CN115146482B - Structural reliability analysis method based on subinterval analysis and Chebyshev sparse model - Google Patents
Structural reliability analysis method based on subinterval analysis and Chebyshev sparse model Download PDFInfo
- Publication number
- CN115146482B CN115146482B CN202210916008.7A CN202210916008A CN115146482B CN 115146482 B CN115146482 B CN 115146482B CN 202210916008 A CN202210916008 A CN 202210916008A CN 115146482 B CN115146482 B CN 115146482B
- Authority
- CN
- China
- Prior art keywords
- chebyshev
- analysis
- interval
- subinterval
- sparse
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000004458 analytical method Methods 0.000 title claims abstract description 66
- 238000000034 method Methods 0.000 claims abstract description 46
- 238000012360 testing method Methods 0.000 claims abstract description 13
- 238000005457 optimization Methods 0.000 claims abstract description 12
- 238000013461 design Methods 0.000 claims abstract description 11
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 10
- 238000012216 screening Methods 0.000 claims abstract description 6
- 230000004044 response Effects 0.000 claims description 22
- 238000000354 decomposition reaction Methods 0.000 claims description 6
- 238000005316 response function Methods 0.000 claims description 6
- 230000014509 gene expression Effects 0.000 claims description 5
- 230000014759 maintenance of location Effects 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 abstract description 14
- 238000011089 mechanical engineering Methods 0.000 abstract description 4
- 230000008569 process Effects 0.000 abstract description 3
- 238000004088 simulation Methods 0.000 abstract 1
- 239000000243 solution Substances 0.000 description 5
- 238000000342 Monte Carlo simulation Methods 0.000 description 2
- 230000007246 mechanism Effects 0.000 description 2
- 238000012512 characterization method Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 239000012088 reference solution Substances 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Complex Calculations (AREA)
Abstract
The invention discloses a structural reliability analysis method based on subinterval analysis and a Chebyshev sparse model, which comprises the steps of firstly estimating each item of sparsity of a function Chebyshev sparse model based on subinterval analysis, establishing a Chebyshev sparse approximation model by screening items with larger coefficients, replacing an original high-dimensional and complex function by the approximation model, and then combining a multi-factor full-level test design method and a discrete optimization algorithm to calculate the upper limit, the lower limit and the structural reliability of the Chebyshev sparse approximation model. The method has good universality and adaptability when the reliability and the safety degree of complex engineering structures based on interval analysis in the fields of civil engineering, mechanical engineering, aerospace and the like are evaluated by using a proxy function method, so that the calculation amount of structure analysis and simulation in the reliability analysis process is greatly reduced, and the calculation efficiency is improved.
Description
Technical Field
The invention relates to the technical field of structural reliability analysis, in particular to a structural reliability analysis method based on subinterval analysis and a Chebyshev sparse model, which relates to the aspect of structural reliability analysis by adopting a complex high-dimensional structural function with a proxy model being approximately real.
Background
The analysis of the structural reliability of products in the fields of civil engineering, mechanical engineering, aerospace and the like is an important content of structural design of engineering products. The analysis of the reliability of the product structure is derived from uncertain factors in the processes of load, material property, product structure manufacturing and use and the like, and has important significance for safety assessment, safety operation and improvement of important influencing factors and safety reserve.
The functional functions of normal working capacity or critical safety of large complex structures or product characterization structures in the fields of civil engineering, mechanical engineering, aerospace and the like are often highly nonlinear and implicitly expressed, classical reliability analysis methods such as a first-order second-order moment method and a Monte Carlo method are not high in precision or are very time-consuming to calculate, and particularly when large-scale numerical methods such as finite elements are needed for carrying out mass analysis, the efficiency and precision requirements of engineering practice reliability analysis are difficult to achieve. On the other hand, product structure uncertainty parameters are extremely important for structure reliability analysis, and reasonable processing of these uncertainty parameters is a precondition for correctly analyzing structure reliability. The traditional uncertainty model relies on sufficient samples to establish an accurate probability distribution model, the cost is high, engineering practice has certain difficulty, and the non-probability interval model only needs little sample information to determine the range of uncertain parameters.
The actual engineering structure has complex function, often has the characteristics of stronger nonlinearity, high dimensionality and the like, and the constructed proxy function approximates the actual function to be used for analyzing the reliability of structures or products in the fields of civil engineering, mechanical engineering, aerospace and the like, and particularly is combined with a Monte Carlo simulation method, so that a large amount of structural response analysis is avoided, good reliability analysis precision can be ensured, the reliability analysis efficiency is greatly improved, and the method is more and more widely valued and applied in engineering practice.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provide a structural reliability analysis method based on subinterval analysis and a Chebyshev sparse model. The analysis method has strong universality and can be suitable for the reliability analysis of the structural interval of various nonlinear and high-dimensional functional functions. Firstly, estimating each item of the function Chebyshev expansion model based on a subinterval analysis method, screening items with larger coefficients to establish a Chebyshev expansion sparse approximation model, replacing the original high-dimensional and complex function by the approximation model, and then combining a multi-factor full-level test design method and a discrete optimization algorithm to calculate and obtain the upper limit, the lower limit and the structural reliability of the Chebyshev expansion sparse approximation model. . The method greatly improves the calculation efficiency of the reliability analysis of the product structure and the applicability of complex high-dimensional problems.
The aim of the invention can be achieved by adopting the following technical scheme:
a structural interval reliability analysis method based on subinterval analysis and Chebyshev sparse model, the reliability analysis method comprising the steps of:
S1, designating a product structure of a field to be analyzed, and a functional function g (x) reflecting normal working capacity or a safe working critical state of the product structure in the field to be analyzed, wherein x= (x 1,…,xk,…,xd) is an interval variable vector, components x k＝[ak,bk, k=1, … and d, selecting a smaller Chebyshev polynomial to develop the highest order N, setting a term retention threshold parameter xi and solving the value of an extremum time variable dividing interval number N, wherein a k、bk is the lower limit and the upper limit of a component x k in the interval variable vector respectively, and d is the number of components in the interval variable vector;
s2, determining interpolation points in the form of a Chebyshev expansion trigonometric function, and taking m=n+1;
S3, screening each item of Chebyshev expansion meeting the condition 0- 1+i2+...+id -n to form a sparse model, wherein i 1,i2,...,id =0, 1,2, and n is the power of a component x 1,x2,…,xd in the interval variable vector respectively;
S4, respectively taking one from m interpolation points of each interval for combination, and obtaining d-dimensional interpolation point sets under m d trigonometric function forms by d interval parameters Converting the interpolation point set omega 1 into d-dimensional interpolation point set/>, under the polynomial standard formWherein/>The jth k interpolation point of the kth interval variable in the form of a trigonometric function,/>For/>Interpolation points under the corresponding polynomial standard form;
S5, substituting the on-axis interpolation points of the interpolation point set omega 2 into a functional function g (x) to obtain structural response;
S6, obtaining structural response of interpolation points of the interpolation point set omega 2 except for on-axis points by using a subinterval decomposition analysis method;
s7, calculating expansion coefficients of the Chebyshev polynomial, and reserving the terms with expansion coefficients larger than xi to obtain a Chebyshev sparse expansion approximate model
S8, dividing any kth interval parameter x k into N equal parts, and obtaining (N+1) d test point sets omega by adopting a multi-factor full-level design method: Searching in (N+1) d test points by using a discrete optimization algorithm to obtain a Chebyshev developed sparse approximation model/> The approximations of the maximum and minimum values are used as the upper limit g max and the lower limit g min of the structural response function, respectively, and the reliability index beta of the structure is calculated according to the following formula:
further, in the step S1, the term retention threshold parameter ζ is set to 10 -10, which satisfies a sparse approximation model formed by all coefficients that ζ > 10 -10, and is sufficient to better approximate the real function response interval.
Further, in the step S2, statistics of the interpolation points m in the form of trigonometric function is performed, and m=n+1 is taken under the requirement of ensuring the calculation efficiency and the calculation precision, so that the approximation result of the Chebyshev sparse model can be ensured.
Further, in the step S4, the interpolation point θ k,j and x k,j in the polynomial standard form are calculated according to the following formula:
The interpolation point standardized conversion can ensure that all variables are subjected to reliability analysis and design in a unified variable space, and the approximation precision of the Chebyshev truncated approximation model is ensured.
Further, in the step S7, coefficients of the approximation model are calculated according to the following expression:
Wherein the method comprises the steps of Coefficients representing the approximate model of the Chebyshev polynomial, g (·) representing the function,Tensor product representing the triangular expansion of a plurality of one-dimensional Chebyshev polynomials, where i 1,i2,...,id = 0,1,2, n is the power of the variable x 1,x2,…,xd in each term, respectively,/>Respectively represent interpolation pointsIs a component of (a). The coefficient of the approximation model directly reflects the approximation result of the model, the items meeting the requirement of 0- 1+i2+...+id -n are screened, the items with smaller coefficient of the approximation model are ignored, on one hand, the calculation cost is greatly reduced, and on the other hand, the accuracy of the structural response can be ensured to be controlled within the accuracy required by structural reliability analysis.
Further, in the step S8, the upper limit g max and the lower limit g min of the structural response function are calculated according to the following expression:
Wherein max (·) and min (·) represent maximum and minimum values. Compared with the traditional optimization algorithm, the discrete optimization algorithm based on the multi-factor full-level test design method can improve the efficiency and reduce the calculation cost in the process of acquiring the response interval of the structural function.
Compared with the prior art, the invention has the following advantages and effects:
(1) The method uses the traditional Chebyshev expansion model to replace the function, combines an optimization algorithm to perform interval reliability analysis, has high precision and large calculated amount, estimates each item of the function Chebyshev expansion model based on a subinterval decomposition analysis method, screens items with larger coefficients to establish a Chebyshev expansion sparse approximation model, ignores items affecting the precision, can solve each item coefficient of the Chebyshev approximation model only by a small number of Chebyshev test design points, replaces the original high-dimensional and complex function with the approximation model to perform reliability analysis, and greatly reduces the calculation times of the function.
(2) The Chebyshev expansion interval analysis is established on the basis of each sub-term interval analysis, the interdependence relation among the sub-terms is not fully considered, the calculation efficiency is high, the error is large, even an error interval analysis result is obtained, the method combines a multi-factor full-level test design method and a discrete optimization algorithm, on the basis of a Chebyshev expansion sparse approximation model, the approximation upper limit, the lower limit and the reliability of the structural response are calculated, the calculation efficiency is greatly improved, and the accuracy requirement of the engineering structure reliability analysis can be met.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a flow chart of a structural reliability analysis method based on subinterval analysis and a Chebyshev sparse model.
FIG. 2 is a schematic view of a slider-crank mechanism in example 2.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
Fig. 1 is a flowchart of a structural reliability analysis method based on subinterval analysis and Chebyshev sparse breaking model disclosed in this embodiment, and this embodiment 1 further illustrates the present invention by using an application example including two interval uncertainty parameters.
The structural reliability analysis method based on subinterval analysis and Chebyshev sparse fracture model comprises the following steps:
s1, specifying a structure to be analyzed, wherein x 1,x2 is an interval variable, and a corresponding function g (x) is as follows:
The present embodiment analyzes through three cases, case one: the interval of both uncertainty parameters is [3.33,4.07], the uncertainty levels are λ 1 =10.0% and λ 2 =10.0%, respectively; and a second case: the interval for both uncertainty parameters is [2.96,4.44], uncertainty level λ 1 =20.0% and λ 2 =20.0%; and a third case: the interval for both uncertainty parameters is [2.59,4.81], uncertainty level λ 1 =30.0% and λ 2 =30.0%. Selecting a smaller Chebyshev polynomial to develop the highest order n=3, setting a subitem retention threshold parameter xi=10 -10, and solving the number of variable dividing intervals N=6 when the extremum is solved;
s2, determining interpolation points in the form of a Chebyshev expansion trigonometric function, and taking m=n+1;
S3, screening each item of Chebyshev expansion meeting the condition 0- 1+i2+...+id -n to form a sparse model, wherein i 1,i2,...,id =0, 1,2, and n is the power of a component x 1,x2,…,xd in the interval variable vector respectively;
S4, respectively taking one from m interpolation points of each interval for combination, and obtaining d-dimensional interpolation point sets under m d trigonometric function forms by d interval parameters Converting the interpolation point set omega 1 into d-dimensional interpolation point set/>, under the polynomial standard formWherein/>The jth k interpolation point of the kth interval variable in the form of a trigonometric function,/>For/>Interpolation points under the corresponding polynomial standard form;
S5, substituting the on-axis interpolation points of the interpolation point set omega 2 into a functional function to obtain a structural response;
S6, obtaining structural response of interpolation points of the interpolation point set omega 2 except for on-axis points by using a subinterval decomposition analysis method;
s7, calculating expansion coefficients of the Chebyshev polynomials, and reserving the items with expansion coefficients larger than xi to obtain a Chebyshev sparse expansion approximate model;
s8, dividing any kth interval parameter x k into N equal parts, and obtaining (N+1) d test point sets omega by adopting a multi-factor full-level design method: Searching in (N+1) d test points by using a discrete optimization algorithm to obtain a Chebyshev developed sparse approximation model/> The approximations of the maximum and minimum values are used as the upper limit g max and the lower limit g min of the structural response function, respectively, and the reliability index beta of the structure is calculated according to the following formula:
The structural response intervals and their relative errors calculated by the reliability analysis method disclosed in example 1 and the other methods are shown in tables 1,2 and 3, and the upper and lower limits obtained by the continuous optimization method are used as accurate solutions. When the uncertainty level lambda=10%, the relative error between the functional function response and the accurate solution obtained by the method is 0, the relative error between the upper limit and the lower limit obtained by the interval first-order taylor expansion method is 2.95% and 2.98%, the functional function of the interval first-order taylor expansion method is calculated for 5 times, and the method is calculated for 13 times. When the uncertainty level lambda=20%, the relative error of the method is equal to 0%, the lower limit relative error calculated by the interval first-order taylor expansion method is 10.43%, and the upper limit relative error is 11.24%, so that when the function is highly nonlinear and the uncertainty level is large, the upper and lower limit accuracy calculated by the interval first-order taylor expansion method is difficult to guarantee. Similarly, when the uncertainty level lambda is 30%, the upper and lower limit precision of the function obtained by the method is high, the relative error of the upper and lower limits is only 0.001% and 0.89%, the function is calculated for 13 times, and the interval first-order Taylor expansion method is calculated for 5 times, so that the calculation cost is slightly higher than that of the interval first-order Taylor expansion method, but the calculation precision is greatly improved.
Table 1. Response intervals calculated by each method at λ=10.0% and relative error table thereof
Table 2. Response intervals calculated by each method at λ=20.0% and relative error table thereof
Table 3 response intervals calculated by each method at λ=30.0% and relative error table thereof
Example 2
This example 2 continues to illustrate the invention with a slider-crank mechanism that includes an application example of 6 interval variables. The structural reliability analysis method based on subinterval analysis and Chebyshev sparse model comprises the following steps:
s1, appointing a structure to be analyzed, wherein the corresponding function g (x) is as follows:
Where x= (a, b, e, μ f,σs), the interval parameters of the six uncertain parameters of this embodiment are shown in table 4. Selecting a smaller Chebyshev polynomial to develop the highest order n=3, setting a subitem retention threshold parameter xi=10 -10, and solving the number of variable dividing intervals N=6 when the extremum is solved;
TABLE 4 statistical parameters of the interval variables
| Variable(s) | Lower limit of interval | Upper limit of interval | Type(s) |
| a | 98 | 102 | Interval variable |
| b | 392 | 408 | Interval variable |
| F | 224000 | 336000 | Interval variable |
| e | 127.8 | 132.2 | Interval variable |
| μf | 0.156 | 0.204 | Interval variable |
| σs | 212.6 | 221.4 | Interval variable |
S2, determining interpolation points in the form of a Chebyshev expansion trigonometric function, and taking m=n+1;
S3, screening each item of Chebyshev expansion meeting the condition 0- 1+i2+...+id -n to form a sparse model, wherein i 1,i2,...,id =0, 1,2, and n is the power of a component x 1,x2,…,xd in the interval variable vector respectively;
S4, respectively taking one from m interpolation points of each interval for combination, and obtaining d-dimensional interpolation point sets under m d trigonometric function forms by d interval parameters Converting the interpolation point set omega 1 into d-dimensional interpolation point set/>, under the polynomial standard formWherein/>The jth k interpolation point of the kth interval variable in the form of a trigonometric function,/>For/>Interpolation points under the corresponding polynomial standard form;
S5, substituting the on-axis interpolation points of the interpolation point set omega 2 into a functional function to obtain a structural response;
S6, obtaining structural response of interpolation points of the interpolation point set omega 2 except for on-axis points by using a subinterval decomposition analysis method;
s7, calculating expansion coefficients of the Chebyshev polynomials, and reserving the items with expansion coefficients larger than xi to obtain a Chebyshev sparse expansion approximate model;
s8, dividing any kth interval parameter x k into N equal parts, and obtaining (N+1) d test point sets omega by adopting a multi-factor full-level design method: Searching in (N+1) d test points by using a discrete optimization algorithm to obtain a Chebyshev developed sparse approximation model/> The approximations of the maximum and minimum values are used as the upper limit g max and the lower limit g min of the structural response function, respectively, and the reliability index beta of the structure is calculated according to the following formula:
The comparison between the structural response interval calculated by the reliability analysis method disclosed in example 2 and other methods and the relative error thereof is shown in table 5, the upper and lower limits obtained by the continuous optimization method are [1.2749 × 107,9.1249 ×107] as accurate solutions, the upper and lower limits of the function obtained by the method proposed by the invention are [1.2060 × 107,9.1806 ×107], the relative error between the upper and lower limits of the function obtained by the reference solution is 5.4% and 0.61%, the upper and lower limits of the function obtained by the interval first-order taylor expansion method are [1.5601 × 107,9.3698 ×107], the relative error between the upper and lower limits is 2.68% and 22.37%, and the function of the interval first-order taylor expansion method is calculated 13 times, the method is calculated 37 times, and the calculation accuracy is greatly improved although the calculation cost is slightly higher than that of the interval first-order taylor expansion method.
TABLE 5 response interval calculated by each method and relative error table thereof
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (5)
1. The structural interval reliability analysis method based on subinterval analysis and Chebyshev sparse model is characterized by comprising the following steps of:
S1, designating a product structure of a field to be analyzed, and a functional function g (x) reflecting normal working capacity or a safe working critical state of the product structure in the field to be analyzed, wherein x= (x 1,…,xk,…,xd) is an interval variable vector, components x k＝[ak,bk, k=1, … and d, selecting a smaller Chebyshev polynomial to develop the highest order N, setting a term retention threshold parameter xi and solving the value of an extremum time variable dividing interval number N, wherein a k、bk is the lower limit and the upper limit of a component x k in the interval variable vector respectively, and d is the number of components in the interval variable vector;
s2, determining interpolation points in the form of a Chebyshev expansion trigonometric function, and taking m=n+1;
S3, screening each item of Chebyshev expansion meeting the condition 0- 1+i2+...+id -n to form a sparse model, wherein i 1,i2,...,id =0, 1,2, and n is the power of a component x 1,x2,…,xd in the interval variable vector respectively;
S4, respectively taking one from m interpolation points of each interval for combination, and obtaining d-dimensional interpolation point sets under m d trigonometric function forms by d interval parameters Converting the interpolation point set omega 1 into d-dimensional interpolation point set/>, under the polynomial standard formWherein/>The jth k interpolation point of the kth interval variable in the form of a trigonometric function,/>For/>Interpolation points under the corresponding polynomial standard form;
S5, substituting the on-axis interpolation points of the interpolation point set omega 2 into a functional function g (x) to obtain structural response;
S6, obtaining structural response of interpolation points of the interpolation point set omega 2 except for on-axis points by using a subinterval decomposition analysis method;
s7, calculating expansion coefficients of the Chebyshev polynomial, and reserving the terms with expansion coefficients larger than xi to obtain a Chebyshev sparse expansion approximate model
S8, dividing any kth interval parameter x k into N equal parts, and obtaining (N+1) d test point sets omega by adopting a multi-factor full-level design method: Searching in (N+1) d test points by using a discrete optimization algorithm to obtain a Chebyshev developed sparse approximation model/> The approximations of the maximum and minimum values are used as the upper limit g max and the lower limit g min of the structural response function, respectively, and the reliability index beta of the structure is calculated according to the following formula:
2. the structural reliability analysis method based on subinterval analysis and Chebyshev sparse model according to claim 1, wherein in the step S4, the interpolation point θ k,j under the trigonometric function form and the interpolation point x k,j under the polynomial standard form are calculated according to the following formula:
3. The structural reliability analysis method based on subinterval analysis and Chebyshev sparse model according to claim 1, wherein in the step S6, the subinterval decomposition analysis method solves for the structural response according to the following expression:
Wherein the method comprises the steps of Represents an interpolation point on the axis of point set Ω 2, g 0 represents an interpolation point/>Structural response at the location.
4. The structural reliability analysis method based on subinterval analysis and Chebyshev sparse model according to claim 1, wherein in step S7, the coefficients of the approximation model are calculated according to the following expression:
Wherein the method comprises the steps of Coefficients representing a Chebyshev polynomial approximation model, g (x) representing a functional function,Tensor product representing the triangular expansion of a plurality of one-dimensional Chebyshev polynomials, where i 1,i2,...,id = 0,1,2, n is the power of the variable x 1,x2,…,xd in each term, respectively,/>Respectively represent interpolation pointsIs a component of (a).
5. The structural reliability analysis method based on subinterval analysis and Chebyshev sparse model according to claim 1, wherein in the step S8, the upper limit g max and the lower limit g min of the structural response function are calculated according to the following expressions:
Where max () and min () represent maximum and minimum values.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210916008.7A CN115146482B (en) | 2022-08-01 | 2022-08-01 | Structural reliability analysis method based on subinterval analysis and Chebyshev sparse model |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210916008.7A CN115146482B (en) | 2022-08-01 | 2022-08-01 | Structural reliability analysis method based on subinterval analysis and Chebyshev sparse model |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115146482A CN115146482A (en) | 2022-10-04 |
| CN115146482B true CN115146482B (en) | 2024-06-14 |
Family
ID=83413657
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210916008.7A Active CN115146482B (en) | 2022-08-01 | 2022-08-01 | Structural reliability analysis method based on subinterval analysis and Chebyshev sparse model |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115146482B (en) |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105912854B (en) * | 2016-04-11 | 2018-05-15 | 西安交通大学 | A kind of sparse representation method of mechanical structure Dynamic Load Identification |
| CN105893716B (en) * | 2016-06-02 | 2018-06-29 | 北京航空航天大学 | A kind of structural break Multidisciplinary systems analysis method based on fractal theory |
| CN114357651A (en) * | 2022-01-04 | 2022-04-15 | 北京理工大学 | Efficient uncertain flexible multi-body system dynamic response prediction method |
-
2022
- 2022-08-01 CN CN202210916008.7A patent/CN115146482B/en active Active
Non-Patent Citations (2)
| Title |
|---|
| Structural Reliability Analysis via the Multivariate Gegenbauer Polynomial-Based Sparse Surrogate Model;Yixuan Dong;《Mathematical Problems in Engineering》;20211027;全文 * |
| 基于Kriging模型的机械结构可靠性分析方法研究;王健;《中国博士学位论文全文数据库基础科学辑》;20220115;A002-133 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115146482A (en) | 2022-10-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Smucler et al. | Robust and sparse estimators for linear regression models | |
| Xi et al. | A comparative study of probability estimation methods for reliability analysis | |
| Shang et al. | Statistical process control for multistage processes with binary outputs | |
| CN108920786B (en) | Section uncertainty analysis method based on Chebyshev polynomial fitting | |
| Guevara et al. | Process capability analysis for nonlinear profiles using depth functions | |
| Glynn et al. | Simulation-based confidence bounds for two-stage stochastic programs | |
| CN110852016B (en) | Reliability simulation test model correction method | |
| CN111797535A (en) | Structure reliability analysis self-adaptive point adding method for multiple agent models | |
| JP2010211684A (en) | Method, program and apparatus for processing data | |
| Erba et al. | Random geometric graphs in high dimension | |
| CN115495871A (en) | Dynamic response and reliability prediction method for hybrid uncertainty system | |
| CN111914386A (en) | Reliability assessment method and system based on uncertain analysis of degradation model | |
| CN115146482B (en) | Structural reliability analysis method based on subinterval analysis and Chebyshev sparse model | |
| Gude et al. | Influence of the Selection of Reaction Curve’s Representative Points on the Accuracy of the Identified Fractional‐Order Model | |
| CN115169246A (en) | Reliability analysis method based on Direct optimization and double-sample-point updating | |
| Bobko et al. | Eigenvalue shrinkage in principal components based factor analysis | |
| US8566064B2 (en) | Estimating polynomial generating device, estimating device, estimating polynomial generating method, and estimating method | |
| CN108229054B (en) | Symmetrical tensioning integral structure shape finding method based on group theory | |
| Lin et al. | Distribution-free prediction regions of multivariate response PLS models with applications to NIR datasets | |
| Sipos et al. | Failure analysis and prediction using neural networks in the chip manufacturing process | |
| Derakhshan et al. | Comparison of homotopy perturbation transform method and fractional Adams–Bashforth method for the Caputo–Prabhakar nonlinear fractional differential equations | |
| CN117973128A (en) | Method for analyzing overall sensitivity of aeroengine wheel disc based on Copula | |
| CN118235145A (en) | Model generation device, model generation method, and data estimation device | |
| Hamad et al. | A comparison of two metamodeling techniques for analog ICs: contemporary Kriging metamodels vs. classical RSMs | |
| CN115392112A (en) | Structure reliability analysis method based on Direct algorithm sampling and support vector machine |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |