CN111797535A - Structure reliability analysis self-adaptive point adding method for multiple agent models - Google Patents

Structure reliability analysis self-adaptive point adding method for multiple agent models Download PDF

Info

Publication number
CN111797535A
CN111797535A CN202010665412.2A CN202010665412A CN111797535A CN 111797535 A CN111797535 A CN 111797535A CN 202010665412 A CN202010665412 A CN 202010665412A CN 111797535 A CN111797535 A CN 111797535A
Authority
CN
China
Prior art keywords
function
point
adaptive
reliability analysis
sample points
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.)
Pending
Application number
CN202010665412.2A
Other languages
Chinese (zh)
Inventor
李国发
陈泽权
何佳龙
钟瑞龄
陈传海
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Jilin University
Original Assignee
Jilin University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Jilin University filed Critical Jilin University
Priority to CN202010665412.2A priority Critical patent/CN111797535A/en
Publication of CN111797535A publication Critical patent/CN111797535A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • General Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • General Health & Medical Sciences (AREA)
  • Mathematical Physics (AREA)
  • Computational Linguistics (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • Biophysics (AREA)
  • Biomedical Technology (AREA)
  • Data Mining & Analysis (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Medical Informatics (AREA)
  • Computer Hardware Design (AREA)
  • Geometry (AREA)
  • Complex Calculations (AREA)

Abstract

The invention discloses a sequence dotting method for structural reliability analysis, which comprises the following steps: specifying a function of a structure to be analyzed, and determining variables and publishing information thereof; obtaining a candidate sample point set by Monte Carlo sampling
Figure 223654DEST_PATH_IMAGE002
(ii) a Obtaining initial points by utilizing Latin hypercube sampling and forming initial sample set
Figure DEST_PATH_IMAGE003
(ii) a Obtaining
Figure 553004DEST_PATH_IMAGE004
The function value of the corresponding function and constructing an agent model; carrying out Monte Carlo numerical simulation on the agent model to obtain the failure rate of the current iteration step; obtaining the final generationPhysical models and failure probabilities. The method has uncommon universality and applicability, can be suitable for a non-kriging model, greatly expands a proxy model method suitable for structural reliability analysis, and has important significance to the field of reliability analysis.

Description

Structure reliability analysis self-adaptive point adding method for multiple agent models
Technical Field
The invention belongs to the field of structural reliability analysis, particularly relates to the aspect of analyzing structural reliability by adopting a proxy model of a self-adaptive point adding method, and particularly relates to a structural reliability analysis self-adaptive point adding method for various proxy models.
Background
The reliability of the structure in the service life is taken into consideration as a quantitative index, the functional function related to the structure is established by taking the load, the boundary condition and the like as influence parameters, and the reliability index of the structure is accurately and quantitatively calculated by utilizing the established functional function. Compared with the traditional deterministic analysis method, various influence parameters of the structure in the service life are fully considered, and the problem of lack of safety or redundancy of the traditional method is effectively avoided. And key parameters influencing the reliability of the structure can be effectively analyzed through sensitivity analysis, and the reliability of the structure can be effectively improved through improving the parameters.
At present, the structure reliability is mainly a first-order reliability method and a second-order reliability method in engineering application. The first order reliability method and the second order reliability method are simple and convenient to calculate, but the first order reliability method and the second order reliability method have poor precision under the condition that the functional function of the structure is strong and nonlinear, and errors can be generated in the probability conversion process. With the development of the problems in the field of structural reliability analysis in the directions of strong nonlinearity, high dimensionality and high precision, the traditional first-order reliability method and the traditional second-order reliability method can not meet the actual engineering requirements to a great extent.
At present, a structure reliability method based on a proxy model is gradually applied to actual engineering, and the essence of the proxy model method is to obtain a substitute model of a real structure function in a certain range through a plurality of sampling samples of the real function and through methods such as interpolation or fitting, so as to obtain a corresponding result of the real function through analysis of the proxy model. The proxy model can be used for processing the implicit structural function and has high calculation precision under the condition that the functional function is high in nonlinearity. Commonly used proxy models include polynomial response surfaces, polynomial chaotic expansion, neural networks, support vector machines, Kriging models and the like.
Before constructing the proxy model, a series of sample points or training points need to be acquired by a certain experimental design method, and the main experimental design method can be divided into two types at present, namely one-time sampling and sequence sampling. The sampling at one time is that a plurality of sample points are selected at one time, and are uniformly distributed in general and used as training sample points of the proxy model. The sequence sampling is to gradually improve the precision of the proxy model by adding sample points according to a certain rule for multiple times until the design requirements are met.
The adaptive dotting is used as one of the sequence sampling, and the next sampling or dotting method is guided mainly by a proxy model and the condition of the existing sample points, so that the adaptive dotting of the proxy model is realized.
At present, the main agent models adopting the self-adaptive point adding method are limited to Kriging models to a great extent, and other agent models can not give the mean square error of the predicted points as the same as the Kriging models in terms of processing the structural reliability analysis problem, so that the self-adaptive point adding is not realized.
Therefore, the adaptive sequence point adding method which is high in applicability and not limited to the kriging model alone is of great significance to the field of structural reliability analysis, particularly to the aspect of structural reliability analysis by adopting a proxy model method.
Disclosure of Invention
The present invention aims to solve the above problems, and provides an adaptive dotting method which has strong applicability and can be applied to various proxy models, is used for structural reliability analysis, and realizes that a non-kriging proxy model can also be applied to the adaptive dotting method, and a non-kriging proxy model can also be applied to the adaptive dotting method, thereby realizing the extension of the structural reliability analysis method.
A sequence dotting method for structure reliability analysis comprises the following steps:
1) specifying a function of a structure to be analyzed
Figure 203834DEST_PATH_IMAGE001
Determining the variables of the function
Figure 745673DEST_PATH_IMAGE002
And its probability distribution information;
2) probability density distribution function of the variable determined according to step 1)
Figure 448050DEST_PATH_IMAGE003
To extract
Figure 75341DEST_PATH_IMAGE004
Candidate sample points forming a set of candidate sample points
Figure 583682DEST_PATH_IMAGE005
；
3) According to the variables determined in the step 1), adopting a Latin hypercube method to obtain the value range of each variable
Figure 232226DEST_PATH_IMAGE006
Internal extraction
Figure 105504DEST_PATH_IMAGE007
An initial random sample point, which constitutes an initial training set
Figure 220090DEST_PATH_IMAGE008
And make an order
Figure 532123DEST_PATH_IMAGE009
For recording the number of iterations.
Wherein
Figure 782976DEST_PATH_IMAGE010
A cumulative distribution function representing a standard normal distribution, and
Figure 827155DEST_PATH_IMAGE011
expressed as the inverse of the cumulative distribution function of the variables;
4) according to a training set
Figure 179770DEST_PATH_IMAGE012
Obtaining
Figure 29915DEST_PATH_IMAGE013
Function values of the corresponding structural function functions, and constructing an agent model;
5) combining the candidate sample point set of the step 2) by using the proxy model established in the step 4
Figure 400853DEST_PATH_IMAGE014
Carrying out numerical simulation to obtain the failure probability of the structure estimated by the proxy model of the current iteration step
Figure 615934DEST_PATH_IMAGE015
；
6) Determining failure probability
Figure 705113DEST_PATH_IMAGE016
And the result of the last iteration
Figure 342636DEST_PATH_IMAGE017
Whether the relative error is less than
Figure 568081DEST_PATH_IMAGE018
To do so
Figure 219642DEST_PATH_IMAGE019
A sufficiently small constant, the convergence condition is:
Figure 530538DEST_PATH_IMAGE020
if the convergence requirement is met, acquiring a final proxy model and a final estimated failure probability;
if the convergence requirement is not satisfied or
Figure 722485DEST_PATH_IMAGE021
Then, the next step is carried out, and adaptive sequence point adding is carried out;
7) using learning functions
Figure 271278DEST_PATH_IMAGE022
For candidate sample point set
Figure 375631DEST_PATH_IMAGE023
Performing numerical simulation and obtaining the latest sample point
Figure 439402DEST_PATH_IMAGE024
And updating the training set
Figure 169461DEST_PATH_IMAGE025
(ii) a Wherein the learning function
Figure 572760DEST_PATH_IMAGE026
The specific expression of (A) is as follows:
Figure 97283DEST_PATH_IMAGE027
wherein,
Figure 900547DEST_PATH_IMAGE028
indicating points
Figure 168717DEST_PATH_IMAGE029
For training set
Figure 426523DEST_PATH_IMAGE030
The average value of the Euclidean distances of each point in the middle,
Figure 387526DEST_PATH_IMAGE031
indicating points
Figure 425889DEST_PATH_IMAGE032
For training set
Figure 435433DEST_PATH_IMAGE033
The minimum value of the Euclidean distance of each point in the middle;
8) will be provided with
Figure 360795DEST_PATH_IMAGE034
Incorporating training sets
Figure 227120DEST_PATH_IMAGE035
Update
Figure 752779DEST_PATH_IMAGE035
Let us order
Figure 362752DEST_PATH_IMAGE036
Returning to the step 4);
said step 7) introduction
Figure 595150DEST_PATH_IMAGE037
In order to ensure that the subsequently adapted sample points are used to improve the extreme state function of the current proxy model
Figure 412803DEST_PATH_IMAGE038
Then the weight is increased where the sample points are least dense, as a global consideration, and, on the other hand,
Figure 894599DEST_PATH_IMAGE039
it is to avoid that the sample points are too dense; while
Figure 511526DEST_PATH_IMAGE040
Can ensure that the estimated failure probability can depend on the whole iteration process
Figure 660747DEST_PATH_IMAGE041
And convergence is carried out, and the robustness of the iterative process is ensured.
Said step 7) of selecting a candidate sample point set
Figure 134454DEST_PATH_IMAGE042
In such a way that the function is learned
Figure 854279DEST_PATH_IMAGE043
The minimum point will be selected by the adaptive sequence as the new sample point;
said step 7) of selecting a candidate sample point set
Figure 9317DEST_PATH_IMAGE044
The specific mathematical expression of (a) is as follows:
Figure 13045DEST_PATH_IMAGE045
。
extraction as described in step 2)
Figure 923232DEST_PATH_IMAGE046
And extracting the candidate sample points by adopting a Monte Carlo sampling method.
The invention provides a sequence dotting method for structure reliability analysis, which comprises the following steps: specifying a function of a structure to be analyzed, and determining variables and publishing information thereof; obtaining a candidate sample point set by Monte Carlo sampling
Figure 582884DEST_PATH_IMAGE047
(ii) a Obtaining initial points by utilizing Latin hypercube sampling and forming initial sample set
Figure 338350DEST_PATH_IMAGE048
(ii) a Obtaining
Figure 194922DEST_PATH_IMAGE049
The function value of the corresponding function and constructing an agent model; carrying out Monte Carlo numerical simulation on the agent model to obtain the failure rate of the current iteration step; and acquiring a final agent model and failure probability. The method has uncommon universality and applicability, can be suitable for a non-kriging model, greatly expands a proxy model method suitable for structural reliability analysis, and analyzes the reliabilityThe field has important significance.
The invention has the following advantages
1) Learning function provided by the invention
Figure 276010DEST_PATH_IMAGE050
By introducing a probability distribution function of the variables
Figure 219695DEST_PATH_IMAGE051
The estimated failure probability can be stably converged, and the robustness of the iterative process is ensured;
2) learning function provided by the invention
Figure 982115DEST_PATH_IMAGE052
The information of the sample points of the self-adaptive point adding and the current model is considered, the new sample points added by the subsequent self-adaptive sequence are ensured, the global and local consideration of the proxy model can be fully considered, the estimation error of the current proxy model is improved to a great extent, and the high efficiency and the accuracy of the structural reliability analysis process of the point adding iteration of the whole self-adaptive sequence are ensured;
3) the adaptive sequence point adding method provided by the invention has uncommon universality and applicability, can be suitable for a non-kriging model, greatly expands a proxy model method suitable for structural reliability analysis, and has important significance to the field of reliability analysis;
4) the self-adaptive sequence point adding method provided by the invention can be used for efficiently and accurately predicting the failure probability of the structure on the premise of adopting a small number of sample points, and different proxy model methods can obtain uncommon accuracy and efficiency, thereby indicating the universality and reliability of the method.
Drawings
FIG. 1 is a flow chart of a sequential dotting method for structural reliability analysis according to the present invention;
FIG. 2 is a diagram of the extreme state function of the structure fitted by using a Gaussian process regression neural network as a proxy model method in embodiment 1 of the present invention;
FIG. 3 is a diagram illustrating an extreme state function of a structure fitted by using an RBF neural network as a proxy model method according to embodiment 1 of the present invention;
FIG. 4 is a schematic view of a configuration of an undamped single degree of freedom oscillation system in embodiment 2 of the present invention;
FIG. 5 is a graph of the convergence of the adaptive sequence-plus-point prediction failure probability using a Gaussian process regression neural network as a proxy model in embodiment 2 of the present invention;
fig. 6 is a graph of convergence of the adaptive sequence plus point prediction failure probability by using the RBF neural network as a proxy model in embodiment 1 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A sequence sampling method for structure reliability analysis comprises the following steps:
1) specifying a function of a structure to be analyzed
Figure 694856DEST_PATH_IMAGE053
Determining the variables of the function
Figure 431999DEST_PATH_IMAGE054
And its probability distribution information; the structural function determined here can be obtained by using a mechanical theory or a finite element simulation method and the like, and is not described in detail for the prior art;
2) probability density distribution function of variable determined according to step 1
Figure 862980DEST_PATH_IMAGE055
Extracting by using Monte Carlo sampling method
Figure 163512DEST_PATH_IMAGE056
Candidate sample points forming a set of candidate sample points
Figure 996339DEST_PATH_IMAGE057
；
3) According to the variables determined in the step 1, adopting a Latin hypercube method to obtain the value range of each variable
Figure 153650DEST_PATH_IMAGE058
Internal extraction
Figure 321195DEST_PATH_IMAGE059
An initial random sample point, which constitutes an initial training set
Figure 425418DEST_PATH_IMAGE060
And make an order
Figure 847172DEST_PATH_IMAGE061
For recording the number of iterations.
Wherein
Figure 440964DEST_PATH_IMAGE062
A cumulative distribution function representing a standard normal distribution, and
Figure 580958DEST_PATH_IMAGE063
expressed as the inverse of the cumulative distribution function of the variables;
4) according to a training set
Figure 488872DEST_PATH_IMAGE064
Obtaining
Figure 47023DEST_PATH_IMAGE065
Function values of the corresponding structural function functions, and constructing an agent model;
5) combining the candidate sample point set of the step 2 by using the proxy model established in the step 4
Figure 546137DEST_PATH_IMAGE066
Carrying out numerical simulation to obtain the failure probability of the structure estimated by the proxy model of the current iteration step
Figure 376690DEST_PATH_IMAGE067
；
6) Determining failure probability
Figure 619453DEST_PATH_IMAGE068
And the result of the last iteration
Figure 281378DEST_PATH_IMAGE069
Whether the relative error is less than
Figure 203591DEST_PATH_IMAGE070
To do so
Figure 521440DEST_PATH_IMAGE071
A sufficiently small constant, the convergence condition is:
Figure 567894DEST_PATH_IMAGE072
if the convergence requirement is met, acquiring a final proxy model and a final estimated failure probability;
if the convergence requirement is not satisfied or
Figure 84325DEST_PATH_IMAGE073
Then, the next step is carried out, and adaptive sequence point adding is carried out;
7) using learning functions
Figure 128505DEST_PATH_IMAGE074
For candidate sample point set
Figure 995967DEST_PATH_IMAGE075
Performing numerical simulation and obtaining the latest sample point
Figure 331264DEST_PATH_IMAGE076
And updating the training set
Figure 905465DEST_PATH_IMAGE077
. Learning function
Figure 917283DEST_PATH_IMAGE078
The specific expression of (A) is as follows:
Figure 740883DEST_PATH_IMAGE079
wherein,
Figure 394718DEST_PATH_IMAGE080
indicating points
Figure 869431DEST_PATH_IMAGE081
For training set
Figure 255413DEST_PATH_IMAGE082
The average value of the Euclidean distances of each point in the middle,
Figure 831888DEST_PATH_IMAGE083
indicating points
Figure 23834DEST_PATH_IMAGE081
For training set
Figure 103786DEST_PATH_IMAGE084
The minimum value of the Euclidean distance of each point in the middle.
Further, at the candidate sample point set
Figure 926248DEST_PATH_IMAGE085
In such a way that the function is learned
Figure 475173DEST_PATH_IMAGE086
The minimum point is selected as a new sample point by the adaptive sequence, and the specific mathematical expression is as follows:
Figure 470810DEST_PATH_IMAGE087
8) will be provided with
Figure 405268DEST_PATH_IMAGE088
Incorporation trainingCollection
Figure 398632DEST_PATH_IMAGE089
Update
Figure 949699DEST_PATH_IMAGE090
Let us order
Figure 470067DEST_PATH_IMAGE091
Returning to the step 4;
fig. 1 is a flowchart of a sequential dotting method for structural reliability analysis according to the present invention, which includes eight steps. This embodiment 1 further illustrates the present invention as a two-dimensional application example.
Example 1
1) Specifying a function of a structure to be analyzed, and determining variables and probability distribution information of the function; the function of the two-dimensional application example is as follows:
Figure 727873DEST_PATH_IMAGE092
wherein,
Figure 688876DEST_PATH_IMAGE093
represents the function of example 1, and
Figure 461659DEST_PATH_IMAGE094
is a variable of the function of the function,
Figure 533521DEST_PATH_IMAGE095
obey a normal distribution with a mean value of 1.5 and a standard deviation of 1, and
Figure 911412DEST_PATH_IMAGE096
obeying a normal distribution with a mean of 2.5 and a standard deviation of 1;
2) probability density distribution function of variable determined according to step 1
Figure 794049DEST_PATH_IMAGE097
Using Monte Carlo sampling methodTo extract
Figure 54129DEST_PATH_IMAGE098
Candidate sample points forming a set of candidate sample points
Figure 867364DEST_PATH_IMAGE099
(ii) a In this example 1, decimation
Figure 896500DEST_PATH_IMAGE100
A candidate sample point. Fig. 2 and 3 both show the obtained set of candidate sample points of the monte carlo sample
Figure 199305DEST_PATH_IMAGE101
；
3) According to the variables determined in the step 1, adopting Latin hypercube sampling to obtain the value range of each variable
Figure 149944DEST_PATH_IMAGE102
Internal extraction
Figure 812875DEST_PATH_IMAGE103
An initial random sample point, which constitutes an initial training set
Figure 962097DEST_PATH_IMAGE104
And make an order
Figure 435804DEST_PATH_IMAGE105
For recording the number of iterations. Wherein
Figure 404897DEST_PATH_IMAGE106
A cumulative distribution function representing a standard normal distribution, and
Figure 107404DEST_PATH_IMAGE107
expressed as the inverse of the cumulative distribution function of the variables;
in this embodiment, the extraction
Figure 314395DEST_PATH_IMAGE108
An initial random sample pointFig. 2 and 3 both show the initial points obtained;
4) according to a training set
Figure 693424DEST_PATH_IMAGE109
Obtaining
Figure 415392DEST_PATH_IMAGE110
Function values of the corresponding structural function, and constructing a proxy model
Figure 374121DEST_PATH_IMAGE111
(ii) a When the agent model is constructed, the existing agent model method can be adopted for construction, such as a polynomial response surface, polynomial chaotic expansion, a neural network, a support vector machine, a Kriging model and the like. The proxy model method and the like are conventional methods and are not described herein. In the embodiment, the agent models are respectively constructed by adopting a Gaussian process regression neural network method and an RBF neural network method, so that the method has strong applicability and can be suitable for the agent model method of the non-kriging model;
5) combining the candidate sample point set of the step 2 by using the proxy model established in the step 4
Figure 232355DEST_PATH_IMAGE112
Carrying out Monte Carlo numerical simulation to obtain the failure probability of the structure estimated by the proxy model of the current iteration step
Figure 565641DEST_PATH_IMAGE113
. The structure reliability analysis by using the Monte Carlo method is a mature method which is not explained here;
6) determining failure probability
Figure 509326DEST_PATH_IMAGE113
And the result of the last iteration
Figure 6167DEST_PATH_IMAGE114
Whether the relative error is less than
Figure 984487DEST_PATH_IMAGE115
Namely:
Figure 970898DEST_PATH_IMAGE116
；
if the convergence requirement is met, acquiring a final proxy model and a final estimated failure probability; if the convergence requirement is not met, performing the next step, and performing adaptive sequence point addition; in addition, when
Figure 605141DEST_PATH_IMAGE117
When the step is skipped, the next step is carried out;
in this embodiment, set up
Figure 453143DEST_PATH_IMAGE118
。
7) Pairing a set of candidate sample points using a learning function LF
Figure 285969DEST_PATH_IMAGE119
Performing numerical simulation and obtaining the latest sample point
Figure 443281DEST_PATH_IMAGE120
And updating the training set
Figure 564821DEST_PATH_IMAGE121
(ii) a Wherein the learning functionLFThe specific expression of (A) is as follows:
Figure 200202DEST_PATH_IMAGE122
wherein,
Figure 402382DEST_PATH_IMAGE123
to represent
Figure 730595DEST_PATH_IMAGE124
Point to point training set
Figure 73852DEST_PATH_IMAGE125
The average value of the Euclidean distances of each point in the middle,
Figure 778502DEST_PATH_IMAGE126
indicating points
Figure 320342DEST_PATH_IMAGE127
For training set
Figure 835768DEST_PATH_IMAGE128
The minimum value of the Euclidean distance of each point in the middle.
Further, at the candidate sample point set
Figure 666321DEST_PATH_IMAGE129
In such a way that the function is learned
Figure 643504DEST_PATH_IMAGE130
The minimum point is selected as a new sample point by the adaptive sequence, and the specific mathematical expression is as follows:
Figure 305430DEST_PATH_IMAGE131
8) will be provided with
Figure 241025DEST_PATH_IMAGE132
Incorporating training sets
Figure 558874DEST_PATH_IMAGE133
Update
Figure 580226DEST_PATH_IMAGE134
Let us order
Figure 362238DEST_PATH_IMAGE135
Returning to the step 4;
fig. 2 and fig. 3 show the final sampling result and the fitting situation of the proxy model and the true extreme state function of the structure in embodiment 1. In which fig. 2 shows the result of using a gaussian process regression neural network, and fig. 3 shows the result of using an RBF neural network as a proxy model method. More detailed results are shown in table 1.
Table 1 comparison of detailed results of the process of the invention and the monte carlo process in example 1
Figure 203155DEST_PATH_IMAGE136
As can be seen from fig. 2, fig. 3 and table 1, the failure probability of the structure can be efficiently and accurately estimated by combining different agent models and comparing monte carlo simulation in analyzing the reliability problem of the structure by using the method of the present invention, so as to meet the actual requirements of the engineering.
Example 2
In order to further show the effectiveness of the method provided by the invention, the method provided by the invention is explained in detail by providing a common engineering system as an example.
9) Specifying a function of a structure to be analyzed, and determining variables and probability distribution information of the function; in this embodiment 2, a schematic structural diagram of a common undamped single-degree-of-freedom oscillation system is shown in fig. 4. Function of oscillator
Figure 8300DEST_PATH_IMAGE137
Is defined as
Figure 592865DEST_PATH_IMAGE138
Wherein,
Figure 980115DEST_PATH_IMAGE139
of variable quantity
Figure 195196DEST_PATH_IMAGE140
The specific probability distribution is shown in table 2.
Figure 18795DEST_PATH_IMAGE141
10) Probability density distribution function of variable determined according to step 1
Figure 407051DEST_PATH_IMAGE142
Extracting by using Monte Carlo sampling method
Figure 632496DEST_PATH_IMAGE143
Candidate sample points forming a set of candidate sample points
Figure 330063DEST_PATH_IMAGE144
(ii) a In this example 2, decimation
Figure 906537DEST_PATH_IMAGE145
A candidate sample point;
11) according to the variables determined in the step 1, adopting a Latin hypercube method to obtain the value range of each variable
Figure 36167DEST_PATH_IMAGE146
Internal extraction
Figure 381698DEST_PATH_IMAGE147
An initial random sample point, which constitutes an initial training set
Figure 898DEST_PATH_IMAGE148
And make an order
Figure 2352DEST_PATH_IMAGE149
For recording the number of iterations;
wherein
Figure 217564DEST_PATH_IMAGE150
A cumulative distribution function representing a standard normal distribution, and
Figure 683181DEST_PATH_IMAGE151
expressed as the inverse of the cumulative distribution function of the variables; in this embodiment, the extraction
Figure 676544DEST_PATH_IMAGE152
An initial random sample point;
12) according to a training set
Figure 696453DEST_PATH_IMAGE153
Obtaining
Figure 230202DEST_PATH_IMAGE154
Function values of the corresponding structural function, and constructing a proxy model
Figure 802523DEST_PATH_IMAGE155
(ii) a When the agent model is constructed, the existing agent model method can be adopted for construction, such as a polynomial response surface, polynomial chaotic expansion, a neural network, a support vector machine, a Kriging model and the like. The proxy model method and the like are conventional methods and are not described herein. In the embodiment, the agent models are respectively constructed by adopting a Gaussian process regression neural network method and an RBF neural network method, so that the method has strong applicability and can be suitable for the agent model method of the non-kriging model;
13) combining the candidate sample point set of the step 2 by using the proxy model established in the step 4
Figure 497946DEST_PATH_IMAGE156
Carrying out Monte Carlo numerical simulation to obtain the failure probability of the structure estimated by the proxy model of the current iteration step
Figure 473992DEST_PATH_IMAGE157
. The structure reliability analysis by using the Monte Carlo method is a mature method which is not explained here;
14) determining failure probability
Figure 811433DEST_PATH_IMAGE158
And the result of the last iteration
Figure 720483DEST_PATH_IMAGE159
Whether the relative error is less than
Figure 55649DEST_PATH_IMAGE160
Namely:
Figure 66462DEST_PATH_IMAGE161
；
if the convergence requirement is met, acquiring a final proxy model and a final estimated failure probability; if the convergence requirement is not met, performing the next step, and performing adaptive sequence point addition; in addition, when
Figure 942014DEST_PATH_IMAGE162
When the step is skipped, the next step is carried out;
in this example 2, the setup
Figure 174412DEST_PATH_IMAGE163
；
15) Pairing a set of candidate sample points using a learning function LF
Figure 211638DEST_PATH_IMAGE164
Performing numerical simulation and obtaining the latest sample point
Figure 224594DEST_PATH_IMAGE165
And updating the training set
Figure 887525DEST_PATH_IMAGE166
(ii) a Wherein the learning functionLFThe specific expression of (A) is as follows:
Figure 974430DEST_PATH_IMAGE167
wherein,
Figure 182557DEST_PATH_IMAGE168
indicating points
Figure 151650DEST_PATH_IMAGE169
For training set
Figure 369005DEST_PATH_IMAGE170
The average value of the Euclidean distances of each point in the middle,
Figure 123465DEST_PATH_IMAGE171
indicating points
Figure 768073DEST_PATH_IMAGE169
For training centralization
Figure 427725DEST_PATH_IMAGE172
The minimum value of the Euclidean distance of each point.
Further, in the candidate sample point set
Figure 183191DEST_PATH_IMAGE173
In such a way that the function is learned
Figure 307005DEST_PATH_IMAGE174
The minimum point is selected as a new sample point by the adaptive sequence, and the specific mathematical expression is as follows:
Figure 325777DEST_PATH_IMAGE175
16) will be provided with
Figure 256080DEST_PATH_IMAGE176
Incorporating training sets
Figure 815237DEST_PATH_IMAGE170
Update
Figure 793558DEST_PATH_IMAGE177
Let us order
Figure 779968DEST_PATH_IMAGE178
Returning to the step 4;
fig. 5 shows the convergence process of the adaptive series-plus-point predicted failure probability using the gaussian process regression neural network as the proxy model method, and fig. 6 shows the convergence process of the adaptive series-plus-point predicted failure probability using the RBF neural network as the proxy model method. More detailed results are shown in table 3.
Figure 414212DEST_PATH_IMAGE179
As can be seen from fig. 5, fig. 6, and table 3, the reliability of the structure can be accurately and efficiently analyzed by using the method of the present invention in combination with different agent models, performing adaptive sequence dotting iteration by using the LF learning function, and comparing with the monte carlo simulation method after meeting the convergence condition.

Claims (5)

1. A structure reliability analysis self-adaptive point adding method for multiple agent models comprises the following steps:
1) specifying a function of a structure to be analyzed
Figure 401770DEST_PATH_IMAGE001
Determining the variables of the function
Figure 703438DEST_PATH_IMAGE002
And its probability distribution information;
2) probability density distribution function of the variable determined according to step 1)
Figure 798433DEST_PATH_IMAGE003
To extract
Figure 513449DEST_PATH_IMAGE004
Candidate sample points forming a set of candidate sample points
Figure 86512DEST_PATH_IMAGE005
；
3) According to the variables determined in the step 1), adopting a Latin hypercube method to obtain the value range of each variable
Figure 85430DEST_PATH_IMAGE006
Internal extraction
Figure 351326DEST_PATH_IMAGE007
An initial random sample point, which constitutes an initial trainingExercise and collection
Figure 225741DEST_PATH_IMAGE008
And make an order
Figure 461551DEST_PATH_IMAGE009
For recording the number of iterations;
wherein
Figure 941074DEST_PATH_IMAGE010
A cumulative distribution function representing a standard normal distribution, and
Figure 174609DEST_PATH_IMAGE011
expressed as the inverse of the cumulative distribution function of the variables;
4) according to a training set
Figure 614949DEST_PATH_IMAGE008
Obtaining
Figure 529815DEST_PATH_IMAGE012
Function values of the corresponding structural function functions, and constructing an agent model;
5) combining the candidate sample point set of the step 2) by using the proxy model established in the step 4
Figure 926161DEST_PATH_IMAGE013
Carrying out numerical simulation to obtain the failure probability of the structure estimated by the proxy model of the current iteration step
Figure 658494DEST_PATH_IMAGE014
；
6) Determining failure probability
Figure 179605DEST_PATH_IMAGE015
And the result of the last iteration
Figure 960479DEST_PATH_IMAGE016
Whether the relative error is less than
Figure 791425DEST_PATH_IMAGE017
To do so
Figure 304446DEST_PATH_IMAGE018
A sufficiently small constant, the convergence condition is:
Figure 703067DEST_PATH_IMAGE019
if the convergence requirement is met, acquiring a final proxy model and a final estimated failure probability;
if the convergence requirement is not satisfied or
Figure 22053DEST_PATH_IMAGE020
Then, the next step is carried out, and adaptive sequence point adding is carried out;
7) by using
Figure 65095DEST_PATH_IMAGE021
Learning function versus set of candidate sample points
Figure 889963DEST_PATH_IMAGE022
Performing numerical simulation and obtaining the latest sample point
Figure 713562DEST_PATH_IMAGE023
And updating the training set
Figure 508343DEST_PATH_IMAGE024
(ii) a Wherein the learning function
Figure 61684DEST_PATH_IMAGE021
The specific expression of (A) is as follows:
Figure 182087DEST_PATH_IMAGE025
wherein,
Figure 227403DEST_PATH_IMAGE026
indicating points
Figure 199776DEST_PATH_IMAGE027
For training set
Figure 482990DEST_PATH_IMAGE028
The average value of the Euclidean distances of each point in the middle,
Figure 571031DEST_PATH_IMAGE029
indicating points
Figure 165961DEST_PATH_IMAGE030
For training set
Figure 833703DEST_PATH_IMAGE028
The minimum value of the Euclidean distance of each point in the middle;
8) will be provided with
Figure 768161DEST_PATH_IMAGE031
Incorporating training sets
Figure 105732DEST_PATH_IMAGE032
Update
Figure 63324DEST_PATH_IMAGE033
Let us order
Figure 331494DEST_PATH_IMAGE034
Go back to step 4).
2. The sequential dotting method for structural reliability analysis according to claim 1, wherein: step 7) introduction
Figure 448355DEST_PATH_IMAGE035
To ensure afterThe adaptive sample points are used to improve the extreme state function of the current proxy model, and
Figure 815882DEST_PATH_IMAGE036
then the weight is increased where the sample points are least dense, as a global consideration, and, on the other hand,
Figure 323087DEST_PATH_IMAGE037
it is to avoid that the sample points are too dense; while
Figure 709462DEST_PATH_IMAGE038
Can ensure that the estimated failure probability can depend on the whole iteration process
Figure 290616DEST_PATH_IMAGE039
And convergence is carried out, and the robustness of the iterative process is ensured.
3. The adaptive dotting method for the structural reliability analysis of multiple proxy models according to claim 1 or 2, characterized in that: step 7) at the set of candidate sample points
Figure 156941DEST_PATH_IMAGE040
In, make learning function
Figure 213759DEST_PATH_IMAGE041
The smallest point will be selected by the adaptive sequence as the new sample point.
4. The adaptive dotting method for the structural reliability analysis of multiple agent models according to claim 3, wherein: step 7) at the set of candidate sample points
Figure 761415DEST_PATH_IMAGE042
The specific mathematical expression of (a) is as follows:
Figure 259392DEST_PATH_IMAGE043
。
5. the adaptive dotting method for the structural reliability analysis of multiple proxy models according to claim 4, wherein: extraction as described in step 2)And extracting the candidate sample points by adopting a Monte Carlo sampling method.
CN202010665412.2A 2020-07-11 2020-07-11 Structure reliability analysis self-adaptive point adding method for multiple agent models Pending CN111797535A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010665412.2A CN111797535A (en) 2020-07-11 2020-07-11 Structure reliability analysis self-adaptive point adding method for multiple agent models

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010665412.2A CN111797535A (en) 2020-07-11 2020-07-11 Structure reliability analysis self-adaptive point adding method for multiple agent models

Publications (1)

Publication Number Publication Date
CN111797535A true CN111797535A (en) 2020-10-20

Family

ID=72808205

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010665412.2A Pending CN111797535A (en) 2020-07-11 2020-07-11 Structure reliability analysis self-adaptive point adding method for multiple agent models

Country Status (1)

Country Link
CN (1) CN111797535A (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113221263A (en) * 2021-04-20 2021-08-06 浙江工业大学 Mechanical product structure failure optimization method considering distribution parameter uncertainty
CN113239495A (en) * 2021-05-31 2021-08-10 复旦大学 Complex structure reliability design method based on vector hybrid agent model
CN115358097A (en) * 2022-10-20 2022-11-18 河北工业大学 Maximum thrust reliability analysis method for solid attitude and orbit control engine gas valve
CN116070924A (en) * 2023-03-07 2023-05-05 西南交通大学 Tunnel supporting scheme decision method and system based on Gaussian process regression

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113221263A (en) * 2021-04-20 2021-08-06 浙江工业大学 Mechanical product structure failure optimization method considering distribution parameter uncertainty
CN113221263B (en) * 2021-04-20 2024-03-26 浙江工业大学 Mechanical product structure failure optimization method considering uncertainty of distribution parameters
CN113239495A (en) * 2021-05-31 2021-08-10 复旦大学 Complex structure reliability design method based on vector hybrid agent model
CN115358097A (en) * 2022-10-20 2022-11-18 河北工业大学 Maximum thrust reliability analysis method for solid attitude and orbit control engine gas valve
CN115358097B (en) * 2022-10-20 2023-01-03 河北工业大学 Maximum thrust reliability analysis method for solid attitude and orbit control engine gas valve
CN116070924A (en) * 2023-03-07 2023-05-05 西南交通大学 Tunnel supporting scheme decision method and system based on Gaussian process regression
CN116070924B (en) * 2023-03-07 2023-06-02 西南交通大学 Tunnel supporting scheme decision method and system based on Gaussian process regression

Similar Documents

Publication Publication Date Title
CN111797535A (en) Structure reliability analysis self-adaptive point adding method for multiple agent models
Tong et al. A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling
CN108664400A (en) A kind of construction method of the fault diagnosis technology based on interdependent Bayesian network
CN108287808B (en) Universal dynamic tracking sequence sampling method for structural reliability analysis
CN112187554B (en) Operation and maintenance system fault positioning method and system based on Monte Carlo tree search
CN110262245A (en) The controller design method of multi-agent system based on event trigger mechanism
CN112580228B (en) Fan blade structural design optimization method for mixed structure of turbofan engine
CN114282725A (en) Construction of transient oil reservoir agent model based on deep learning and oil reservoir prediction method
Lugaresi et al. Real-time validation of digital models for manufacturing systems: A novel signal-processing-based approach
CN112327810A (en) Fault estimation method of dynamic event triggered transmission Markov jump system
Xu et al. Robust filter design for asymmetric measurement noise using variational Bayesian inference
Sathe et al. Creating probabilistic databases from imprecise time-series data
CN113609763B (en) Uncertainty-based satellite component layout temperature field prediction method
Yu et al. Running time analysis: Convergence-based analysis reduces to switch analysis
CN116467466A (en) Knowledge graph-based code recommendation method, device, equipment and medium
CN116540546A (en) Recommendation method, system, equipment and medium for control parameters of process control system
CN114757391B (en) Network data space design and application method oriented to service quality prediction
Dutordoir et al. Deep Gaussian process metamodeling of sequentially sampled non-stationary response surfaces
CN111694969B (en) User identity identification method and device
Lin et al. Smart building uncertainty analysis via adaptive Lasso
CN111783236A (en) Turbine casing sensitivity analysis method based on self-adaptive model and subset simulation
Behrensdorf et al. Interval Predictor Model for the Survival Signature Using Monotone Radial Basis Functions
Lokshina et al. Accelerated rare event simulation with Markov chain modelling in wireless communication networks
Li et al. Reliability-based design optimization based on weighted simulation and Kriging model
Xu et al. Online personalized QoS prediction approach for cloud services

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
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20201020