CN107480344A - A kind of series stress-strength system reliability self-adaptive estimation method - Google Patents
A kind of series stress-strength system reliability self-adaptive estimation method Download PDFInfo
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Abstract
The invention discloses a kind of series stress-strength system reliability self-adaptive estimation method, carry out Monte-carlo Simulation identification failure sample to failure mode every time by iteration, and select a new failure mode adaptively to assess Series System Reliability so as to realize, it can effectively reduce calculating consumption.This method step is simple, assesses obtained system dependability monotonic increase and progressively restrains, and calculates that consumption is few, assesses for the system dependability for engineering structure of connecting and provides a kind of new scheme.
Description
Technical field
The invention belongs to structural reliability assessment technology field, more particularly to a kind of series stress-strength system reliability are adaptive
Appraisal procedure.
Background technology
In Practical Project, structural failure is often the system dependability problem for including multi-failure pattern.Structural failure is pressed
Relation between failure mode can be divided into train, parallel system and combined hybrid system.Train refers to arbitrarily lose in system
Effect pattern occurs destruction and results in system global failure；Parallel system refer in system all failure modes occur to destroy just make be
System global failure；Combined hybrid system refers to not only include series connection failure mode but also the system for including failure mode in parallel.As can be seen that string
It is minimum to be coupled construction system redundancy, it is more dangerous.The example of many trains in engineering structure be present, such as truss, side
Slope, retaining wall, pipeline, transmission tower etc..These engineering structures usually contain a large amount of failure modes, due to that can not determine which loses
Effect pattern is most likely to occur, and all failure modes need to be analyzed when assessing system dependability, what system dependability was assessed
Complexity and calculating consumption are higher.
At present, traditional structural reliability appraisal procedure has Taylor series expansion method (such as FOSM, single order can
By degree method, second order reliability method etc.), Response surface meth od (such as general polynomial response surface, Hermite polynomial response surfaces,
Sparse polynomial response surface etc.), Method of Stochastic (such as Monte Carlo simulation (Monte Carlo simulation, MCS),
Subset simulation, importance sampling etc.) etc..Although these methods are used equally for structural reliability to assess, but still lack to tandem junction
The fast evaluation method of construction system reliability.Specifically, Taylor series expansion method, Response surface meth od are generally used for structure list
The Reliability assessment of one failure mode, if they are assessed applied to system dependability, it calculates performance and is limited by failure mode
The nonlinear degree of quantity and power function.By comparison, above mentioned problem is then not present in stochastic simulation Reliability assessment method, fits
In solving the problems, such as Series System Reliability.By taking Monte Carlo simulation as an example, it by produce it is a series of obey given distribution with
Press proof sheet and analytical structure system, which respond, carrys out evaluation structure system dependability, has the advantages that concept is simple, easily implements.So
And traditional analogy method needs to produce substantial amounts of random sample, and using every group of sample as input, analysis calculates all failures
Pattern obtains structural system response, finally gives structural systems reliability, and it is huge that the process calculates consumption.For including 103It is individual
Failure mode, failure probability 10-3Series stress-strength system, according to Monte-carlo Simulation Method to the cascaded structure system
System reliability analysis, typically at least needs 104Random sample is organized to ensure that the coefficient of variation for assessing obtained failure probability is less than
0.3, then the process should at least analyze calculating 103×104=107Subfunction function.As can be seen here, it is reliable with traditional structure
There is many limitations in degree appraisal procedure, it is big to calculate consumption when carrying out Reliability assessment to series stress-strength system.
In view of above-mentioned analysis, it is necessary to propose a kind of new, efficient series stress-strength system Reliability assessment method.
The content of the invention
, should in view of the deficiencies of the prior art, the present invention provides a kind of series stress-strength system reliability self-adaptive estimation method
Method advantageously reduces the calculating consumption of series stress-strength system Reliability assessment process.
The technical solution adopted in the present invention is：Step 1：Determine the input parameter of series stress-strength system, stochastic variable and
Failure mode and its power function；
Step 2：The N group random samples of given stochastic variable distribution are obeyed using Monte Carlo simulation generation；
Step 3：Iterations k=1 is made, it is the failure mode do not analyzed to mark all failure modes, marks all samples
For the sample do not analyzed；
Step 4：A failure mode do not analyzed is selected from all failure modes of series stress-strength system, makes its function letter
Number is gk；
Step 5：Caused N groups sample is as input using in step 2, power function g corresponding to failure mode selected by substitutionk
MCS analyses are carried out, and it is the failure mode analyzed to mark the failure mode；
Step 6：Obtain power function gkN number of structural response, structural response be less than specific threshold sample be fail
Sample, these failure samples are added into a failure sample set；Number of samples is N in the failure sample setf,k, all samples
Originally it is thrashing sample, then the Failure Probability of Structural Systems that current iteration obtains is Pf,k=Nf,k/N；
Step 7：The one group of failure do not analyzed sample is selected from failure sample set, if being not present in failure sample set
The failure sample do not analyzed, then from remaining N-Nf,kOne group of sample is selected in group sample；
Step 8：Using selected sample as input, analysis calculates the response of all power functions of series stress-strength system, and marks
It is the failure sample analyzed to remember the sample；
Step 9：Judge whether to meet the condition of convergence；
Iterations k=k+1 is made if being unsatisfactory for, return to step 4 repeats step 4- steps 9；
If meeting the condition of convergence, iteration is terminated, series stress-strength system failure probability is Pf,sys=Nf,k/N。
The beneficial effects of the invention are as follows：
Compared with prior art, traditional Monte-carlo Simulation Method every time using one group of sample as input and analysis system in
The response of all failure modes, once analysis at most confirm that one group of sample is low for failure sample, computational efficiency.It is of the invention substantial
It is more efficiently to identify failure sample by analyzing failure mode, while new mistake is identified further through analysis failure sample
Effect pattern, it is achieved thereby that adaptively assessing series stress-strength system failure probability.Increase with iterations, the failure sample of identification
Originally it is on the increase, System failure probability is in monotonic increase and Step wise approximation convergence.Shown by instance analysis, it is proposed by the invention
Series stress-strength system reliability self-adaptive estimation method can to series stress-strength system failure probability realize efficiently and accurately comment
Estimate.
Brief description of the drawings
Fig. 1 is the flow chart of the embodiment of the present invention.
Fig. 2 is power function schematic diagram in the embodiment of the present invention 1.
Fig. 3 is System failure probability adaptive change figure in the embodiment of the present invention 1.
Fig. 4 is the slope sliding face schematic diagram in the embodiment of the present invention 2.
Fig. 5 is the System failure probability adaptive change figure in the embodiment of the present invention 2.
Embodiment
Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with the accompanying drawings and embodiment is to this hair
It is bright to be described in further detail, it will be appreciated that implementation example described herein is merely to illustrate and explain the present invention, not
For limiting the present invention.
As shown in figure 1, the present invention proposes a kind of series stress-strength system reliability self-adaptive estimation method, below for 2
Individual embodiment describes technical scheme provided by the invention in detail.Embodiment 1 is by 1000 failure modes structure in series
System, embodiment 2 are a side slope train.But protection scope of the present invention is not limited to the embodiment.
Embodiment 1：
The system is in series by 1000 failure modes, and the power function of failure mode is Z=a1X1+a2X2+βe, wherein
0≤a1≤ 1,Stochastic variable X1、X2Independent standard normal distribution is obeyed, takes β heree=2.326 may be such that often
The failure probability of individual failure mode is equal, and about 0.01.Fig. 2 depicts 1 all power functions of embodiment in standard normal space
Schematic diagram.The series stress-strength system failure probability will be assessed using technical scheme proposed by the present invention below.
Step 1：Determine input parameter, stochastic variable and the failure mode and its power function of series stress-strength system；
Step 2：The N group random samples of given stochastic variable distribution are obeyed using Monte Carlo simulation generation.For implementing
Example 1, the two-dimentional independent standard normal distribution random sample of N=10000 groups can be generated；
Step 3：Iterations k=1 is made, it is the failure mode do not analyzed to mark all failure modes, marks all samples
For the sample do not analyzed；
Step 4：A failure mode do not analyzed is selected from all failure modes of structural system, makes its power function determine
Justice is gk.If the 1st iteration (i.e. k=1), random selection One function function is as g1.If kth (k=2,
3 ...) secondary iteration, all power function responses that can obtain step 8 arrange from small to large, select first not analyze
Power function is as gk；
Step 5：Using N groups sample caused by step 2 as input, power function g is substituted intokMCS analyses are carried out, and marks and is somebody's turn to do
Failure mode is the failure mode analyzed；
Step 6：The power function g obtained according to step 5kN number of structural response, structural response is less than specific threshold (i.e. gk
<0) sample is the sample that fails, and these failure samples are added into a failure sample set.Number of samples is in the set
Nf,k, all samples are thrashing sample, then the Failure Probability of Structural Systems that current iteration obtains is Pf,k=Nf,k/N；
Step 7：The one group of failure do not analyzed sample is selected from failure sample set, if being not present in failure sample set
The failure sample do not analyzed, then from remaining N-Nf,kOne group of sample is selected in group sample.Here arbitrary sample can be selected.Pin
To embodiment 1, by power function gkN number of sample responses value arrange from small to large and select first sample do not analyzed；
Step 8：Using selected sample as input, the response of all power functions of analytical structure system, and mark the sample
To have analyzed；
Step 9：Judge whether to meet the condition of convergence；
Iterations k=k+1 is made if being unsatisfactory for, return to step 4 repeats step 4- steps 9.For embodiment 1,
If iterations k is more than the number of structural system failure mode, or the continuous a iteration steps of System failure probability that step 6 obtains
Do not change, i.e. Pf,k-a/Pf,k>0.995, then it is assumed that meet the condition of convergence, otherwise return to step 4 repeats step 4- steps
Rapid 9.Here a=20 is taken.
If meeting the condition of convergence, iteration, Failure Probability of Structural Systems P are terminatedf,sys=Nf,k/N。
According to above step, adaptive approach proposed by the present invention is applied to embodiment 1, obtained structural system failure
Probability is shown in Fig. 3.It can be seen that the failure probability monotonic increase that iteration obtains, it is only necessary to which 38 times iteration reaches convergence, obtains embodiment 1 and goes here and there
Connection Failure Probability of Structural Systems is Pf,sys=2.66 × 10-2, fitted like a glove with the result of Monte Carlo simulation.
The equivalent sample analysis times N of generally useTCarry out the calculating consumption of reliable degree method.It is N for number of samples
For=10000 Monte Carlo simulation, its equivalent sample analysis number is NT,MCS=N=10000；And the inventive method is each
Iteration is related to the structural system response analysis of one group of sample and the sound of input analysis simple function function is used as using N groups sample
Should, though number of samples is equally N=10000, its equivalent sample analysis number is only NT,ADP=38 × (1,+10 000/1000)
=418.The calculating consumption of the inventive method just corresponds to 418/10 000=4.18% of Monte Carlo simulation.
In order to further illustrate the convergence and computational efficiency of institute's extracting method of the present invention, the inventive method and illiteracy are repeated
Each 50 times of special Carlow analogy method, obtains the system dependability assessment result of embodiment 1 and is shown in Table 1.
The system dependability assessment result of 1 embodiment of table 1
Note：(a) 50 simulations are repeated to obtain.
The result of table 1 is shown, uses the average system failure probability that the inventive method is repeatedly simulated to obtain as 2.61 × 10-2,
The System failure probability that Monte-carlo Simulation Method obtains is 2.66 × 10-2, the two almost fits like a glove, and demonstrates present invention side
Method has good convergence.In order to consider the calculating consumption of assessment system failure probability and variability, calculate respectively
The Unit COV values of two methods.The Unit COV of Monte-carlo Simulation Method are 5.82, and the Unit COV of the inventive method are
1.43, only the 1/4 of Monte-carlo Simulation Method.The result shows under the premise of identical System failure probability variability, this
Equivalent sample size needed for inventive method is only the 1/16 of Monte-carlo Simulation Method.The above results illustrate the inventive method
Accuracy and computational efficiency advantage for extensive series stress-strength system Reliability assessment.
Embodiment 2：
Unstability, which occurs, for any one sliding surface in slope project causes slope system to fail, therefore side slope is generally viewed as going here and there
Contact system.As shown in figure 4, the embodiment is an individual layer slight slope, division has 12659 sliding surfaces, and each sliding surface is one
Failure mode, the slight slope can be considered as including the series stress-strength system reliability issues of 12659 failure modes.
Severe γ=20kN/m of the individual layer slight slope soil body3, cohesive strength c and internalfrictionangleφ obey logarithm normal distribution,
Average be respectively 10kPa, 30 °, the coefficient of variation is respectively 0.3 and 0.2.Cohesive strength and internal friction angle are negatively correlated, coefficient correlation
For -0.7.In addition, using the Spatial Variability of random field stimulation Soil Parameters, fluctuation range is respectively 20m and 2m, dependency structure
For exponential type.Soil Parameters are taken with average and carries out Analysis of Slope Stability and can obtain critical certainty sliding surface (see Fig. 4).
For embodiment 2, the power function expression formula of each failure mode (sliding surface) is Z=FS-1, and wherein FS is should
The safety coefficient of sliding surface, it need to be obtained by Analysis of Slope Stability.Being assessed below using technical scheme proposed by the present invention should
The system dependability of side slope.
Step 1：Determine input parameter, stochastic variable and the failure mode and its power function of series stress-strength system；
Step 2：The N group random samples of given stochastic variable distribution are obeyed using Monte Carlo simulation generation；For implementing
Example 2, the logarithm normal distribution sample that N=5000 groups obey soil strength parameter distribution can be generated.
Step 3：Iterations k=1 is made, it is the sliding surface do not analyzed to mark all sliding surfaces, marks all samples as not
The sample of analysis；
Step 4：A sliding surface do not analyzed is selected from all sliding surfaces of slope system, makes the implicit work(of the sliding surface
Energy function is defined as gk.For embodiment 2, if the 1st iteration (i.e. k=1), can randomly choose a sliding surface, here
Select sliding surface of the critical certainty sliding surface (see Fig. 4) as the 1st iteration.(k=2,3 ...) the secondary iteration if kth,
All sliding surface responses that step 8 can be obtained arrange from small to large, select sliding surface of first mark for analysis；
Step 5：Using N groups sample caused by step 2 as input, sliding surface g is substituted intokMCS analyses are carried out, and marks and is somebody's turn to do
Sliding surface is the sliding surface analyzed；
Step 6：The sliding surface g obtained according to step 5kN number of structural response, structural response is less than specific threshold (Z<0 or
FS<1) sample is the sample that fails, and these failure samples are added into a failure sample set.Number of samples is in the set
Nf,k, all samples are thrashing sample, then the Failure Probability of Structural Systems that current iteration obtains is Pf,k=Nf,k/N；
Step 7：The one group of failure do not analyzed sample is selected from failure sample set, if being not present in failure sample set
The failure sample do not analyzed, then from remaining N-Nf,kOne group of sample is selected in group sample.For embodiment 2, here in failure sample
The failure sample do not analyzed is selected in this set, if being not present, by sliding surface gkThe response of other samples is arranged from small to large
Row, select first group of sample do not analyzed；
Step 8：Using selected sample as input, all sliding surfaces carry out stability analysis in side slope, and mark the sample
This is to have analyzed sample.For embodiment 2, if the response minimum value of all sliding surfaces is less than specific threshold (Z<0 or min (FS)<
1), then the sample is added into failure sample set；
Step 9：Judge whether to meet the condition of convergence；
Iterations k=k+1 is made if being unsatisfactory for, return to step 4 repeats step 4- steps 9.For embodiment 2,
If iterations k is more than the number of structural system failure mode, or the System failure probability that step 6 obtains is after a iteration steps
Keep almost unchanged, i.e. Pf,k-a/Pf,k>0.995, then it is assumed that meet the condition of convergence, otherwise return to step 4 repeats step 4-
Step 9.Because side slope non linear efficacy function is stronger, a=100 is taken here.
If meeting the condition of convergence, iteration, Failure Probability of Structural Systems P are terminatedf,sys=Nf,k/N。
According to above-mentioned steps, adaptive approach proposed by the present invention is applied to embodiment 2, obtained System failure probability
See Fig. 5.It can be seen that the failure probability monotonic increase that iteration obtains, it is only necessary to which 112 times iteration restrains, and it is general to obtain train failure
Rate is Pf,sys=4.20 × 10-3, fitted like a glove with the result of Monte Carlo simulation, result verification the inventive method can answer
Assessed for engineering slope system dependability.
For embodiment 2, the equivalent sample analysis number of Monte-carlo Simulation Method is NT,MCS=5000；And present invention side
Equivalent sample analysis number needed for method is NT,ADP=112 × (1+5 000,/12 659)=156, only Monte Carlo simulation side
The 3.12% of method.
In order to further illustrate the convergence and computational efficiency of institute's extracting method of the present invention, this is repeated for embodiment 2
Inventive method 30 times, obtained system dependability assessment result are shown in Table 2.
The system dependability assessment result of 2 embodiment of table 2
The result of table 2 shows that it is 4.30 × 10 that the inventive method, which repeatedly simulates obtained average system failure probability,-3, cover special
The System failure probability that Carlow analogy method obtains is 4.20 × 10-3, the two almost fits like a glove.Monte-carlo Simulation Method
Unit COV are 15.41, and the Unit COV of the inventive method are 2.33, only the 1/6 of Monte-carlo Simulation Method less than.The knot
Fruit shows that under the premise of identical System failure probability variability the equivalent sample size needed for the inventive method is only Meng Teka
The 1/36 of Lip river analogy method.The above results show that the inventive method can be used for the system for accurately and efficiently assessing slope project can
Assessed by degree.
It should be appreciated that the part that this specification does not elaborate belongs to prior art.
It should be appreciated that the above-mentioned description for preferred embodiment is more detailed, therefore can not be considered to this
The limitation of invention patent protection scope, one of ordinary skill in the art are not departing from power of the present invention under the enlightenment of the present invention
Profit is required under protected ambit, can also be made replacement or deformation, be each fallen within protection scope of the present invention, this hair
It is bright scope is claimed to be determined by the appended claims.
Claims (4)
- A kind of 1. series stress-strength system reliability self-adaptive estimation method, it is characterised in that comprise the following steps：Step 1：Determine input parameter, stochastic variable and the failure mode and its power function of series stress-strength system；Step 2：The N group random samples of given stochastic variable distribution are obeyed using Monte Carlo simulation generation；Step 3：Iterations k=1 is made, it is the failure mode do not analyzed to mark all failure modes, marks all samples as not The sample of analysis；Step 4：A failure mode do not analyzed is selected from all failure modes of series stress-strength system, makes its power function be gk；Step 5：Caused N groups sample is as input using in step 2, power function g corresponding to failure mode selected by substitutionkCarry out MCS is analyzed, and it is the failure mode analyzed to mark the failure mode；Step 6：Obtain power function gkN number of structural response, structural response be less than specific threshold sample be fail sample, These failure samples are added into a failure sample set；Number of samples is N in the failure sample setf,k, all samples are Thrashing sample, the then Failure Probability of Structural Systems that current iteration obtains are Pf,k=Nf,k/N；Step 7：The one group of failure do not analyzed sample is selected from failure sample set, is not divided if being not present in failure sample set The failure sample of analysis, then from remaining N-Nf,kOne group of sample is selected in group sample；Step 8：Using selected sample as input, analysis calculates the response of all power functions of series stress-strength system, and marks and be somebody's turn to do Sample is the failure sample analyzed；Step 9：Judge whether to meet the condition of convergence；Iterations k=k+1 is made if being unsatisfactory for, return to step 4 repeats step 4- steps 9；If meeting the condition of convergence, iteration is terminated, series stress-strength system failure probability is Pf,sys=Nf,k/N。
- 2. series stress-strength system reliability self-adaptive estimation method according to claim 1, it is characterised in that：In step 4, A failure mode do not analyzed is randomly choosed, or a failure mode is selected according to the response of failure mode.
- 3. series stress-strength system reliability self-adaptive estimation method according to claim 1, it is characterised in that：In step 7, A failure sample do not analyzed is randomly choosed, or a sample is selected according to the response of sample.
- 4. series stress-strength system reliability self-adaptive estimation method according to claim 1, it is characterised in that：In step 9, If iterations k is more than the number of structural system failure mode, or the continuous a iteration steps of System failure probability that step 6 obtains Do not change, then it is assumed that meet the condition of convergence.
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| CN109063285A (en) * | 2018-07-18 | 2018-12-21 | 南昌大学 | A kind of slight slope layout scheme of boreholes design method |
| CN110532513A (en) * | 2019-07-11 | 2019-12-03 | 肇庆学院 | Vehicle rollover prediction algorithm based on radius importance sampling failure probability method |
| CN110737988A (en) * | 2019-10-17 | 2020-01-31 | 武汉大学 | slope reliability self-adaptive evaluation method |
| CN111695222A (en) * | 2020-05-25 | 2020-09-22 | 智强通达科技（北京）有限公司 | Finished oil reserve optimization method and decision-making assisting system based on cost limitation |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109063285A (en) * | 2018-07-18 | 2018-12-21 | 南昌大学 | A kind of slight slope layout scheme of boreholes design method |
| CN109063285B (en) * | 2018-07-18 | 2022-12-02 | 南昌大学 | Design method of earth slope drilling arrangement scheme |
| CN110532513A (en) * | 2019-07-11 | 2019-12-03 | 肇庆学院 | Vehicle rollover prediction algorithm based on radius importance sampling failure probability method |
| CN110737988A (en) * | 2019-10-17 | 2020-01-31 | 武汉大学 | slope reliability self-adaptive evaluation method |
| CN111695222A (en) * | 2020-05-25 | 2020-09-22 | 智强通达科技（北京）有限公司 | Finished oil reserve optimization method and decision-making assisting system based on cost limitation |
| CN111695222B (en) * | 2020-05-25 | 2023-08-04 | 智强通达科技（北京）有限公司 | Finished oil storage optimization method based on cost limitation and auxiliary decision-making system |
| CN113343431A (en) * | 2021-05-19 | 2021-09-03 | 暨南大学 | Structural system reliability analysis method based on differential evolution algorithm and equivalent plane method |
| CN113343431B (en) * | 2021-05-19 | 2022-03-22 | 暨南大学 | Structural system reliability analysis method based on differential evolution and equivalent plane method |
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