CN115146466A - System failure probability calculation method under multi-failure mode based on multi-point and point-adding criterion - Google Patents
System failure probability calculation method under multi-failure mode based on multi-point and point-adding criterion Download PDFInfo
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Abstract
The invention relates to a system failure probability calculation method under multiple failure modes based on a multipoint adding point criterion, which comprises the following steps: setting a learning function of the system and a failure mode needing to be updated; constructing a Kriging model of each failure mode according to the initial training sample set, and judging the convergence of the Kriging model; when a second convergence condition is met, classifying the sample set S, and carrying out optimization solution on a new clustering quality evaluation function J to obtain k final classification center sample points; calculating failure modes needing to be updated corresponding to the classification center sample points and merging the points with the same failure modes; updating the training sample set corresponding to each mode, and continuously constructing the Kriging model of each failure mode according to the training sample set at the moment; until the first convergence condition is satisfied, calculating the failure probability of the system. The improved composite criterion method based on the multipoint adding criterion can improve the calculation efficiency while ensuring the calculation accuracy when calculating the failure probability of the system.
Description
Technical Field
The invention relates to the technical field of structural system reliability, in particular to a method for calculating system failure probability under a multi-failure mode based on a multi-point and point-adding criterion.
Background
Efficient solution of failure probability of a structural system in a multi-failure mode is one of key problems in reliability research of the structural system. Compared with the failure probability solution of a single failure mode, the strong correlation between failure modes in the structural system under multiple failure modes and the complex relationship between the input variable and the system failure event all cause the difficulty and high cost in calculating the failure probability of the structural system under multiple failure modes.
Aiming at the reliability solving problem of a structural system with multiple failure modes, the solving strategy based on the self-adaptive Kriging agent model (AK-MCS) method mainly comprises three types: single mode surrogate, extreme surrogate, composite criterion. The composite criterion method only focuses on fitting the failure interface of the structural system, so that fitting between input variables and extreme values is avoided, and the method has greater advantages in calculating the failure probability of the structural system compared with other two methods. Corresponding learning function U sK (x) Comprises the following steps:
in the formula (I), the compound is shown in the specification,
for a system predictor containing l failure modes, for a series system,
predict values for each failure mode
Minimum of (i), i.e.
The mode needing to be updated is
For a parallel system, the number of parallel systems,
the mode needing to be updated is
The corresponding predicted standard deviation.
However, since the learning function in the composite rule method is used to identify the pattern of the extreme value under the Kriging agent model which is not converged, it is easy to cause the key that the influence on the system failure is the greatestThe failure mode is identified incorrectly, which further affects the final calculation efficiency and calculation result. For example, for a series system with two failure modes, at a given sample point x (*) The true function value is:
at this point, the true system state is invalid. The function values predicted by the current Kriging agent model which is not converged are as follows:
at this time, the Kriging agent model g constructed for Pattern 1 at present 1K At x (*) The prediction of mode 1 is inaccurate, i.e. the learning function U of mode 1 1 (x (*) ) Is less than 2; and Kriging agent model g constructed aiming at failure mode 2 2K At x (*) The prediction of mode 2 is accurate, i.e. U 2 (x (*) ) Not less than 2. According to a learning function U in a composite criterion method s (x) Is the minimum value pattern corresponds to x (*) The value of the learning function at, this time, x (*) The mode of the minimum value is "2", so x (*) Learning function value U of agent system failure boundary s (x (*) )＝U 2 (x (*) ) Not less than 2, namely the Kriging proxy model pair x constructed for each failure mode currently (*) The state of the system is judged to be safe and the judgment at that point is considered to be accurate, which is clearly not in accordance with the true system state.
In addition, when the failure probability of the system is calculated by the traditional compound criterion algorithm, only a Kriging agent model of each mode is constructed in a single-point adding mode. Although the single-point adding method can select the point in the sample pool which has the largest contribution to system failure boundary identification, the distance information among the samples is ignored, so that information redundancy is easily caused to the selected sample due to the fact that the distance is short, a Kriging model needs to be reconstructed every time the training sample set is updated, and the Kriging model is very time-consuming to construct due to the single-point adding method. Therefore, it is inefficient to calculate the probability of failure of a system with multiple failure modes based on a single point plus point approach.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a system failure probability calculation method under a multi-failure mode based on a multi-point and point criterion, and solves the defects of the conventional system failure probability calculation method.
The purpose of the invention is realized by the following technical scheme: a system failure probability calculation method under multiple failure modes based on a multipoint plus point criterion comprises the following steps:
s1, respectively setting a learning function of a system and a failure mode needing to be updated as U C And C, and calculating a learning function U C ；
S2, constructing a Kriging model of each failure mode according to the initial training sample set, and judging the convergence of the current Kriging model;
s3, when the second convergence condition is met, classifying the sample set S based on the weighted K-medoids algorithm, carrying out optimization solution on the new clustering quality evaluation function J, and obtaining K final classification center sample points { x o1 ,x o2 ,...,x ok }；
S4, calculating sample points { x) of classification centers o1 ,x o2 ,...,x ok A corresponding failure mode needing to be updated is combined with the points of the same failure mode;
s5, updating the training sample set corresponding to each mode, and continuously constructing the Kriging model of each failure mode according to the training sample set at the moment;
and S6, calculating the failure probability of the system according to the failure domain indication functions of the series system and the parallel system of the Kriging model until the first convergence condition is met.
The system failure probability calculation method further comprises a step S0, wherein the step S0 comprises the steps of generating a sample pool S and constructing Kriging models of failure models according to initial training sample sets corresponding to failure modes generated by the sample pool S.
The step of generating the sample pool S and constructing the Kriging model of each failure model according to the initial training sample set corresponding to each failure mode generated by the sample pool S specifically comprises the following steps:
s01, through inputting the joint probability density function f of the random variable X X (x) Generating a pool of samples S = { x) of capacity N 1 ,x 2 ,...,x N }；
S02, randomly extracting N in S 0 A sample is obtained, and each failure mode is calculated in N 0 The real function values under each sample form initial training sample sets corresponding to respective failure modes by the initial input samples and the output response values of the failure modes respectively;
and S03, constructing a Kriging model of each failure mode by using the initial training sample set corresponding to each failure mode.
The compute classification center sample point { x } o1 ,x o2 ,...,x ok The corresponding failure modes needing to be updated and the merging treatment of the points of the same failure modes comprise:
s41, calculating { x) according to failure mode C updated by system requirements o1 ,x o2 ,...,x ok The corresponding mode number;
s42, calculating { x o1 ,x o2 ,...,x ok Corresponding each sample point in the data to the real output of the failure mode;
and S43, combining the input sample points and the output sample points with the same pattern number to serve as a training sample set needing to be updated in the pattern.
The first convergence condition is
At the moment, the accuracy of the sign of the output response value corresponding to each sample point in the sample pool S is judged by the Kriging model to reach a preset value, and the self-adaptive learning process is stopped; the second convergence condition
At the moment, the Kriging model judges that the accuracy of the sign of the output response value corresponding to each sample point in the sample pool S does not reach the preset value, and then the self-adaptive learning is continued.
The invention has the following advantages: a system failure probability calculation method under multiple failure modes based on a multipoint plus point criterion reserves extreme information predicted by a Kriging model of each failure mode and accelerates the identification speed of a system failure boundary; the method solves the problem of point selection redundancy caused by only considering U value information and neglecting distance information between sample points in the traditional single-point adding mode based on the weighted clustering multi-point adding criterion, and can select the number of a plurality of sample points needing to be updated due to one-time learning, thereby quickening the construction efficiency of the corresponding Kriging agent model and improving the calculation efficiency.
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FIG. 1 is a schematic flow diagram of the present invention;
figure 2 is a schematic view of the structure of the landing gear.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the detailed description of the embodiments of the present application provided below in connection with the appended drawings is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application. The invention is further described below with reference to the accompanying drawings.
The invention provides a system failure probability calculation method based on a multi-point adding criterion and an improved composite criterion, aiming at the problems that the system failure probability is not converged or the calculation efficiency is low due to wrong system state judgment in the traditional composite criterion method, information redundancy is easily generated in a single-point adding mode, and time consumption is consumed for constructing a Kriging proxy model. The method improves the probability of wrong judgment of the extreme value mode due to non-convergence of the Kriging model in iterative updating, simultaneously reserves the extreme value information predicted by the Kriging model of each failure mode to accelerate the identification speed of the system failure boundary, and selects a plurality of points which have larger contribution to the precision simulation of the system failure boundary by one-time screening, thereby reducing the times of constructing the Kriging proxy model and finally improving the calculation efficiency of the system failure probability with multiple failure modes.
1. In order to solve the problem that the system failure probability is not converged or the calculation efficiency is low due to the wrong judgment of the system state in the traditional composite criterion method, aiming at a series system and a parallel system, new learning functions are respectively defined as follows:
a. for series systems, new learning functions
And failure mode C requiring updating series Respectively as follows:
in the formula, g iK (x j ) At sample point x for the ith failure mode j Corresponding Kriging agent model, U i (x j ) For this pattern at sample point x j Corresponding U learning function value, set II series ＝{i|g iK (x j )≤0,i＝1,2,...,l}。
b. For parallel systems, a new learning function
And failure modes requiring updatingC parallel Respectively as follows:
in the formula, set II parallel ＝{i|g iK (x j )＞0,i＝1,2,...,l}。
According to the newly defined learning function, the learning function provided by the invention avoids the situation that the extreme mode is judged wrongly because the Kriging model is in a non-convergence state in iterative updating in the traditional composite criterion method, so that the result is not converged or the calculation efficiency is influenced to a certain extent finally, simultaneously retains extreme information predicted by the Kriging model of each failure mode, and accelerates the identification speed of the system failure boundary.
2. In order to solve the problems of information redundancy easily generated by a single-point adding mode adopted in the traditional composite criterion method when the system failure probability is calculated and time consumption for constructing a Kriging agent model, a multi-point adding criterion based on cluster analysis is provided, and the basic idea is as follows: based on the idea of K-medoids clustering, adding the U value information of the system as weight into the distance calculation between each sample point, and classifying the target sample groups until the clustering quality meets the requirement, wherein the central points of the various types are the training sample points needing to be updated. Wherein the new cluster quality evaluation function J is defined as:
in the formula (I), the compound is shown in the specification,
n is the sample size of the sample set S, w j (j =1,2,.., N) is called "weight" and represents the cluster of proxy model precision feature pairs for the jth sample point in the sample set"contribution rate" satisfying
Distance between two adjacent plates
Taking the euclidean distance as an example,
the expression of (a) is:
according to the newly defined clustering quality evaluation function, the current weight value w j When the distances are smaller and closer, the sample points with more consistent precision contribution degrees and close distances of the proxy model can be divided into a class, and the class of sample points are close to each other to the maximum extent. At the moment, the central sample points representing the class not only have position information, but also contain precision information of the current proxy model representing the class, and the central sample points of the classes are used as training sample points needing to be updated, so that the problem of point selection redundancy caused by the fact that only U value information is considered and distance information between the sample points is ignored in a traditional single point adding mode can be solved. Meanwhile, the total classification number is the number of the added points, so that the number of a plurality of sample points needing to be updated can be selected by one-time learning, and the construction efficiency of the corresponding Kriging agent model is accelerated.
As shown in fig. 1, after defining the learning function, the failure mode to be updated and the cluster quality evaluation function, the method specifically executes the following steps:
the first step is as follows: a sample cell S is generated. Joint probability density function f by inputting random variable X X (x) Generating a pool of N samples S = { x = 1 ,x 2 ,...,x N }。
The second step: and respectively generating an initial training sample set corresponding to each failure mode. Randomly extracting N in S 0 A sample (where N is 0 N), calculating each failure mode at N 0 And (3) respectively forming initial training sample sets corresponding to respective failure modes by using the initial input samples and the output response values of the failure modes according to the real function values of the samples.
The third step: constructing Kriging model g of each failure mode by using initial training sample set corresponding to each failure mode iK (i＝1,2,...,l)。
The fourth step: calculating U based on formula (4) or formula (6) C And (4) learning the function.
The fifth step: and judging the convergence of the current Kriging model. When in use
Then, the current Kriging model can judge the sign of the output response value corresponding to each sample point in the sample pool S with 97.7% accuracy, namely, the self-adaptive learning process can be stopped, and the ninth step is executed; if it is
The sixth step is executed.
And a sixth step: and classifying the sample set S based on a weighted K-medoids algorithm. According to the weighted K-medoids algorithm provided by the invention, the formula (8) is optimized and solved to obtain K final classification center sample points { x } o1 ,x o2 ,...,x ok }。
The seventh step: calculate the classification center sample point { x } o1 ,x o2 ,...,x ok And (4) carrying out merging treatment on points of the same failure modes corresponding to the failure modes needing to be updated. First, { x is calculated based on formula (5) or formula (7) } o1 ,x o2 ,...,x ok The corresponding mode number; then, { x ] is calculated o1 ,x o2 ,...,x ok Corresponding each sample point in the data to the real output of the failure mode; and finally, combining the input sample points and the output sample points with the same pattern number to serve as a training sample set needing to be updated in the pattern.
Eighth step: and updating the training sample set corresponding to each mode, and returning to the third step.
The ninth step: computing system failure summaryAnd (4) rate. Respectively substituting the updated Kriging model of each failure mode into a formula (10) or a formula (11) according to the serial and parallel conditions of the system to calculate a system failure domain indication function
The estimated value of the failure probability of the structural system can be obtained according to the formula (12).
The failure domain indicator function of a tandem system based on the Kriging model can be expressed as:
the failure domain indicator function of the parallel system based on the Kriging model can be expressed as follows:
therefore, the estimation formula of the failure probability of the structural system is:
to verify the analysis method of the present invention, the reliability of an aircraft landing gear retraction mechanism of the type shown in fig. 2 was analyzed as an example.
Inputting an aircraft landing gear retraction mechanism shown in fig. 2 into a dynamics analysis software, and establishing the following structural function by simulating the load and constraint conditions borne by the landing gear retraction mechanism:
wherein, g 1 (X) and g 2 (X) are respectively structural responses, F max To the maximum allowable pressure, F Lmax Maximum driving force for retracting the actuator cylinder, R max For allowing at the hinge BMaximum radius of circle, r B Is the actual radius of the circle at hinge B. The distribution type and individual parameters of each input variable are shown in table 1.
TABLE 1 distribution parameters of aircraft landing gear Structure input variables
To more intuitively illustrate the accuracy and computational efficiency of the analysis method results of the present invention, the failure results, the calculated total amount, and the calculated time obtained by the analysis method of the present invention were compared with the results obtained by the conventional composite criteria method and the monte carlo method, as shown in table 2.
TABLE 2 calculation results
As can be seen from table 2, the failure probability estimated by the method of the present invention is very close to the failure probability estimated by the monte carlo method, but the calculation amount of the method provided by the present invention is significantly smaller than that of the monte carlo method, which indicates that the method of the present invention greatly improves the reliability analysis efficiency compared with the monte carlo method under the condition of similar estimation accuracy; under the condition of equivalent calculation amount, compared with the traditional compound criterion method, under the condition of shorter total calculation time, the relative error of the failure probability estimated by the method is lower, which shows that under the condition of equivalent calculation amount, the method can simultaneously improve the calculation efficiency and the calculation precision of the traditional compound criterion method in the reliability analysis.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (5)
1. A system failure probability calculation method under multiple failure modes based on a multipoint adding point criterion is characterized in that: the system failure probability calculation method comprises the following steps:
s1, respectively setting a learning function of the system and a failure mode needing to be updated as U C And C, and calculating a learning function U C ；
S2, constructing a Kriging model of each failure mode according to the initial training sample set, and judging the convergence of the current Kriging model;
s3, when the second convergence condition is met, classifying the sample set S based on the weighted K-medoids algorithm, carrying out optimization solution on the new clustering quality evaluation function J, and obtaining K final classification center sample points { x o1 ,x o2 ,...,x ok }；
S4, calculating sample points { x) of classification centers o1 ,x o2 ,...,x ok Corresponding failure modes needing to be updated and carrying out merging processing on points of the same failure modes;
s5, updating the training sample set corresponding to each mode, and continuously constructing the Kriging model of each failure mode according to the training sample set at the moment;
and S6, calculating the failure probability of the system according to the failure domain indication functions of the series system and the parallel system of the Kriging model until the first convergence condition is met.
2. The method for calculating the system failure probability under the multi-failure mode based on the multi-point and point criterion according to claim 1, characterized in that: the system failure probability calculation method further comprises a step S0, wherein the step S0 comprises the steps of generating a sample pool S and generating an initial training sample set corresponding to each failure mode according to the sample pool S to construct a Kriging model of each failure model.
3. The method for calculating the system failure probability under the multi-failure mode based on the multi-point and point criterion as claimed in claim 2, wherein: the step of generating the sample pool S and constructing the Kriging model of each failure model according to the initial training sample set corresponding to each failure mode generated by the sample pool S specifically comprises the following steps:
s01, through inputting the joint probability density function f of the random variable X X (x) Generating a pool of N samples S = { x = 1 ,x 2 ,...,x N }；
S02, randomly extracting N in S 0 A sample is calculated for each failure mode in N 0 The real function value under each sample forms the initial training sample set corresponding to each failure mode by the initial input samples and the output response values of each failure mode;
and S03, constructing a Kriging model of each failure mode by using the initial training sample set corresponding to each failure mode.
4. The method for calculating the system failure probability under the multi-failure mode based on the multi-point and point criterion according to claim 1, characterized in that: the compute classification center sample point { x o1 ,x o2 ,...,x ok The corresponding failure modes needing to be updated and the merging treatment of the points of the same failure modes comprise:
s41, calculating { x) according to failure mode C updated by system requirements o1 ,x o2 ,...,x ok The corresponding mode number;
s42, calculating { x o1 ,x o2 ,...,x ok Corresponding each sample point in the } to the real output of the failure mode;
and S43, combining the input sample points and the output sample points with the same mode number to be used as a training sample set needing to be updated in the mode.
5. The method for calculating the system failure probability under the multi-failure mode based on the multi-point and point criterion according to any one of claims 1 to 4, wherein: the first convergence condition is
At the moment, the accuracy of the sign of the output response value corresponding to each sample point in the sample pool S is judged by the Kriging model to reach a preset value, and the self-adaptive learning process is stopped; the second convergence condition
At this time, the accuracy of the sign of the output response value corresponding to each sample point in the sample pool S is judged by the Kriging model to not reach the preset value, and then the self-adaptive learning is continued.
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