A structural reliability prediction method and device based on adaptive grid

Abstract

The present invention discloses a structural reliability prediction method, device, medium and product based on adaptive grid, which relates to the field of structural reliability analysis. The method comprises applying an adaptive grid algorithm to grid a k-dimensional hyper-rectangular space corresponding to an input variable, determining the type of grid unit according to the functional function value of the grid node divided, and determining the reliability of the structure to be predicted according to the type of grid unit and the reliability of the grid unit. The present invention improves the efficiency and accuracy of reliability prediction by applying an adaptive grid algorithm.

Description

Technical Field

[0001] The invention relates to the field of structural reliability analysis, and in particular to a structural reliability prediction method and device based on an adaptive grid. Background Art

[0002] Since the action and resistance of engineering structures and systems are naturally random, there is a probability of failure. Generally speaking, the failure probability of a structure or system is within 10 -7 to 10 3 At the order of magnitude, how to fully and effectively estimate the failure probability, there are currently two main methods: one is the probability analysis model based on probability theory, and the other is the Monte Carlo simulation based on mathematical statistics methods.

[0003] The probability analysis model uses a mechanics-based probability model to predict the failure probability. The model parameters are given by mechanical analysis or by optimizing the test data. Therefore, the probability analysis model can give a complete reliability distribution for simple structures and systems.

[0004] Monte Carlo simulation based on mathematical statistics is the mainstream method of reliability analysis because it can deal with complex structures and systems, but it has a high computational cost. In order to balance the computational cost and evaluation accuracy, there are generally four directions: improved sampling method, reliability approximation, alternative model and search algorithm. Improved sampling method can significantly reduce the number of samples, but with the reduction of samples, the error is further enlarged, especially when the curvature of the limit-state surface (LSS) is large; in the direction of reliability approximation, there are many methods based on design points, such as the first-order reliability method (FORM) widely used in engineering, the second-order reliability method (SORM), and other methods using multiple design points and high-order moments. However, when the LSS deviates significantly from the assumed functional form, the design point-based method may not provide an accurate answer; in the alternative model-based method, the original performance function (PF) is replaced by some models with lower computational costs. However, like the reliability approximation method, if the PF on LLS has nonlinearity and large curvature, it will also produce large errors.

[0005] Compared with the above three methods, the search algorithm can improve the effectiveness and accuracy of such nonlinear and large curvature conditions. The search algorithm is usually composed of a search algorithm and a sampling method, which can reduce redundant sampling and improve accuracy, and has better compatibility and stability. However, the current search algorithms either ignore the input space to a large extent, or use a large amount of sampling costs to access the entire input space. These two shortcomings directly lead to errors in reliability estimation and high computational costs. Summary of the invention

[0006] The purpose of the present invention is to provide a method and device for predicting structural reliability based on an adaptive grid, which can improve the efficiency and accuracy of reliability prediction.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A structural reliability prediction method based on adaptive grid, the method comprising:

[0009] The reliability influencing variables of the structure to be predicted are converted into standard Gaussian variables through Nataf transformation;

[0010] An adaptive grid algorithm is applied to the k-dimensional hyper-rectangular space corresponding to the standard Gaussian variable to perform grid division, the type of grid unit is determined according to the functional function value of the divided grid node, and the reliability of the structure to be predicted is determined according to the type of grid unit and the reliability of the grid unit; the k-dimensional hyper-rectangular space is a space composed of the value intervals of k standard Gaussian variables; the functional function value of the divided grid node is determined according to the variable value and the functional function corresponding to the node; the functional function is used to describe the relationship between the performance index of the structure to be measured and the reliability influencing variable.

[0011] A computer device comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of any one of the above-mentioned methods for predicting structural reliability based on an adaptive grid.

[0012] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of any one of the above-mentioned methods for predicting structural reliability based on an adaptive grid.

[0013] A computer program product comprises a computer program, wherein when the computer program is executed by a processor, the computer program implements the steps of any one of the above-mentioned methods for predicting structural reliability based on an adaptive grid.

[0014] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0015] The present invention provides a structural reliability prediction method and device based on an adaptive grid, which applies an adaptive grid algorithm supervised by reliability error, traverses the entire input space (a hyper-rectangular space formed by the value range of reliability influencing variables), and efficiently completes reliability analysis on the premise of traversing the entire input space, and ensures the accuracy of reliability prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments 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.

[0017] Figure 1 A schematic diagram of a flow chart of a structural reliability prediction method based on an adaptive grid provided in Embodiment 1 of the present invention;

[0018] Figure 2 A schematic diagram of a two-dimensional super-rectangular space and a two-dimensional super-rectangular space grid division and a grid tree structure provided in Example 1 of the present invention;

[0019] Figure 3 A schematic diagram of omnidirectional two-division of a grid provided in Example 1 of the present invention;

[0020] Figure 4 A schematic diagram of a three-dimensional prediction sample set provided in Embodiment 1 of the present invention;

[0021] Figure 5 A schematic diagram of an adaptive grid for reliability error control of Example 1 provided in Embodiment 1 of the present invention;

[0022] Figure 6 A structural diagram of the mooring structure and a force diagram of the mooring structure provided in Example 1 of the present invention;

[0023] Figure 7 A schematic diagram of horizontal plane probability distribution provided in Example 1 of the present invention;

[0024] Figure 8 A schematic diagram of a finite element model and analysis results provided in Example 1 of the present invention;

[0025] Fig. 9 A schematic diagram of an adaptive grid for reliability error control of Example 2 provided in Embodiment 1 of the present invention;

[0026] Fig.10 This is a diagram of the internal structure of a computer device. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] The purpose of the present invention is to provide a structural reliability prediction method and device based on an adaptive grid. In order to efficiently complete the reliability analysis under the premise of traversing the entire input space, a type of active learning algorithm based on an adaptive grid is proposed, namely, an adaptive grid algorithm with reliability error supervision. The search method of the algorithm adopts a breadth-first search algorithm to ensure the traversal of the input space. The sampling method is based on an adaptive grid of active learning to reduce the number of sampling times, reduce the computational cost of reliability estimation, and improve the efficiency of reliability estimation. Since the entire input space composed of input variables is comprehensively searched, the accuracy of reliability calculation is improved.

[0029] Active learning is reflected in two aspects: the first is the pruning strategy, and the second is to use the existing vertex values ​​to predict the center point. If the vertices have the same sign, the center point is predicted to have the same sign, and the center point value is the average of the maximum and minimum values ​​of the vertices.

[0030] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] Example 1

[0032] like Figure 1 As shown, a structural reliability prediction method based on an adaptive grid in this embodiment includes:

[0033] S1: Convert the reliability influencing variables of the structure to be predicted into standard Gaussian variables through Nataf transformation.

[0034] In practical engineering applications, the original input variables of the project (i.e., the reliability influencing variables of the structure to be predicted) are generally converted into standard normal input variables through Natav transformation. Assume that the input x = [x1, x2, …, x k ] T In the joint cumulative distribution function Φ x The output under the action is G(x) (performance function, PF), where x e ∈[l e ,u e ], that is, the hyperrectangular space C k Its length of the e-th dimension is C e =u e-l e , =1,2,...,k.

[0035] The utility function of a structure can be defined as:

[0036] G = RS;

[0037] Among them, S is the effect caused by the action on the structure (cause of internal force and deformation of the structure, such as load, uneven settlement, temperature deformation, shrinkage deformation, earthquake and other random variables), such as bending moment M, axial force N, shear force V, torque T, deflection f, crack width w, etc.; R is the structural resistance, that is, the ability of the structure to resist the effect of the action, which is derived from the material properties (strength, deformation modulus, etc.) and geometric parameters (component size, etc.) through mechanical assumptions, such as the bending bearing capacity M u , shear bearing capacity V u , allowable deflection [f], allowable crack width [w], etc.

[0038] G>0 means the structure is safe and reliable, G<0 means the structure is unsafe and unreliable. Considering the randomness of R and S, the value of G is also random.

[0039] S2: Apply an adaptive grid algorithm to grid the k-dimensional hyper-rectangular space corresponding to the standard Gaussian variable, determine the type of grid unit according to the functional function value of the divided grid node, and determine the reliability of the structure to be predicted according to the type of grid unit and the reliability of the grid unit; the k-dimensional hyper-rectangular space is a space composed of the value intervals of k standard Gaussian variables; the functional function value of the divided grid node is determined according to the variable value and functional function corresponding to the node; the functional function is used to describe the relationship between the performance index of the structure to be measured and the reliability influencing variable.

[0040] By adaptively partitioning the security region (hyperrectangular space when G(x)>0, see Figure 2 The shaded part of (a) in the figure) and the failure domain (the hyperrectangular space when G(x)≤0, see Figure 2 The non-shaded part of (a) is used to calculate the hyperrectangular space C k The rows are divided from coarse inside and outside to fine edge, so as to effectively calculate the failure probability of the structure. Figure 2 The implementation of the algorithm in the 2-dimensional case is shown.

[0041] The core idea of ​​the method of the present invention is to divide the input hyperrectangular space into two layers in an omnidirectional manner (see Figure 3 ), generate the corresponding grid tree structure ( Figure 2(c) in the figure, in this process, active learning is used to predict the positive and negative values ​​of PF on the grid nodes, and the grid safety type judgment criteria are introduced to prune, skipping the generation of some unnecessary grids, and then traversing the grid tree structure through breadth-first search (i.e., visiting all grids from left to right from low to high level by level) to calculate the reliability. For convenience, the spatial grids generated in the process of hyper-rectangular space division are referred to as cells (also called grid cells) below. According to the positive and negative values ​​of PF on the grid nodes, the grid nodes are divided into positive points and negative points, and the values ​​of PF on the points are called the values ​​of the points; according to the positive and negative signs of all vertices of the unit, the units can be divided into positive units with all positive vertices, negative units with all negative vertices, and positive and negative mixed units. Therefore, the judgment of the unit type depends on the positive and negative values ​​of the unit vertices.

[0042] Specifically, step S2 includes:

[0043] (1) The level is initialized to 1, the total reliability is initialized to 0, and the total reliability error is initialized to 0. The k-dimensional hyperrectangular space (regarded as the first-level grid) is fully divided into two to obtain a second-level grid, and the functional function value of the node of each grid unit of the current level is determined; let the second-level grid be the current level.

[0044] For a k-dimensional hyperrectangular space C k In terms of its existence k vertices, and bisection is performed on each dimension to obtain 2 k sub-hyperrectangular spaces of the same dimension, when the rectangular space C k Perform an omnidirectional two-way division (see Figure 2 ), determine its 2 k The number of non-repeating vertices required for a sub-hyperrectangular space is In more detail, these vertices can be arranged in a hyperrectangular space C k The sub-hyperrectangular space C g (0≤g≤k) for classification (see Table 1), each vertex corresponds to the center point of the corresponding sub-hyperrectangular space, the rectangular space C k The sub-rectangular space C g The number n g As shown below:

[0045]

[0046] The number of these sub-rectangular spaces corresponds to the rectangular space C k The number of various vertices generated in a full-directional binary division process, taking three dimensions as an example: 1D represents the midpoint of a line, 2D represents the midpoint of a surface, and 3D represents the midpoint of a volume.

[0047] Table 1. Number of subspaces in k-dimensional rectangular space

[0048]

[0049] The first meshing requires points (for the hyperrectangular space C k All dimensions are binary space divided into 2 k Grids need Points (see Figure 3 ). For example, for a two-dimensional plane, 9 points are needed to fully divide its two dimensions, namely, 4 plane vertices (0-dimensional center points), 4 edge midpoints (1-dimensional center points), and 1 face midpoint (2-dimensional center point). The function value of each center point is determined according to the variable value corresponding to the point and the function function.

[0050] (2) Traverse the i-th grid unit of the current level and determine the type of the i-th grid unit according to the functional function value of the node of the i-th grid unit; i = 1, 2, ..., n M ;n M Indicates the total number of grid cells in the Mth level grid.

[0051] (3) When the type of the i-th grid unit is a positive unit or a negative unit, the reliabilities of all positive units and negative units that have been traversed in all levels are accumulated as the current total reliability; and i=i+1 is set, and the step of "traversing the i-th grid unit of the current level" is returned; the function function values ​​of each vertex of the positive unit are greater than 0; the function function values ​​of each vertex of the negative unit are less than 0.

[0052] Because the unit type is determined only based on the mesh vertices, the positive units and negative units are not necessarily safe units with all positive values ​​and failed units with all negative values ​​of the internal points. However, based on the basic situation that the safety domain is simply connected with a concentrated center and has a gentle curvature in actual engineering problems, it can be considered that the probability of positive units and negative units in actual engineering problems being not all positive or not all negative can be ignored. Therefore, during the execution of the algorithm, it is assumed that the units that only contain positive nodes and negative nodes are only positive units and negative units.

[0053] The reliability of the unit is calculated by the following formula:

[0054]

[0055] Among them, R E is the reliability of all units, and is Ω E is the domain of the unit (the space occupied by the unit), Ω s is the safety domain, and ∩ is the intersection operator. The reliability of the negative unit is 0, so the above calculation becomes:

[0056]

[0057] Among them, R SE is the reliability of the positive unit, Ω SE is the domain of positive units, is each reliability influencing variable x e The joint probability density function (1≤e≤k). When each reliability affects the variable x e When they are independent of each other, they can be further simplified to:

[0058]

[0059] Among them, u e and l e are the upper and lower bounds of the unit in the e-th dimension, respectively.

[0060] (4) When the type of the i-th grid unit is a positive-negative mixed unit, the reliabilities of all the positive-negative mixed units that have been traversed in the current level are accumulated as the total reliability error of the current level; the i-th grid unit is omnidirectionally divided into two to obtain the next level grid, and the functional function value of the node of each grid unit in the next level grid is determined; and i=i+1 is set, and the step of "traversing the i-th grid unit of the current level" is returned; the functional function value of each vertex of the positive-negative mixed unit includes a value greater than 0 and a value less than 0.

[0061] The generation of mesh depends on the generation of vertices, and the adaptation of mesh also depends on the prediction of vertices. The prediction of the physical or function results corresponding to the vertices is a necessary condition for adaptive mesh generation. k The sub-rectangular space C g For the center point of Figure 4 As shown) is the sub-rectangular space C g of 2 g A set of 0-dimensional points.

[0062] In the subsequent meshing process, it is not necessary to apply the variable value and function to each node with unknown function value to determine the function value. The function value of the node can also be predicted using the prediction standard, that is, the value of the center point (the mesh node with unknown function value after meshing) is predicted using the prediction standard with the value of the existing vertex and the positive and negative values ​​are recorded (see Figure 2 (b) in the figure). The prediction criterion is: the sub-hyperrectangular space C g The center point passes through the sub-hyperrectangular space C g vertices to make predictions (see Figure 4), if the vertices have the same sign, the predicted center point will have the same sign, and the center point value will be the average of the maximum and minimum values ​​of the vertices. If the vertices have different signs, the prediction criteria are not met, and it is necessary to further use the variable value of the point and the function function to calculate the value of the center point and record the positive and negative. In other words, when determining the function function value of the node of each grid unit in the next level grid, it can be determined according to the positive and negative function function value of the vertex of the corresponding previous level grid, specifically:

[0063] (1) If the functional values ​​of adjacent vertices of the previous level grid are all positive or negative, then the functional value of the prediction point between the adjacent vertices is positive or negative; the prediction point refers to the node with unknown functional value in the next level grid.

[0064] (2) If the functional values ​​of adjacent vertices of the previous level grid are not all positive or negative, the functional value of the prediction point between adjacent vertices is determined according to the value of the prediction point and the functional function.

[0065] The present invention applies a pruning strategy: positive and negative units do not participate in the grid division of the next layer, and the positive and negative mixed units continue to perform subsequent divisions. The positive and negative units that do not perform grid division are larger grids in the adaptive grid, and the positive and negative mixed units continue to generate fine grids in the adaptive grid after subsequent division, thereby reducing the number of sampling times.

[0066] (5) After all grid cells of the current level have been traversed, determine whether the total reliability error obtained by summing up the reliabilities of all positive and negative mixed cells in the current level is less than the error threshold.

[0067] (6) If not, set the next level grid as the current level and return to step “traversing the i-th grid unit of the current level”.

[0068] (7) If yes, then traverse each grid unit of the next level and determine the type of each grid unit according to the functional function value of the node of each grid unit.

[0069] (8) The difference reliability of the positive and negative mixed units and the reliability of the positive units in the next level are added to the total reliability output by the previous level to obtain the final reliability of the structure to be tested; the difference reliability of the positive and negative mixed units is determined based on the reliability and proportion coefficient of the positive and negative mixed units; the proportion coefficient is the proportion of the hypervolume of the safety domain to the hypervolume of the entire unit domain.

[0070] The calculation formula of the difference reliability of positive and negative mixed units (reliability of limit state units) is:

[0071]

[0072] Among them, V safeis the hypervolume of the safety domain of the positive and negative mixed units. The safety domain refers to the space where the functional function values ​​are all greater than zero; V LSE is the total hypervolume of the positive and negative mixed units; Ω LSE is the domain of the mixed positive and negative units.

[0073] The basic principle of the adaptive grid algorithm with reliability error supervision is based on the following two points:

[0074] 1. In the process of generating an M-layer tree structure by adaptive grid division in hyper-rectangular space, all positive units in the entire tree structure contain the reliability information of the structure, and the positive and negative mixed units of the Mth layer contain the calculation error information of the structural reliability.

[0075] 2. As the number of levels increases, the total domain of positive and negative mixed units in the Mth layer gradually decreases, that is, the error of effective reliability decreases layer by layer. For example, if there are a total of p positive units in the M-layer tree structure, then the calculated effective reliability of the structure is is the reliability of the i-th positive unit; there are q positive and negative mixed units in the M-th layer, and the maximum error of the reliability of the structure does not exceed And it decreases monotonically with the increase of M. is the reliability of the jth positive-negative mixed unit calculated as a positive unit.

[0076] Two examples are given below to illustrate the effectiveness and practical application of the method of the present invention.

[0077] Example 1:

[0078] The advantages of the proposed algorithm are verified by a two-dimensional highly nonlinear series system problem.

[0079]

[0080] Where x1 and x2 obey the standard normal distribution, and their value intervals are [-6,6] and [-4,4] respectively. The functional function of g in the input space and the nonlinearity of the limit state surface are as follows: Figure 5 To verify the accuracy and advantages of the algorithm, the maximum error of the adaptive grid algorithm for reliability error control is set to 0.001, and the grid tree level is set to 8 times. The failure probability of the structure is calculated by Monte Carlo sampling 10 8 Next, calculate Figure 5 The sampling results of the algorithm and the obtained safety domain are shown, and Table 2 shows the comparison of its corresponding reliability estimate with Monte Carlo sampling.

[0081] pass Figure 5 From Table 2, we can see that:

[0082] 1. Through the adaptive grid that is divided into two parts and subdivided layer by layer, the algorithm realizes the traversal of the entire input space;

[0083] 2. Through active learning to predict and prune the safety type judgment criteria of the grid, the algorithm greatly reduces the computational cost;

[0084] 3. The algorithm has a better effect while ensuring accuracy in the case where the security domain has a single connected center and a gentle curvature.

[0085] 4. Since the algorithm only uses the positive and negative judgment of the functional function to iterate, it avoids the influence of the nonlinearity of the functional function on the reliability estimation.

[0086] Table 2 Comparison of reliability estimation results

[0087]

[0088] Example 2:

[0089] The following demonstrates the application of the algorithm through the reliability estimation of a ship-berthing structure.

[0090] The mooring structure is mainly composed of a concrete foundation, a superstructure (not shown), a rubber fender and a steel pipe structure. Figure 6 Part (a) in the figure. Engineering practice shows that the steel tube structure is the most vulnerable structure, so this section estimates the reliability of the steel tube structure while ignoring the reliability of other parts. For conservative estimation, this structure can be simplified into a double-cantilever four-span simply supported continuous beam under the action of the mooring impact load and gravity. The longitudinal length, transverse outer radius and wall thickness of the steel tube are 18.0m, 1.0m and 24mm respectively. Since the rubber fender has a buffering effect, the mooring impact load can be equivalent to two static line loads evenly distributed from 2.5m below the river surface to 1m above the river surface through the principle of conservation of energy. By Figure 6 From part (b), we can see that when the water level is lower than 146.5m, the ship impact load will be redistributed evenly; if the water level is higher than 164.5m, the steel pipe will not bear the impact load. Therefore, the ship impact line load q can be expressed as follows:

[0091]

[0092] Where w is the river surface height, F is the equivalent ship impact load, and the effective length l of the ship impact line load can be expressed as:

[0093]

[0094] In the reliability estimation of steel pipe structure, its yield stress f yThe equivalent berthing impact load is considered as a log-normal distribution variable with a mean of 1442.0 KN and a variance of 48.1 KN. The river surface height is calculated according to the recorded data. Figure 7 The empirical cumulative distribution function is used to describe the structure. For safety reasons, if there is any plastic strain in the mooring structure, the structure is considered to have failed. Because the mooring impact line load is randomly distributed on the entire steel pipe and the failure mechanism is also variable, its function function may be highly nonlinear and the limit state surface may be complex. Therefore, a complete search of the entire input space is required to ensure sufficient accuracy.

[0095] In order to obtain the failure probability of the moored structure, the yield stress f of the steel pipe is y , the equivalent berthing impact load F and the river water surface height w are transformed into standard normal variables x1, x2 and x3 respectively. At the same time, the number of iterations of the algorithm is set to 5 and the reliability error is set to 1×10 -4 .

[0096] The two algorithms are implemented through MATLAB, and ABAQUS2020 is called by calling Python scripts to pass parameters for finite element analysis. The specific steps are as follows:

[0097] 1. Pass x1, x2 and x3 to the Python script when calling the function through the MATLAB program;

[0098] 2. Python modifies the input file of ABAQUS and guides it to perform finite element analysis;

[0099] 4. The MATLAB program obtains the negative value of the maximum plastic strain and uses it as the output of the function in step 1 to further calculate the reliability.

[0100] When modeling the steel pipe structure, the longitudinal unit size is set to 0.1m, the transverse radius size is set to 12mm, and the corresponding cross-sectional center angle is 5 degrees. Figure 8 Shows f y =212.65Mpa, F=1646.7KN and w=145.0m corresponding to the finite element model and its analysis results.

[0101] Fig. 9 The results of the reliability error supervised adaptive mesh algorithm when calculating 306 finite element analysis times are shown. As the entire input space is traversed, the probability of the docking component failure event caused by the docking event is estimated by the reliability error supervised adaptive mesh algorithm to be 2.46×10 -6The results show that the proposed algorithm is effective for engineering problems with highly nonlinear performance functions and complex limit state surfaces.

[0102] Example 2

[0103] A computer device comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a structural reliability prediction method based on an adaptive grid in Embodiment 1.

[0104] Example 3

[0105] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a structural reliability prediction method based on an adaptive grid in embodiment 1.

[0106] Example 4

[0107] A computer program product includes a computer program, which implements the steps of a structural reliability prediction method based on an adaptive grid in embodiment 1 when executed by a processor.

[0108] Example 5

[0109] A computer device, which may be a database, may have an internal structure as shown in Fig.10 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. Among them, the processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store pending transactions. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a structural reliability prediction method based on an adaptive grid in Example 1 is implemented.

[0110] It should be noted that the object information (including but not limited to object device information, object personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in the present invention are all information and data authorized by the object or fully authorized by all parties, and the collection, use and processing of relevant data need to comply with relevant laws, regulations and standards of relevant countries and regions.

[0111] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided by the present invention may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited thereto. The processor involved in each embodiment provided by the present invention may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited thereto.

[0112] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0113] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A structural reliability prediction method based on adaptive grid, characterized in that: The method comprises: The reliability influencing variables of the structure to be predicted are converted into standard Gaussian variables through Natav transformation; the structure to be predicted refers to the steel pipe structure in the berthing structure; the reliability influencing variables include the yield stress of the steel pipe, the equivalent berthing impact load and the river water surface height; The k-dimensional hyper-rectangular space corresponding to the standard Gaussian variable is grid-divided by an adaptive grid algorithm, the type of the grid unit is determined according to the functional function value of the grid node, and the reliability of the structure to be predicted is determined according to the type of the grid unit and the reliability of the grid unit; the k-dimensional hyper-rectangular space is a space composed of the value intervals of k standard Gaussian variables; the functional function value of the grid node is determined according to the variable value and the functional function corresponding to the node; the functional function is used to describe the relationship between the performance index of the structure to be measured and the reliability influencing variable; Applying an adaptive grid algorithm to grid the k-dimensional hyperrectangular space corresponding to the standard Gaussian variable, determining the type of grid unit according to the functional function value of the divided grid node, and determining the reliability of the structure to be predicted according to the type of grid unit and the reliability of the grid unit itself, specifically including: Performing omnidirectional binary division on the k-dimensional hyper-rectangular space to obtain a second-level grid, and determining the functional function value of the node of each grid unit of the current level; setting the second-level grid as the current level; Traverse the i-th grid unit of the current level, and determine the type of the i-th grid unit according to the functional function value of the node of the i-th grid unit; i = 1, 2, ..., n M ;n M Represents the total number of grid cells in the Mth level grid; When the type of the i-th grid unit is a positive unit or a negative unit, the reliabilities of all positive units and negative units that have been traversed in all levels are accumulated as the current total reliability; and i=i+1, return to the step of "traversing the i-th grid unit of the current level"; the function function values ​​of each vertex of the positive unit are greater than 0; the function function values ​​of each vertex of the negative unit are less than 0; the reliability of the negative unit is 0; the expression of the reliability of the positive unit is: Among them, R SE is the reliability of the positive unit, Ω SE is the domain of positive units, is the joint probability density function of k reliability influencing variables; x1 to x k represents k reliability influencing variables; When the type of the i-th grid unit is a positive-negative mixed unit, the reliabilities of all the positive-negative mixed units that have been traversed in the current level are accumulated as the total reliability error of the current level; the i-th grid unit is omnidirectionally divided into two to obtain the next level grid, and the functional function value of the node of each grid unit in the next level grid is determined; and i=i+1 is set, and the step of "traversing the i-th grid unit of the current level" is returned; the functional function value of each vertex of the positive-negative mixed unit includes a value greater than 0 and a value less than 0; the reliability of the positive-negative mixed unit is calculated by treating the positive-negative mixed unit as a positive unit and according to the expression of the reliability of the positive unit; After all grid cells of the current level have been traversed, it is determined whether the total reliability error obtained by summing up the reliability of all positive and negative mixed cells in the current level is less than the error threshold; If not, set the next level grid as the current level, and return to step "traversing the i-th grid unit of the current level"; If yes, then traverse each grid unit of the next level and determine the type of each grid unit according to the functional function value of the node of each grid unit; The difference reliability of the positive and negative mixed units and the reliability of the positive units in the next level are added to the total reliability output by the previous level to obtain the final reliability of the structure to be tested; the difference reliability of the positive and negative mixed units is determined based on the reliability and proportion coefficient of the positive and negative mixed units; the proportion coefficient is the proportion of the hypervolume of the safety domain to the hypervolume of the entire unit domain.

2. The method for predicting structural reliability based on adaptive grid according to claim 1, characterized in that: When determining the function value of the node of each grid unit in the next level grid, it is determined according to the positive or negative function value of the vertex of the corresponding previous level grid, specifically: If the function function values ​​of adjacent vertices of the previous level grid are all positive, the function function value of the predicted point between adjacent vertices is positive; if the function function values ​​of adjacent vertices of the previous level grid are all negative, the function function value of the predicted point between adjacent vertices is negative; the predicted point refers to the node with unknown function function value in the next level grid; If the power function values ​​of adjacent vertices of the previous level grid are not all positive or negative, the power function value of the prediction point between the adjacent vertices is determined according to the value of the prediction point and the power function.

3. The method for predicting structural reliability based on adaptive grid according to claim 1, characterized in that: The calculation formula of the difference reliability of the positive and negative mixed unit is: Among them, R LSE is the difference reliability of the positive and negative mixed units; V safe is the hypervolume of the safety domain of the positive and negative mixed units. The safety domain refers to the input space where the function values ​​are all greater than zero; V LSE is the total hypervolume of the positive and negative mixed units; Ω LSE is the domain of the mixed positive and negative units.

4. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the steps of a structural reliability prediction method based on an adaptive grid as described in any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of a structural reliability prediction method based on an adaptive grid as described in any one of claims 1 to 3 are implemented.

6. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of a structural reliability prediction method based on an adaptive grid as described in any one of claims 1 to 3 are implemented.

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