CN110110369B - Truss structure reliability optimization method based on general generation function - Google Patents
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Abstract
The invention discloses a truss structure reliability optimization method based on a general generation function. The reliability of the truss structure is calculated by adopting a general generation function method instead of a traditional double-circulation method, and the main failure mode of the truss structure is searched and identified by judging that the structure reaches the limit failure criterion of the bearing capacity; establishing a general generating function model of truss structure reliability; processing by using a K-means clustering algorithm, and carrying out data compound operation by using a general generation function method to generate a large number of discrete random data clusters and merging, so that the calculation workload is reduced; and finally, establishing a mathematical model for optimizing the reliability, and carrying out structural reliability optimization design by taking the minimum quality of the structure as a target and taking the reliability index as a constraint condition for meeting certain requirements.
Description
Technical Field
The invention relates to a structure reliability optimization method, in particular to a reliability optimization based on a general generation function in truss structure reliability analysis.
Background
With the continuous development of technology, engineering structures become more complex, and the reliability design of the structures is now the most concerned problem. For some complex structures, such as airplanes, ships, submarines and the like, any part in the complex structures fails, the complex structures can be seriously damaged, so that national property is lost, and even people are threatened. It follows that the theory of structural reliability is of great importance in structural design. In conventional structural engineering, engineers often add redundant constraints to the structure to improve the reliability of the structure in order to provide higher security to the structure. Although this approach provides a high level of security to the structure, the extra constraints increase the manufacturing costs of the project and waste resources. For conventional structural reliability optimization, sufficient safety can be achieved with the lightest structural weight. But the optimization efficiency of the conventional structural reliability model is low. In optimizing a large complex structure using conventional methods, most of the time is wasted on computation. Therefore, it is urgent to develop an efficient reliability optimization algorithm.
Disclosure of Invention
1. Object of the invention
In order to solve the problems of multiple constraint conditions and overlarge calculated amount, the invention provides a structure reliability optimization method based on a general generation function.
2. The invention adopts the technical proposal that
The truss structure reliability optimization method based on the general generation function provided by the invention is carried out according to the following steps:
the first step: the failure mode of the truss structure is based on the plastic limit analysis of the structure, and the formation and the position of a plastic hinge are obtained;
and a second step of: describing reliability problems, taking a truss structure as a research object, and defining the reliability of the structure as A on the assumption that the model function of the structure to be researched is g (X);
and a third step of: establishing a general generation function model of the discrete random variable, and setting the possible realization value of the discrete random variable X as (X 1 ,x 2 ,……,x N ) The probability corresponding to this is (p 1 ,p 2 ,……p N ). The general generation function model of the discrete random variable X is defined as:
and is also provided with
Fourth step: processing by using a K-means clustering algorithm, so that the workload is greatly reduced, and the calculation efficiency is improved;
fifth step: establishing a reliability optimized mathematical model, taking the minimum quality of a structure as a target, taking a certain requirement met by a reliability index as a constraint condition, and establishing the optimized mathematical model as follows:
the first step specifically comprises the following steps:
1.1 Using a plastic hinge as a failure element, when the plastic hinge is developed to a certain quantity, the structure forming mechanism loses the bearing capacity, and the failure elements form a failure sequence of the structure, if E ij Represents the jth failure event (failure path progresses to the formation of the jth plastic hinge) in the ith failure sequence, m i Representing the failure element number of the ith failure sequence, the ith failure sequence can be expressed as:
1.2 Multiple failure sequences can result in the same failure mode (same organization). In calculating the failure probability of a system, only those failure sequences with a high failure probability, namely significant failure sequences, are generally considered, and the significant failure sequences are identified by the following criteria:
P(E 1 ∩…∩E Ms )≥VP ref (4)
wherein V is the truncation (branching) parameter, ms is the number of failure events for the failure sequence, P ref For truncating the reference probability value.
1.3 The primary failure mode that controls structural failure forms the basis for structural system reliability analysis. The failure domain of the ith primary failure mode can be expressed as:
wherein R is j Is the plastic ultimate bending moment, P j Is an external load, a ij 、b ij Is a constant related to the geometry of the structure, N r Is the number of plastic hinges formed, N p Is the number of external loads.
The second step specifically comprises the following steps:
2.1) Definition of a random input variable x= [ x ] 1 ,x 2 ,……x N ] T And a joint probability density function f (x);
2.2 Constructing a functional function g (X) according to the main failure mode of the truss structure to give the failure probability p of the truss structure F Reliability analysis was performed.
The fourth step is specifically as follows:
4.1 Randomly assigning k cluster centers (m) 1 ,m 2 ,…,m k ) Initializing and taking a value;
4.2 For each sample x i Finding the cluster center nearest to it and assigning it to the class;
4.3 Recalculating new centers for each cluster;
N i is the current sample number of the ith cluster;
4.4 A) the deviation is calculated and,
4.5 If the E value is converged, returning (m) 1 ,m 2 ,…,m k ) The algorithm is terminated; otherwise, go to 4.2.
3. The invention has the beneficial effects that
(1) According to the invention, the discrete general generation function model is established through the third step, and compared with the traditional reliability analysis methods such as a primary second-order moment method and the like, the calculation accuracy is greatly improved.
(2) The method uniformly adopts a general generation function method to replace the traditional double-circulation method to calculate the reliability of the truss structure, and the main failure mode of the truss structure is searched and identified by judging that the structure reaches the limit failure criterion of the bearing capacity; establishing a general generating function model of truss structure reliability; processing by using a K-means clustering algorithm, and carrying out data compound operation by using a general generation function method to generate a large number of discrete random data clusters and merging, so that the calculation workload is reduced; and finally, establishing a mathematical model for optimizing the reliability, and carrying out structural reliability optimization design by taking the minimum quality of the structure as a target and taking the reliability index as a constraint condition for meeting certain requirements.
(3) Compared with the existing reliability analysis method, the reliability optimization method has the advantages that the reliability optimization of the complex structure is realized, the accuracy is ensured, and the working efficiency is improved.
(4) Compared with the existing reliability analysis method, the method has the advantages of low dependence on the initial point and certain engineering adaptability.
Drawings
FIG. 1 is a logical block diagram of the method of the present invention;
FIG. 2 is a matlab main program diagram of the method of the present invention;
FIG. 3 is a matlab subroutine diagram of the method of the present invention;
FIG. 4 is a graph of the results of the optimization of the method of the present invention;
FIG. 5 is a flow chart of a k-means clustering algorithm.
Detailed description of the preferred embodiments
As shown in fig. 1-3, the structural reliability optimization method based on the general generation function of the invention is carried out according to the following steps:
the first step: the failure mode of the truss structure is based on the plastic limit analysis of the structure, and the formation and the position of a plastic hinge are obtained;
a plastic hinge is used as a failure element. When the plastic hinge has progressed to a certain level, the structure is formed into a mechanism, the bearing capacity is lost, and the failure elements form a failure sequence of the structure. A failure sequence is formed by a failure path of a structure through different stages of development, and multiple failure sequences can result in the same failure mode (same organization). When the failure probability of the system is calculated, only those failure sequences with larger failure probability, namely obvious failure sequences, are generally considered, and the main failure modes which play a role in controlling the structural damage only form the basis of the structural system reliability analysis because a plurality of failure sequences can lead to the same failure mode.
And a second step of: describing reliability problems, taking a truss structure as a research object, and defining the reliability of the structure as A on the assumption that the model function of the structure to be researched is g (X);
define the limit state function as g (x) =x 1 2 +x 2 2 -x 1 x 2 -1.5(x 1 +x 2 ) +1.5 where the random variable x 1 And x 2 Independent of each other, random variable x 1 And x 2 Obeying the lognormal distribution and the weibull distribution, respectively.
And a third step of: establishing a general generation function model of the discrete random variable, and setting the possible realization value of the discrete random variable X as (X 1 ,x 2 ,……,x N ) The probability corresponding to this is (p 1 ,p 2 ,……p N ). The general generation function model of the discrete random variable X is defined as:
and is also provided with
And comparing Monte Carlo methods according to the specific columns of the second step, and distinguishing the general generation function method from the first-order second-order moment method. The following table shows:
| monte Carlo process | General function method of generating | First order second moment method | |
| Reliability degree | 0.9999 | 0.99989 | 0.99854 |
| Calculation time | 180s | 2s | 2s |
| Error of | 0.01％ | 0.136％ |
The table shows that the general generation function skill ensures accuracy, can greatly shorten calculation time and improve working efficiency.
Fourth step: processing by using a K-means clustering algorithm, so that the workload is greatly reduced, and the calculation efficiency is improved;
and clustering is realized through continuous iteration, and the iteration process is terminated when the algorithm converges to the end condition, so that a clustering result is obtained. The mean clustering algorithm uses a cluster error sum-of-squares function E as a clustering criterion function, wherein,
x ij is the ith class, jth sample, m i Is the cluster center or centroid of class i, n i Is the number of samples of class i. The essence of the K-means clustering algorithm is that K optimal clustering centers are found through repeated iteration, all n sample points are distributed to the nearest clustering centers, and the square sum E of clustering errors is minimized:
4.1 Randomly assigning k cluster centers (m) 1 ,m 2 ,…,m k ) Initializing and taking a value;
4.2 For each sample x i Finding the cluster center nearest to it and assigning it to the class;
4.3 Recalculating new centers for each cluster;
N i is the current sample number of the ith cluster;
4.4 A) the deviation is calculated and,
4.5 If the E value is converged, returning (m) 1 ,m 2 ,…,m k ) The algorithm is terminated; otherwise, go to 4.2.
FIG. 5 is a flowchart of a k-means clustering algorithm;
fifth step: establishing a reliability optimized mathematical model, taking the minimum quality of a structure as a target, taking a certain requirement met by a reliability index as a constraint condition, and establishing the optimized mathematical model as follows:
as shown in fig. 4, repeated iterative optimization is performed by taking the reliability index as a constraint condition, and an optimal K-means clustering interval is found, so that the method has more accurate accuracy, high reliability, greatly reduced time for solving, and more suitability for actual practical situations, and the technical effect is remarkable.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (3)
1. The truss structure reliability optimization method based on the general generation function is characterized by comprising the following steps of:
the first step: the failure mode of the truss structure is based on the plastic limit analysis of the structure, and the formation and the position of a plastic hinge are obtained;
and a second step of: describing reliability problems, taking a truss structure as a research object, and defining the reliability of the structure as A on the assumption that the model function of the structure to be researched is g (x);
and a third step of: establishing a general generation function model of the discrete random variable, and setting the possible realization value of the discrete random variable X as (X 1 ,x 2 ,……,x N ) The probability corresponding to this is (p 1 ,p 2 ,……p N ) The method comprises the steps of carrying out a first treatment on the surface of the The general generation function model of the discrete random variable X is defined as:
and is also provided with
Fourth step: processing the general generation function model by using a K-means clustering algorithm;
fifth step: the method comprises the following steps of:
min W＝W(x) (2)
wherein W (X) represents the mass of the truss structure;
representing allowable reliability, beta s (x) Representing the reliability of the truss structure;
the first step specifically comprises the following steps:
1.1 Using a plastic hinge as a failure element, when the plastic hinge is developed to a certain quantity, the structure forming mechanism loses the bearing capacity, and the failure elements form a failure sequence of the structure, if so
Indicating the development of a failure path to the jth event in the jth failure sequence of formation of the jth plastic hinge, m i Representing the failure element number of the ith failure sequence, the ith failure sequence can be expressed as:
1.2 Multiple failure sequences can lead to the same failure mode, and when the failure probability of the system is calculated, only those failure sequences with larger failure probability, namely obvious failure sequences, are considered, wherein the obvious failure sequences are identified by the following criteria:
P(E 1 ∩…∩E Ms )≥VP ref (4)
wherein V is a cutoff parameter, ms is the failure event number of the failure sequence, P ref A truncated reference probability value;
1.3 The primary failure mode that controls structural failure forms the basis for structural system reliability analysis, and the failure domain of the ith primary failure mode can be expressed as:
wherein R is j Is the plastic ultimate bending moment, P j Is an external load, a ij 、b ij Is a constant related to the geometry of the structure, N r Is the number of plastic hinges formed, N p Is the number of external loads.
2. The truss structure reliability optimization method based on the general generation function according to claim 1, wherein: the second step specifically comprises the following steps:
2.1 Defining a random input variable x= [ x ] 1 ,x 2 ,……x N ] T And a joint probability density function f (x);
2.2 Constructing a functional function g (X) according to the main failure mode of the truss structure to give the failure probability p of the truss structure F Reliability analysis is performed
3. The truss structure reliability optimization method based on the general generation function according to claim 1, wherein: the fourth step is specifically as follows:
4.1 Randomly assigning k cluster centers (m) 1 ,m 2 ,…,m k ) Initializing and taking a value;
4.2 For each sample x i Finding the cluster center nearest to it and assigning it to the class;
4.3 Recalculating new centers for each cluster;
n i is the current sample number of the ith cluster;
4.4 A) the deviation is calculated and,
4.5 If the E value is converged, returning (m) 1 ,m 2 ,…,m k ) The algorithm is terminated; otherwise, go to 4.2.
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| CN106777492A (en) * | 2016-11-16 | 2017-05-31 | 北京航空航天大学 | A kind of structural system Multidisciplinary systems Optimization Design |
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| CN106777492A (en) * | 2016-11-16 | 2017-05-31 | 北京航空航天大学 | A kind of structural system Multidisciplinary systems Optimization Design |
| CN108763608A (en) * | 2018-03-23 | 2018-11-06 | 江苏理工学院 | A kind of composite laminated plate reliability estimation method based on generating functon method |
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