each geometric unit becomes a node, and each node can be determined as a representative discrete point. The number and position of the nodes can depend on the density of the meshing and the complexity of the target spherical shell.

[0077] Further, Figure 3 FIG. 4 is a flow chart showing a target correlation function determination process provided by an embodiment of the present invention; Figure 3 As shown, for determining the target correlation function, step S102 may include:

[0078] Step S301: based on the spherical shell defect information, obtaining a target length parameter corresponding to the target spherical shell; the target length parameter represents the range information corresponding to the target random field;

[0079] In a specific embodiment, the target length parameter c can be a correlation length, and the target length parameter can characterize the range information corresponding to the target random field, that is, the correlation length c can be used to represent the correlation range of the random field. The target length parameter can be pre-set or adaptively modified according to different simulated spherical shell data.

[0080] Step S302: Calculating target distance parameters based on the spherical shell geometry information;

[0081] In a specific embodiment, the target distance parameter g can be a geodesic distance, and the geodesic distance between any two points on the target spherical shell is the shortest arc length passing through the two points on the target spherical shell; a coordinate system can be established according to the radius r of the spherical shell and the thickness t of the spherical shell and the position of the center of the spherical shell can be determined, and then any two points on the target spherical shell can be determined, and the shortest arc length can be determined according to the coordinate values ​​of the any two points, thereby obtaining the geodesic distance, that is, the target distance parameter g.

[0082] Step S303: constructing the target correlation function based on the target length parameter and the target distance parameter.

[0083] In a specific embodiment, the target correlation function may be a correlation function corresponding to the initial defect of the target spherical shell, which may be represented by a Gaussian correlation function. The expression of the target correlation function R(g,c) may be:

[0084] R(g,c)=exp(-g 2 / c 2 )

[0085] Among them, g is the target distance parameter and c is the target length parameter.

[0086] Step S103: determining a correlation coefficient matrix corresponding to the spherical shell defect information based on the target correlation function, the representative discrete points and the spherical shell defect information;

[0087] In a specific embodiment, the correlation coefficient matrix may be the correlation coefficient between any two representative discrete points, and the correlation coefficient may be determined based on the target correlation function and the geodesic distance between any two representative discrete points. The correlation coefficient matrix R may be:

[0088]

[0089] Among them, R ij Represents a discrete point P i (x i ,y i ,z i ) and P j (x j ,y j ,z j ) is the correlation coefficient between them.

[0090] Specifically, Figure 4 The first flow chart corresponding to the correlation coefficient matrix provided in the embodiment of the present invention is as follows: Figure 4 As shown, for determining the correlation coefficient matrix, step S103 may include:

[0091] Step S401: performing probability distribution type judgment on the spherical shell defect information to obtain a type judgment result;

[0092] In a specific embodiment, the spherical shell defect information can characterize the initial defects of the target spherical shell. The initial defects can be the geometric shape of the target spherical shell (the geometric shape is the distance that the actual position of the target spherical shell deviates from the ideal position of the target spherical shell), the elastic modulus of the target spherical shell, and the spherical shell thickness of the target spherical shell, etc.

[0093] The initial defects of the target spherical shell may include probability distribution type, mean, standard deviation, target correlation function and correlation length, etc., which can generally be determined by consulting literature and existing research. The spherical shell defect information of the target spherical shell can be determined after constructing the target spherical shell.

[0094] In an embodiment of the present invention, the spherical shell defect information may be a geometrical defect of the target spherical shell, where the geometrical defect means that due to manufacturing process errors, the actual radius r′ at different positions of the spherical shell deviates from the theoretical radius r, and the deviation difference Δr is a random field. According to references, the mean μ of the deviation difference Δr is 0 and the standard deviation σ is 2.

[0095] In a specific embodiment, the probability distribution type of spherical shell defect information may include at least normal distribution and lognormal distribution; since different probability distribution types correspond to different correlation coefficient determination methods, before calculating the correlation coefficient between any two representative discrete points, it is necessary to first determine the probability distribution type included in the spherical shell defect information.

[0096] Step S402: when the type judgment result indicates that the spherical shell defect information corresponds to a normal distribution, based on the target correlation function, sequentially calculating a first correlation coefficient between any two representative discrete points among a plurality of representative discrete points;

[0097] In a specific embodiment, when the type judgment result indicates that the probability distribution type corresponding to the spherical shell defect information is a normal distribution, the target correlation function can be used to determine the correlation coefficient; the correlation coefficient determined using the target correlation function is the first correlation coefficient. The first correlation coefficient and the second correlation coefficient are used to represent the correlation coefficients corresponding to different probability distributions, rather than distinguishing the correlation coefficients in order or in any other sense.

[0098] Specifically, the target correlation function is used to determine any two representative discrete points (x i ,y i ,z i ) and (x j ,y j ,z j ) The first correlation coefficient corresponding to can be:

[0099] R ij =exp(-g ij 2 / c 2 ),i=1,2…,n;j=1,2,…n

[0100] Among them, the geodesic distance g between any two discrete points ij for:

[0101] g ij = r * arccos[(x i x j +y i y j +z i z j ) / r 2 ]

[0102] Step S403: constructing the correlation coefficient matrix based on the first correlation coefficients corresponding to the multiple representative discrete points.

[0103] Specifically, after determining the first correlation coefficients corresponding to any two representative discrete points among the plurality of representative discrete points, a correlation coefficient matrix is ​​constructed based on the plurality of first correlation coefficients.

[0104] In another specific embodiment, the probability distribution type corresponding to the spherical shell defect information may also be a log-normal distribution; Figure 5 The second flow chart corresponding to the correlation coefficient matrix provided in the embodiment of the present invention is as follows: Figure 5 As shown, when the type judgment result indicates that the probability distribution type corresponding to the spherical shell defect information is a log-normal distribution, the method further includes:

[0105] Step S501: when the type judgment result indicates that the spherical shell defect information corresponds to a logarithmic normal distribution, determining a correlation coefficient calculation formula based on the target correlation function;

[0106] In a specific embodiment, when the probability distribution type in the spherical shell defect information corresponds to the logarithmic normal distribution, it is necessary to first determine the correlation coefficient calculation formula; specifically, the correlation coefficient calculation formula can be determined based on the target correlation function, and the correlation coefficient calculation formula R(g,c) can be:

[0107]

[0108] Wherein δ is the coefficient of variation, which can be determined based on the standard deviation and mean corresponding to the spherical shell defect information. Specifically, δ=standard deviation:mean.

[0109] Step S502: based on the correlation coefficient calculation formula, sequentially calculating a second correlation coefficient between any two representative discrete points among the plurality of representative discrete points;

[0110] Step S503: constructing the correlation coefficient matrix based on the second correlation coefficients corresponding to the plurality of representative discrete points.

[0111] Specifically, the correlation coefficient determined using the correlation coefficient calculation formula is the second correlation coefficient, and the second correlation coefficient is the correlation coefficient between any two representative discrete points among the multiple representative discrete points. After the second correlation coefficient is obtained, a correlation coefficient matrix is ​​constructed based on the second correlation coefficient.

[0112] Step S104: performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field;

[0113] In a specific embodiment, for the correlation coefficient matrix R, there may be a matrix calculation formula:

[0114] R=Ψ T ΛΨ

[0115] Λ=diag(λ1,λ2,…,λn )

[0116]

[0117] Where: Λ is the eigenvalue matrix, Ψ is the eigenvector matrix, T is the transposed matrix of the eigenvector matrix; i (i=1,2,..,n) are the eigenvalues ​​arranged from large to small, is the eigenvalue corresponding to i The eigenvector of is a vector with n rows and 1 column.

[0118] Specifically, Figure 6 A schematic diagram of a process flow for determining a standard random field according to an embodiment of the present invention; Figure 6 As shown, step S104 may include:

[0119] Step S601: performing eigenvalue decomposition on the correlation coefficient matrix to obtain an eigenvalue matrix and an eigenvector matrix corresponding to the correlation coefficient matrix;

[0120] In a specific embodiment, the correlation coefficient matrix R is subjected to eigenvalue decomposition using the above-mentioned matrix calculation formula to obtain an eigenvalue matrix and an eigenvector matrix corresponding to the correlation coefficient matrix; wherein the eigenvector matrix may include a first eigenvector matrix and a second eigenvector matrix, and the second eigenvector matrix is ​​a transposed matrix of the first eigenvector matrix.

[0121] Step S602: determining the target number of the random variables based on the reconstruction threshold calculation formula and the reconstruction threshold parameter; the target number of the random variables is less than the number of the representative discrete points;

[0122] In a specific embodiment, there is a reconstruction threshold calculation formula:

[0123]

[0124] Where n represents the total number of discrete points, n' is the target number of random variables required, and β is the reconstruction threshold parameter; where n' is the minimum value that makes the reconstruction threshold calculation formula valid; set the reconstruction threshold parameter to 95%, substitute β = 95% into the reconstruction threshold calculation formula, and solve for the target number of random variables corresponding to n'. Using the reconstruction threshold β = 95% can reduce the number of random variables required, thereby improving the efficiency of random field construction.

[0125] Step S603: Determine a target eigenvalue matrix, a target eigenvector matrix, and a target random vector parameter based on the target number of the random variables, the eigenvalue matrix, and the eigenvector matrix;

[0126] In a specific embodiment, the target number of random variables required is substituted into the eigenvalue matrix and the eigenvector matrix respectively to determine the target eigenvalue matrix, the target eigenvector matrix and the target random vector parameter. n′ is a diagonal matrix consisting of the previous target number of eigenvalues, and the target eigenvector matrix Ψ n′ is a matrix composed of the first target number of eigenvectors in the eigenvector matrix. The target random vector parameter u is a column vector that obeys the standard normal distribution and has a dimension of target number × 1, that is, n′×1.

[0127] Step S604: construct the standard random field based on the target eigenvalue matrix, the target eigenvector matrix and the target vector parameters.

[0128] In a specific embodiment, the standard random field Y0 can be based on the target eigenvalue matrix Λ n′ 、Target eigenvector matrix Ψ n′ and the target vector parameter u, which can be specifically:

[0129]

[0130] The standard random field Y0 is a vector with n rows and 1 column, and corresponds one-to-one to the n representative discrete points of the target spherical shell. The random field value is assigned to the corresponding node or integral point in the finite element model according to the discrete point number, so that the finite element model considering the random field can be generated. By repeatedly generating the column vector of the standard normal distribution, different standard normal distribution random fields can be obtained.

[0131] It should be noted that no matter the probability distribution type corresponding to the spherical shell defect information is normal distribution or log-normal distribution, the above steps S601 to S604 can be used to determine the standard random field.

[0132] Step S105: Based on the random field transformation formula, the standard random field is transformed to obtain a target random field corresponding to the spherical shell defect information.

[0133] In a specific embodiment, the random field transformation formula includes a first random field transformation formula and a second random field transformation formula, and the corresponding transformation formula can be determined based on the probability distribution type corresponding to the spherical shell defect information to generate a target random field corresponding to the target spherical shell. The probability distribution type corresponding to the first random field transformation formula is normal distribution, and the probability distribution type corresponding to the second random field transformation formula is lognormal distribution.

[0134] Specifically, Figure 7 A schematic diagram of a corresponding process for determining a target random field provided in an embodiment of the present invention; Figure 7 As shown, step S105 may include:

[0135] Step S701: Obtain the mean and standard deviation corresponding to the spherical shell defect information;

[0136] Step S702: inputting the mean, the standard deviation and the standard random field into the random field transformation formula to obtain the target random field.

[0137] In a specific embodiment, when the probability distribution type is normal distribution, it is necessary to use the first random field transformation formula to determine the target random field Y. The first random field transformation formula is:

[0138] Y=μ+σY0

[0139] In another specific embodiment, when the probability distribution type is lognormal distribution, it is necessary to use the second random field transformation formula to determine the target random field Z. The second random field transformation formula is:

[0140] Z=F -1 {Φ[Y0]}

[0141] in,

[0142] In the formula, F -1 {} represents the inverse function of the lognormal cumulative distribution function, and Φ[] represents the cumulative distribution function of the standard normal distribution function.

[0143] Figure 8-Figure 13 The following is an example of the initial defect random field implementation of the spherical shell normal distribution and logarithmic normal distribution corresponding to the specific embodiment of the present invention. Each case contains three groups of different correlation lengths, and each correlation length includes two random sample implementations. Figure 8-Figure 13 , the random field modeling method for quantifying the initial defects of the spherical shell structure of the present invention is described using normal distribution and lognormal distribution as specific embodiments.

[0144] Embodiment 1: The probability distribution type of the spherical shell defect information corresponding to the target spherical shell is normal distribution;

[0145] Figure 8-Figure 10 For the same probability distribution type (all normal distribution), the same mean and standard deviation, and different correlation lengths c, the random field implementation examples corresponding to the spherical shell, the numerical units can correspond to mm; Figure 8 The correlation length c can be 100, Fig. 9 The correlation length c can be 200, Fig.10 The correlation length c can be 400, and Figure 8-Figure 10 The mean is 0 and the standard deviation is 2; Figure 8-Figure 10 It can be seen that different correlation lengths have different effects on the random field corresponding to the spherical shell; please refer to Figure 8-Figure 10 The random field modeling method for quantifying the initial defects of a spherical shell structure as a normal distribution provided by an embodiment of the present invention comprises the following steps:

[0146] Step 1: Determine the geometric information and material information of the spherical shell to be simulated; taking a manned submersible pressure shell as an example, through literature research, the radius of the spherical shell is r = 1050mm, the thickness is t = 21mm, the material is 980 steel, and the elastic modulus is 2×105MPa.

[0147] Step 2: Determine the initial defect type of the spherical shell to be simulated; the initial defect type can be determined as a geometric shape initial defect, where the geometric shape means that due to the manufacturing process error, the actual radius r′ at different positions of the spherical shell will deviate from the theoretical radius r, and the deviation difference Δr is a random field. According to the reference, the mean μ of the deviation difference Δr is 0 and the standard deviation σ is 2; the related function type is Gaussian, expressed as:

[0148] R(g,c)=exp(-g 2 / c 2 )

[0149] Here, the relevant length c can be set to 200 mm.

[0150] Step 3: Determine the representative discrete points of the spherical shell; using ABAQUS finite element analysis software as a platform, establish a finite element model of the spherical shell to be simulated, divide the model into triangular grids, and the grid size is about 50 mm. The discretized model contains 5722 nodes and 11440 units. The defect type is geometric shape defect, and the nodes are selected as representative discrete points.

[0151] Step 4: Determine the correlation coefficient matrix; there are 5722 discrete points, and any two points (x i ,y i ,z i ) and (x j ,y j ,z j ) ij for:

[0152] R ij =exp(-g ij 2 / c 2 ),i=1,2…,n;j=1,2,…n

[0153] Where n = 5722; the geodesic distance g between any two discrete points ij for:

[0154] g ij = r * arccos[(x i xj +y i y j +z i z j ) / r 2 ]

[0155] The correlation coefficient matrix is ​​a (5722×5722) logarithmic matrix, specifically:

[0156]

[0157] Step 5: Perform eigenvalue decomposition based on the correlation coefficient matrix to generate the standard normal distribution random field corresponding to the spherical shell.

[0158] Perform eigenvalue decomposition on the correlation coefficient matrix R, and obtain the corresponding eigenvalue matrix: Λ=diag(λ1,λ2,…,λ n );where: i (i=1,2,..,n) are the eigenvalues ​​arranged from large to small; the eigenvector matrix is: Where: is the eigenvalue corresponding to i The eigenvector of is a vector with n rows and 1 column.

[0159] Determine the reconstruction threshold β = 95%, and for the case of c = 200 mm, the following equation holds true:

[0160]

[0161] The minimum n′ value is 331. Then the standard normal random field of the initial defect of the spherical shell is determined as:

[0162]

[0163] In the formula, Λ n′ is the diagonal matrix consisting of the first 331 eigenvalues ​​of Λ, Ψ n′ is a matrix consisting of the first 331 eigenvectors of Ψ, u is a random column vector that obeys the standard normal distribution, and its dimension is 331×1.

[0164] Step 6: Transform the standard normal distribution random field generated in step 5 to generate the target distribution random field of the initial defect. The geometric shape random field is based on Δr = μ + σY0 = 2Y0.

[0165] Embodiment 2: The probability distribution type of the spherical shell defect information corresponding to the target spherical shell is a log-normal distribution;

[0166] Figure 11-13For the same probability distribution type (all lognormal distribution), the same mean and standard deviation, and different correlation lengths c, the random field implementation examples corresponding to the spherical shell, the numerical units can correspond to MPa; Fig.11 The relevant length c can be 100 mm, Fig.12 The relevant length c can be 200mm, Fig.13 The relevant length c may be 400 mm, and Figure 11-13 The mean is 200000 and the standard deviation is 10000; Figure 11-13 It can be seen that different correlation lengths have different effects on the random field corresponding to the spherical shell; please refer to Figure 11-13 The random field modeling method for quantifying the initial defects of a spherical shell structure as a normal distribution provided by an embodiment of the present invention comprises the following steps:

[0167] Step 1: Determine the geometric information and material information of the spherical shell to be simulated. Taking a manned submersible pressure shell as an example, through literature research, the radius of the spherical shell is r = 1050 mm, the thickness is t = 21 mm, the material is 980 steel, and the elastic modulus is 2×10 5 MPa.

[0168] Step 2: Determine the initial defect type of the spherical shell. The initial defect type can be determined as the elastic modulus initial defect of the material. The elastic modulus E can be a random field of logarithmic normal distribution, and the mean value can be μ = 2 × 10 5 MPa, the standard deviation can be σ=1×10 4 MPa, the coefficient of variation can be δ=0.05, the correlation function type is Gaussian, and the expression is:

[0169] R(g,c)=exp(-g 2 / c 2 )

[0170] Here, the relevant length c can be set to 100 mm.

[0171] Step 3: Determine the representative discrete points of the spherical shell, and use ABAQUS finite element analysis software as the platform to establish a finite element model of the spherical shell. The model is divided into triangular grids with a grid size of approximately 50 mm. The discretized model contains 5722 nodes and 11440 units. The defect type is elastic modulus, and the unit integration points are selected as representative discrete points.

[0172] Step 4: Determine the correlation coefficient matrix. There are 11440 discrete points in total. Any two points (x i ,y i ,z i ) and (x j ,y j ,z j) ij for:

[0173]

[0174] In the formula, the geodesic distance g between any two discrete points is ij for:

[0175] g ij = r * arccos[(x i x j +y i y j +z i z j ) / r 2 ]

[0176] The correlation coefficient matrix is ​​a (11440×11440) logarithmic matrix, specifically:

[0177]

[0178] Step 5: Perform eigenvalue decomposition on the correlation coefficient matrix to generate a standard normal distribution random field.

[0179] Perform eigenvalue decomposition on the correlation coefficient matrix R, and obtain the corresponding eigenvalue matrix: Λ=diag(λ1,λ2,…,λ n );where: i (i=1,2,..,n) are the eigenvalues ​​arranged from large to small; the eigenvector matrix is: Where: is the eigenvalue corresponding to i The eigenvector of is a vector with n rows and 1 column.

[0180] Determine the reconstruction threshold β = 95%, and for the case of c = 100 mm, the following equation holds true:

[0181]

[0182] The minimum n′ value is 1309. Then the standard normal random field of the initial defect of the spherical shell is determined as:

[0183]

[0184] In the formula, Λ n′ is the diagonal matrix consisting of the first 1309 eigenvalues ​​of Λ, Ψ n′ is a matrix consisting of the first 1309 eigenvectors of Ψ, u is a random column vector that obeys the standard normal distribution, and its dimension is 1309×1.

[0185] Step 6: Transform the standard normal distribution random field generated in step 5 to generate the target distribution random field of the initial defect, that is, the logarithmic normal distribution random field of the initial defect of the elastic modulus:

[0186] Z=F -1 {Φ[Y0]}

[0187] in,

[0188] In the formula, F -1 {} represents the inverse function of the lognormal cumulative distribution function, and Φ[] represents the cumulative distribution function of the standard normal distribution function.

[0189] Compared with the prior art, the technical solution disclosed in the present invention has the following beneficial effects:

[0190] 1. By introducing the geodesic distance, the spherical shell random field is established based on the eigenvalue decomposition method, which can accurately quantify the intrinsic correlation of the initial defects of the spherical shell;

[0191] 2. By setting the reconstruction threshold, the eigenvalues ​​to be retained can be selected according to the actual situation, thereby greatly reducing the number of random variables used in the numerical simulation of random fields;

[0192] 3. Generating a non-normal distribution random field directly through equal probability transformation will change the correlation function of the random field. The present invention can directly realize the simulation of the log-normal random field by transforming the form of the correlation function in combination with the change of the cumulative distribution function, and keep the probability distribution and the correlation function consistent with the target.

[0193] The embodiment of the present invention also provides a random field modeling device for quantifying the initial defects of a spherical shell structure, such as Fig.14 As shown, the device comprises:

[0194] The simulation information acquisition module 1410 is used to acquire simulated spherical shell data for constructing a target spherical shell; the simulated spherical shell data includes spherical shell geometry information, spherical shell material information and spherical shell defect information;

[0195] A spherical shell parameter determination module 1420 is used to determine a target correlation function and a representative discrete point corresponding to the spherical shell defect information based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information;

[0196] A correlation matrix determination module 1430 is used to determine a correlation coefficient matrix corresponding to the spherical shell defect information based on the target correlation function, the representative discrete points and the spherical shell defect information;

[0197] An eigenvalue decomposition module 1440 is used to perform eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field;

[0198] The random field determination module 1450 is used to perform random field transformation on the standard random field based on the random field transformation formula to obtain the target random field corresponding to the spherical shell defect information.

[0199] In some other embodiments, the spherical shell parameter determination module 1420 further includes:

[0200] A first parameter determination module is used to obtain a target length parameter corresponding to the target spherical shell based on the spherical shell defect information; the target length parameter represents the range information corresponding to the target random field;

[0201] A second parameter determination module, used for calculating a target distance parameter based on the spherical shell geometry information;

[0202] A correlation function determination module is used to construct the target correlation function based on the target length parameter and the target distance parameter.

[0203] In some other embodiments, the spherical shell parameter determination module 1420 further includes:

[0204] A spherical shell modeling processing module, used for performing modeling processing based on the spherical shell geometric information and the spherical shell material information to obtain the target spherical shell;

[0205] The discrete point determination module is used to perform grid division on the target spherical shell to obtain the representative discrete points.

[0206] In some other embodiments, the correlation matrix determination module 1430 further includes:

[0207] A distribution type judgment module is used to perform probability distribution type judgment on the spherical shell defect information to obtain a type judgment result;

[0208] A first coefficient determination module is used to sequentially calculate a first correlation coefficient between any two representative discrete points among a plurality of representative discrete points based on the target correlation function when the type judgment result indicates that the spherical shell defect information corresponds to a normal distribution;

[0209] The first matrix construction module is used to construct the correlation coefficient matrix based on the first correlation coefficients corresponding to the multiple representative discrete points.

[0210] In some other embodiments, the device further comprises:

[0211] A formula determination module, used to determine a correlation coefficient calculation formula based on the target correlation function when the type judgment result indicates that the spherical shell defect information corresponds to a logarithmic normal distribution;

[0212] A second coefficient determination module, configured to sequentially calculate a second correlation coefficient between any two representative discrete points among the plurality of representative discrete points based on the correlation coefficient calculation formula;

[0213] The second matrix construction module is used to construct the correlation coefficient matrix based on the second correlation coefficients corresponding to the multiple representative discrete points.

[0214] In some other embodiments, the eigenvalue decomposition module 1440 further includes:

[0215] A matrix determination module, used for performing eigenvalue decomposition on the correlation coefficient matrix to obtain an eigenvalue matrix and an eigenvector matrix corresponding to the correlation coefficient matrix;

[0216] A random variable quantity determination module, used to determine a target quantity of random variables based on a reconstruction threshold calculation formula and a reconstruction threshold parameter; the target quantity of random variables is less than the quantity of representative discrete points;

[0217] A third parameter determination module is used to determine a target eigenvalue matrix, a target eigenvector matrix and a target random vector parameter based on the target number of random variables, the eigenvalue matrix and the eigenvector matrix;

[0218] The first random field construction module is used to construct the standard random field based on the target eigenvalue matrix, the target eigenvector matrix and the target random vector parameter.

[0219] In some other embodiments, the random field determination module 1450 further includes:

[0220] A numerical determination module is used to obtain the mean and standard deviation corresponding to the spherical shell defect information;

[0221] The second random field construction module is used to input the mean, the standard deviation and the standard random field into the random field transformation formula to obtain the target random field.

[0222] The device and method embodiments in the device embodiment are based on the same inventive concept and are used to implement the above-mentioned random field modeling method for quantifying the initial defects of the spherical shell structure.

[0223] An embodiment of the present invention also provides an electronic device, comprising: a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by the processor to implement a random field modeling method for quantifying initial defects of a spherical shell structure as described in any one of the method embodiments.

[0224] An embodiment of the present invention also provides a storage medium, which can be set in a server to store at least one instruction, at least one program, code set or instruction set used to implement the above-mentioned method embodiments. The at least one instruction, the at least one program, the code set or instruction set is loaded and executed by the processor to implement the random field modeling method for quantifying the initial defects of the spherical shell structure as described in any of the method embodiments.

[0225] The above-mentioned computer-readable storage medium can be a tangible device that can keep and store the instructions used by the instruction execution device. The computer-readable storage medium can be, for example, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device or any suitable combination thereof. A more specific example (non-exhaustive list) of a computer-readable storage medium includes: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, for example, a punch card or a convex structure in a groove on which instructions are stored, and any suitable combination thereof. The computer-readable storage medium used here is not interpreted as a transient signal itself, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagated by a waveguide or other transmission medium (for example, a light pulse by an optical fiber cable), or an electrical signal transmitted by a wire.

[0226] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0227] The computer program instructions for performing the operation of the present disclosure may include assembly instructions, instruction set architecture instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C+, etc., and conventional procedural programming languages ​​such as "C" language or similar programming languages. Computer-readable program instructions can be executed entirely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (e.g., using an Internet service provider to connect through the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA) or a programmable logic array (PLA) is personalized by using the state information of the computer-readable program instructions, and the electronic circuit can execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0228] It can be seen from the embodiments provided by the present invention that, in the present invention, the target correlation function and the representative discrete points are determined according to the simulated spherical shell data corresponding to the target spherical shell, wherein the target distance parameters involved in the target correlation function are determined based on the specific simulated spherical shell data, and the correlation coefficient matrix is ​​determined according to the target correlation function and the representative discrete points, and then the correlation coefficient matrix is ​​subjected to eigenvalue decomposition, which can accurately quantify the intrinsic correlation of the initial defects of the target spherical shell; at the same time, for different initial probability distribution types, different random field transformation formulas are used, which can ensure the correlation and matching degree between the random field and the spherical shell defects, thereby improving the accuracy of quantification of the initial defects of the spherical shell, and then improving the reliability of the performance analysis of the spherical shell.

[0229] It should be noted that various embodiments of the present disclosure have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The choice of terms used in this article is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A random field modeling method for quantifying the initial defects of spherical shell structures, characterized in that: The method comprises: Determining simulated spherical shell data for constructing a target spherical shell; the simulated spherical shell data includes spherical shell geometry information, spherical shell material information, and spherical shell defect information; Based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information, determining a target correlation function and a representative discrete point corresponding to the spherical shell defect information; Determine a correlation coefficient matrix corresponding to the spherical shell defect information based on the target correlation function, the representative discrete points and the spherical shell defect information; Performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field; Based on the random field transformation formula, the standard random field is transformed to obtain the target random field corresponding to the spherical shell defect information.

2. A random field modeling method for quantifying initial defects of spherical shell structures according to claim 1, characterized in that: The determining, based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information, a target correlation function and a representative discrete point corresponding to the spherical shell defect information comprises: Based on the spherical shell geometry information and the spherical shell material information, modeling processing is performed to obtain the target spherical shell; The target spherical shell is meshed to obtain the representative discrete points.

3. A random field modeling method for quantifying initial defects of a spherical shell structure according to claim 2, characterized in that: The determining, based on the spherical shell geometry information, the spherical shell material information, and the spherical shell defect information, a target correlation function and a representative discrete point corresponding to the target spherical shell comprises: Based on the spherical shell defect information, a target length parameter corresponding to the target spherical shell is obtained; the target length parameter represents the range information corresponding to the target random field; Calculating target distance parameters based on the spherical shell geometry information; The target correlation function is constructed based on the target length parameter and the target distance parameter.

4. A random field modeling method for quantifying initial defects of a spherical shell structure according to claim 1, characterized in that: The number of the discrete points is multiple; The step of determining a correlation coefficient matrix based on the target correlation function, the representative discrete points and the spherical shell defect information includes: Performing probability distribution type judgment on the spherical shell defect information to obtain a type judgment result; When the type judgment result indicates that the spherical shell defect information corresponds to a normal distribution, based on the target correlation function, sequentially calculating a first correlation coefficient between any two representative discrete points among the plurality of representative discrete points; The correlation coefficient matrix is ​​constructed based on the first correlation coefficients corresponding to the multiple representative discrete points.

5. A random field modeling method for quantifying initial defects of a spherical shell structure according to claim 4, characterized in that: The method further comprises: In the case where the type judgment result indicates that the spherical shell defect information corresponds to a logarithmic normal distribution, determining a correlation coefficient calculation formula based on the target correlation function; Based on the correlation coefficient calculation formula, sequentially calculating a second correlation coefficient between any two representative discrete points among the plurality of representative discrete points; The correlation coefficient matrix is ​​constructed based on the second correlation coefficients corresponding to the multiple representative discrete points.

6. A random field modeling method for quantifying initial defects of spherical shell structures according to claim 1, characterized in that: The step of performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field includes: Performing eigenvalue decomposition on the correlation coefficient matrix to obtain an eigenvalue matrix and an eigenvector matrix corresponding to the correlation coefficient matrix; Determining a target number of random variables based on a reconstruction threshold calculation formula and a reconstruction threshold parameter; the target number of random variables is less than the number of representative discrete points; Determine a target eigenvalue matrix, a target eigenvector matrix, and a target random vector parameter based on the target number of random variables, the eigenvalue matrix, and the eigenvector matrix; The standard random field is constructed based on the target eigenvalue matrix, the target eigenvector matrix and the target random vector parameters.

7. A random field modeling method for quantifying initial defects of a spherical shell structure according to claim 1, characterized in that: The method of performing random field transformation on the standard random field based on the random field transformation formula to obtain the target random field corresponding to the target spherical shell includes: Obtain the mean and standard deviation corresponding to the spherical shell defect information; The mean, the standard deviation and the standard random field are input into the random field transformation formula to obtain the target random field.

8. A random field modeling device for quantifying the initial defects of a spherical shell structure, characterized in that: The device comprises: A simulation information acquisition module, used to acquire simulated spherical shell data for constructing a target spherical shell; the simulated spherical shell data includes spherical shell geometry information, spherical shell material information and spherical shell defect information; A spherical shell parameter determination module, used to determine a target correlation function and a representative discrete point corresponding to the spherical shell defect information based on the spherical shell geometry information, the spherical shell material information and the spherical shell defect information; A correlation coefficient matrix determination module, used to determine the correlation coefficient matrix corresponding to the spherical shell defect information based on the target correlation function, the representative discrete points and the spherical shell defect information; An eigenvalue decomposition module, used for performing eigenvalue decomposition on the correlation coefficient matrix to obtain a standard random field; The random field determination module is used to perform random field transformation on the standard random field based on the random field transformation formula to obtain the target random field corresponding to the spherical shell defect information.

9. An electronic device, comprising a processor and a memory, wherein the memory stores at least one instruction and at least one program, and the at least one instruction and the at least one program are loaded and executed by the processor to implement the random field modeling method for quantifying the initial defects of a spherical shell structure as described in any one of claims 1 to 7.

10. A computer storage medium, wherein at least one instruction and at least one program are stored in the computer storage medium, wherein the at least one instruction and the at least one program are loaded and executed by a processor to implement the random field modeling method for quantifying initial defects of a spherical shell structure as described in any one of claims 1 to 7.

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