CN110162898A - A kind of non-precision probabilistic reliability design method for equipping airborne air bag buffer - Google Patents
A kind of non-precision probabilistic reliability design method for equipping airborne air bag buffer Download PDFInfo
- Publication number
- CN110162898A CN110162898A CN201910449281.1A CN201910449281A CN110162898A CN 110162898 A CN110162898 A CN 110162898A CN 201910449281 A CN201910449281 A CN 201910449281A CN 110162898 A CN110162898 A CN 110162898A
- Authority
- CN
- China
- Prior art keywords
- formula
- probability
- probability box
- interval
- variable
- 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.)
- Withdrawn
Links
- 238000000034 method Methods 0.000 title claims abstract description 36
- 238000013461 design Methods 0.000 title claims abstract description 32
- 230000001186 cumulative effect Effects 0.000 claims abstract description 48
- 238000005315 distribution function Methods 0.000 claims abstract description 48
- 239000013598 vector Substances 0.000 claims abstract description 47
- 230000002068 genetic effect Effects 0.000 claims abstract description 9
- 230000003139 buffering effect Effects 0.000 claims abstract description 6
- 238000005457 optimization Methods 0.000 claims description 40
- 238000009826 distribution Methods 0.000 claims description 26
- 238000013507 mapping Methods 0.000 claims description 21
- 238000012545 processing Methods 0.000 claims description 8
- 230000008569 process Effects 0.000 claims description 7
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 5
- 238000006243 chemical reaction Methods 0.000 claims description 5
- 239000011541 reaction mixture Substances 0.000 claims description 3
- 238000010586 diagram Methods 0.000 description 4
- 238000005516 engineering process Methods 0.000 description 3
- WVAKRQOMAINQPU-UHFFFAOYSA-N 2-[4-[2-[5-(2,2-dimethylbutyl)-1h-imidazol-2-yl]ethyl]phenyl]pyridine Chemical compound N1C(CC(C)(C)CC)=CN=C1CCC1=CC=C(C=2N=CC=CC=2)C=C1 WVAKRQOMAINQPU-UHFFFAOYSA-N 0.000 description 1
- 238000010521 absorption reaction Methods 0.000 description 1
- 230000001133 acceleration Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000008570 general process Effects 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 239000012528 membrane Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011084 recovery Methods 0.000 description 1
- 238000009827 uniform distribution Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
-
- 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
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Data Mining & Analysis (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Software Systems (AREA)
- Databases & Information Systems (AREA)
- Algebra (AREA)
- Evolutionary Biology (AREA)
- Life Sciences & Earth Sciences (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Bioinformatics & Computational Biology (AREA)
- Computing Systems (AREA)
- Operations Research (AREA)
- Probability & Statistics with Applications (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a kind of non-precision probabilistic reliability design method for equipping airborne air bag buffer, this method describes random vector and probability box vector by probabilistic model and probability BOX Model respectively；In order to effectively construct the cumulative distribution function of probability box variable, guarantee the consistency of cumulative distribution function using moment condition, guarantees the validity of cumulative distribution function using shape condition；While the uniqueness in order to guarantee cumulative distribution function, based on the cumulative distribution function of principle of maximum entropy reconstruct probability box variable, and passes through intergeneration projection genetic algorithm and solve the reliability index for equipping airborne air bag buffer；The present invention not only can effectively construct the uncertain variable equipped in airborne air bag buffering course, and can inherently improve the computational efficiency for solving reliability index and solve quality, have extensive engineering application value equipping airborne security fields.
Description
Technical Field
The invention relates to the field of equipment airborne safety protection, in particular to a non-accurate probability reliability design method for an equipment airborne air bag buffer device.
Background
The air bag buffer device has been widely applied to the technical fields of equipment airborne landing, unmanned aerial vehicle recovery, aerospace return and the like due to the characteristics of light weight, good energy absorption effect and the like, and becomes an important component part of equipment safety guarantee.
Aiming at the design of an air-drop airbag buffer device, the existing design method has the following problems:
1. most of existing design methods for equipment airborne airbag buffer devices are developed and researched under the condition that a system parameter model is in a deterministic condition, but in the actual equipment airborne process, due to the fact that errors or uncertainties exist in boundary conditions, initial conditions and measurement conditions, if the factors are still treated as deterministic factors, the system response and the actual response generate large deviation.
2. For a reliability design method for equipping an airborne airbag buffer device, some existing methods describe uncertain design variables by using a probability model, but in the actual design process, the probability distribution density of many uncertain variables is unknown due to the lack of enough sample data, so that the probability distribution of the uncertain design variables is difficult to accurately obtain.
3. For a reliability design method for equipping an airborne airbag buffer device, some existing methods describe uncertain design variables by adopting a non-probabilistic convex set model, and although the non-probabilistic convex set model describing the uncertain design variables does not need accurate probability distribution, a conservative design is caused due to the fact that the non-probabilistic convex set model emphasizes extreme working conditions too much.
Disclosure of Invention
In order to overcome the problems, the invention provides a non-precise probability reliability design method for equipping an airborne airbag buffer device.
The technical scheme adopted by the invention for solving the technical problems is as follows: a design method for the non-precise probability reliability of an air-drop air bag buffer device comprises the following steps:
step 1: analyzing uncertainty factors in the air-drop airbag buffering process, and dividing uncertainty vectors into random vectors and probability box vectors according to the information of the sample points; random vector X ═ X1,Xμ,...,XW) 1,2, W is described using a probability model, a probability box vectorDescribing by adopting a probability box model; probability box variablesIs composed of n focal elements in formula (1):
in the formula (1), yiThe (i) th focal element is shown,an interval representing the ith focal element, aiAnd biThe interval end point of the ith focal element is shown,representing the mass of the ith focal element;
step 2: calculating probability box variables based on equations (2) and (3)Origin moment and center moment of (c):
in the formula (2) and the formula (3),representing probability box variablesThe s-th order origin moment of (c),representing probability box variablesThe s-th central moment of (a);
and step 3: to probability box variableDividing contribution degree units;
the pair probability box variableThe division of the contribution degree unit comprises the following sub-steps:
step 31: variable of probability boxOrdering the endpoints of all included focal elements from small to large { d1,d2,...,de}；
Step 32: grouping every two adjacent end points into a group, and respectively forming a new section of contribution degree unit { [ d { [ D ]1,d2],[d2,d3],[d3,d4],...,[de-1,de]}；
Step 33: superposing the original focal element quality in each contribution degree unit interval to form the quality of a new contribution degree unit, and forming a new contribution degree unit as shown in formula (4):
in the formula (4), crDenotes the r-th contribution unit, drAnd dr+1Represents the interval end point of the r-th contribution degree unit,representing the quality of the r-th contribution unit;
and 4, step 4: each contribution degree unit can move up and down according to the mass of the previous contribution degree unit to determine the position of the previous contribution degree unit in the cumulative distribution function, and the distance h for moving up and down of the contribution degree unit is selected as a design variable as shown in formula (5):
wherein,
and 5: sorting the upper and lower boundaries of the unit mass of each contribution degree from small to largeWherein, F1 new＝0，Then, every two adjacent boundaries are grouped into a group, new focal element quality is formed according to the difference between the upper boundary and the lower boundary of the two adjacent boundaries, and the end points corresponding to the upper boundary and the lower boundary of the new focal element are selected as the interval of the new focal element, so as to form the interval shown in the formula (6)New contribution unit shown:
in the formula (6), the first and second groups,the z-th new focal element is represented,andthe interval end point of the z-th new focal element is shown,representing the mass of the z-th new focal element;
step 6: the uncertainty optimization problem shown in equation (7) is established to obtain the probability box variablesCumulative distribution function of (2):
wherein,
in the formula (7), the first and second groups,the interval of the original k-th order origin moment,the interval of the original q-th order central moment; superscripts L and R represent the lower and upper boundaries of the interval, respectively;as a constraint condition of the moment of origin,the two moment constraint conditions are used for ensuring the consistency of the cumulative distribution function;andthe shape constraint condition is used for ensuring the effectiveness of the cumulative distribution function; objective function f (Y) for obtaining probability box variablesThe maximum entropy of the cumulative distribution function is ensured;
and 7: converting the uncertainty optimization problem shown in formula (7) into an unconstrained certainty optimization problem;
the conversion of the uncertainty optimization problem shown in the formula (7) into an unconstrained certainty optimization problem comprises the following sub-steps:
step 71: processing the constraint function by using the interval possibility degree;
moment condition of equality constraint in equation (7) for uncertainty optimization problemDescribing the interval uncertainty constraint with the interval likelihood level can be converted to a deterministic equality constraint as shown in equation (8):
in the formula (8), the first and second groups,representing probability box variables made up of new focal elementsOf the kth origin moment, and similarly, the equation constraint moment conditionDescribing the interval uncertainty constraint with the interval likelihood level can be converted to a deterministic equality constraint as shown in equation (9):
in the formula (9), the reaction mixture,representing probability box variables made up of new focal elementsThe interval of the qth order central moment of (a);
step 72: obtaining an unconstrained deterministic optimization problem by using a penalty function method;
constraining equations (8), (9) and (9) by penalty function methodAndprocessing can further be achieved as follows with a penalty function fp(Y) an unconstrained deterministic optimization problem:
in the formula (10), λ, φ and ε are penalty factors;τk，ξq，ψqθ and η are penalty functions, which can be obtained by the following equations:
and 8: solving an unconstrained deterministic optimization problem formula (10) by using an alternate mapping genetic algorithm to obtain a probability box variableA cumulative distribution function;
and step 9: constructing a limit state function g (X, Y) of the air-drop air bag buffer device, and setting a random vector X as (X)1,Xμ,...,XW) And probability box vectorMapping to standard normal space U to obtain new extreme state function G (U)X,UY) Wherein, UXFor vectors in which the random vector X is mapped to a standard normal space, UYMapping the probability box vector Y to a vector under a standard normal space;
step 10, establishing an optimization problem shown as a formula (17) and a formula (18) so as to solve the minimum reliability index β of the air-bag buffer device for air-drop equipmentLAnd a maximum reliability index βR。
Wherein,
wherein,
preferably, in step 9, the random vector X may be (X) according to equations (19) and (20)1,Xμ,...,XW) And probability box vectorMapping to the standard normal space U:
in equations (19) and (20), Φ is a cumulative distribution function of the normal distribution, Φ-1Which is the cumulative distribution inverse of a standard normal distribution,is a random variable XμThe cumulative distribution function of (a) is,as a probability box variableThe lower boundary of the cumulative distribution function of (c),as a probability box variableUpper boundary of the cumulative distribution function of (1);is a random variable XμA variable mapped to a standard normal space,as a probability box variableMaps to the lower boundary of the variable under the standard normal space,as a probability box variableMapping to the upper boundary of the variable under the standard normal space.
Preferably, in the step 10, the minimum reliability index β of the air-drop airbag buffer device is solved by using an alternate generation mapping genetic algorithmLAnd a maximum reliability index βR。
The invention has the beneficial effects that:
1. aiming at the 1 st point provided by the background technology, the invention adopts a probability box model to model the uncertain design variables of the air-drop airbag buffer device, thereby considering the influence of the uncertain factors on the design result.
2. Aiming at the 2 nd point of the background technology, the probability box model adopted by the invention is used for modeling the uncertainty design variables of the air-drop airbag buffer device, only the interval and the quality of the focal elements (basic credibility, similar to a probability density function in a probability theory) contained in each uncertainty variable need to be known in the modeling process, the interval and the quality of the focal elements can be obtained through limited samples, and a large number of sample points are not needed to construct an accurate probability model, so that the difficulty of constructing the uncertainty design variable model is greatly reduced.
3. Aiming at the 3 rd point provided by the background technology, the probability box model adopted by the invention is used for modeling the uncertain design variables of the air-drop air bag buffer device, and the focal elements contained in each uncertain variable have two elements of interval and quality, while the non-probability convex set model is only described by the interval, so that the conservative design can be effectively avoided when the adopted probability box model is used for reliability design.
Note: the foregoing designs are not sequential, each of which provides a distinct and significant advance in the present invention over the prior art.
Drawings
FIG. 1 is a flow chart of the method for designing the non-precision probability reliability of an airborne airbag cushion apparatus of the present invention
FIG. 2 is a schematic view of a model of an airborne airbag cushion assembly according to an embodiment
FIG. 3 is a variable Y of the probability box in an embodiment1Is a cumulative distribution function boundary diagram
FIG. 4 is a variable Y of the probability box in an embodiment2Is a cumulative distribution function boundary diagram
FIG. 5 is a variable Y of the probability box in an embodiment3Is a cumulative distribution function boundary diagram
In the figures, the reference numerals are as follows:
1. airborne equipment 2, gasbag buffer 3, exhaust hole 4, ground
Detailed Description
The general process of the invention is described below with reference to the accompanying drawings:
as shown in fig. 1, a design method for non-precision probability reliability of an airborne airbag cushion apparatus includes the following steps:
step 1: analyzing uncertainty factors in the air-drop airbag buffering process, and dividing uncertainty vectors into random vectors and probability box vectors according to the information of the sample points; random vector X ═ X1,Xμ,...,XW) 1,2, W is described using a probability model, a probability box vectorDescribing by adopting a probability box model; probability box variablesIs composed of n focal elements in formula (1):
in the formula (1), yiThe (i) th focal element is shown,an interval representing the ith focal element, aiAnd biThe interval end point of the ith focal element is shown,representing the mass of the ith focal element;
step 2: calculating probability box variables based on equations (2) and (3)Origin moment and center moment of (c):
in the formula (2) and the formula (3),representing probability box variablesThe s-th order origin moment of (c),representing probability box variablesThe s-th central moment of (a);
and step 3: to probability box variableDividing contribution degree units;
the pair probability box variableThe division of the contribution degree unit comprises the following sub-steps:
step 31: variable of probability boxOrdering the endpoints of all included focal elements from small to large { d1,d2,...,de}；
Step 32: grouping every two adjacent end points into a group, and respectively forming a new section of contribution degree unit { [ d { [ D ]1,d2],[d2,d3],[d3,d4],...,[de-1,de]}；
Step 33: superposing the original focal element quality in each contribution degree unit interval to form the quality of a new contribution degree unit, and forming a new contribution degree unit as shown in formula (4):
in the formula (4), crDenotes the r-th contribution unit, drAnd dr+1Represents the interval end point of the r-th contribution degree unit,representing the quality of the r-th contribution unit;
and 4, step 4: each contribution degree unit can move up and down according to the mass of the previous contribution degree unit to determine the position of the previous contribution degree unit in the cumulative distribution function, and the distance h for moving up and down of the contribution degree unit is selected as a design variable as shown in formula (5):
wherein,
and 5: sorting the upper and lower boundaries of the unit mass of each contribution degree from small to largeWherein, F1 new＝0，Then, every two adjacent boundaries are grouped, new focal element quality is formed according to the difference between the upper boundary and the lower boundary of the two adjacent boundaries, and the end points corresponding to the upper boundary and the lower boundary of the new focal element are selected as the interval of the new focal element, so as to form a new contribution degree unit as shown in formula (6):
in the formula (6), the first and second groups,the z-th new focal element is represented,andthe interval end point of the z-th new focal element is shown,representing the mass of the z-th new focal element;
step 6: the uncertainty optimization problem shown in equation (7) is established to obtain the probability box variablesCumulative distribution function of (2):
wherein,
in the formula (7), the first and second groups,the interval of the original k-th order origin moment,the interval of the original q-th order central moment; superscripts L and R represent the lower and upper boundaries of the interval, respectively;as a constraint condition of the moment of origin,as central moment constraints, the two moment constraints are usedEnsuring the consistency of the cumulative distribution function;andthe shape constraint condition is used for ensuring the effectiveness of the cumulative distribution function; objective function f (Y) for obtaining probability box variablesThe maximum entropy of the cumulative distribution function is ensured;
and 7: converting the uncertainty optimization problem shown in formula (7) into an unconstrained certainty optimization problem;
the conversion of the uncertainty optimization problem shown in the formula (7) into an unconstrained certainty optimization problem comprises the following sub-steps:
step 71: processing the constraint function by using the interval possibility degree;
moment condition of equality constraint in equation (7) for uncertainty optimization problemDescribing the interval uncertainty constraint with the interval likelihood level can be converted to a deterministic equality constraint as shown in equation (8):
in the formula (8), the first and second groups,representing probability box variables made up of new focal elementsOf the kth origin moment, and similarly, the equation is aboutRestraint the condition of momentDescribing the interval uncertainty constraint with the interval likelihood level can be converted to a deterministic equality constraint as shown in equation (9):
in the formula (9), the reaction mixture,representing probability box variables made up of new focal elementsThe interval of the qth order central moment of (a);
step 72: obtaining an unconstrained deterministic optimization problem by using a penalty function method;
constraining equations (8), (9) and (9) by penalty function methodAndprocessing can further be achieved as follows with a penalty function fp(Y) an unconstrained deterministic optimization problem:
in the formula (10), λ, φ and ε are penalty factors;τk，ξq，ψqθ and η are penalty functions, which can be obtained by the following equations:
and 8: solving an unconstrained deterministic optimization problem formula (10) by using an alternate mapping genetic algorithm to obtain a probability box variableA cumulative distribution function;
and step 9: constructing a limit state function g (X, Y) of the air-drop air bag buffer device, and changing the random vector X into (X) according to the formula (17) and the formula (18)1,Xμ,...,XW) And probability box vectorMapping to standard normal space U to obtain new extreme state function G (U)X,UY) Wherein, UXFor vectors in which the random vector X is mapped to a standard normal space, UYMapping the probability box vector Y to a vector under a standard normal space;
in the formula (17) and the formula (18), Φ is a cumulative distribution function of the normal distribution, Φ-1Which is the cumulative distribution inverse of a standard normal distribution,is a random variable XμThe cumulative distribution function of (a) is,as a probability box variableThe lower boundary of the cumulative distribution function of (c),as a probability box variableUpper boundary of the cumulative distribution function of (1);is a random variable XμA variable mapped to a standard normal space,as a probability box variableMaps to the lower boundary of the variable under the standard normal space,as a probability box variableMapping to the upper boundary of the variable under the standard normal space;
step 10, establishing an optimization problem shown as a formula (19) and a formula (20), and solving a minimum reliability index β of the air-drop airbag buffer device by adopting an alternate mapping genetic algorithmLAnd a maximum reliability index βR。
Wherein,
wherein,
to further explain the present invention in detail, the following describes a solution of the present invention with reference to a specific embodiment. The present embodiment is designed based on the reliability of the air-drop airbag cushion device, and is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.
Fig. 2 is a schematic model diagram of an airborne airbag cushion apparatus equipped according to the method of the present invention. The procedure was as shown in FIG. 1. A design method for the non-precise probability reliability of an equipment airborne airbag buffer device aims at the equipment airborne airbag buffer device shown in figure 2 and comprises the following specific steps:
step 1: analyzing uncertainty factors in the buffering process of the air-dropping air bag, and determining the bottom area X of the air bag1(m2) Initial bag height of air bag X2(m) and vertical airbag landing velocity X3(m/s) is divided into random variables, and a random vector X ═ X1,X2,X3) Is described using a probabilistic model, in which a random variable Xμμ ═ 1,2,3, described by the probability distribution shown in table (1);
TABLE 1 random variable distribution types for airbag cushions
In Table (1), for a random variable X following a lognormal distribution1Distribution parameter 1 and distribution parameter 2 represent mean and standard deviation, respectively; for random variable X obeying normal distribution2Distribution parameter 1 and distribution parameter 2 represent mean and standard deviation, respectively; for random variables X subject to uniform distribution3Distribution parameter 1 and distribution parameter 2 represent the lower and upper bounds of the interval, respectively.
The air bag is initially encapsulated and pressed Y1(Pa), air bag burst membrane pressure Y2(Pa) and air bag vent area Y3(m2) Divided into probability box variables, probability box vector Y ═ (Y)1,Y2,Y3) Described using a probability box model, wherein the probability box variablesComposed of the focal elements shown in Table (2);
TABLE 2 probability box variable distribution parameters for airbag cushions
Step 2: calculating probability box variables based on equations (21) and (22)First 4 origin moments and first 4 central moments:
in the formula (21) and the formula (22),representing probability box variablesThe s-th order origin moment of (c),representing probability box variablesThe s-th central moment of (a); probability box variables are listed in tables 3, 4 and 5, respectivelyThe first four-order origin moment and the central moment.
TABLE 3 probability box variables Y1Moment information of
TABLE 4 probability box variables Y2Moment information of
TABLE 5 probability box variables Y3Moment information of
And step 3: to probability box variableDividing contribution degree units;
the pair probability box variableThe division of the contribution degree unit comprises the following sub-steps:
step 31: variable of probability boxOrdering the endpoints of all included focal elements from small to large { d1,d2,...,de}；
Step 32: every two adjacent endpoints are oneGroups, each constituting a new contribution unit interval { [ d ]1,d2],[d2,d3],[d3,d4],...,[de-1,de]}；
Step 33: superposing the original focal element quality in each contribution degree unit interval to form the quality of a new contribution degree unit, and forming a new contribution degree unit shown in a table (6);
TABLE 6 contribution unit parameters corresponding to probability box variables
And 4, step 4: probability box variablesEach contribution unit in (1) can move up and down according to the mass of the previous contribution unit to determine its position in the cumulative distribution function, and the distance h for moving up and down of the contribution unit is selected as a design variable as shown in equation (23):
wherein,
and 5: variable of probability boxThe upper and lower boundaries of the unit mass of each contribution degree in the table are sorted from small to largeWherein, F1 new＝0，Then, every two adjacent boundaries are grouped, new focal element quality is formed according to the difference between the upper boundary and the lower boundary of the two adjacent boundaries, and the end points corresponding to the upper boundary and the lower boundary of the new focal element are selected as the interval of the new focal element, so as to form a new contribution degree unit as shown in a formula (24):
in the formula (24), the first and second groups,the z-th new focal element is represented,andthe interval end point of the z-th new focal element is shown,representing the mass of the z-th new focal element;
step 6: the uncertainty optimization problem shown as equation (25), equation (26) and equation (27) is established to obtain the probability box variablesCumulative distribution function of (2):
0≤h1≤0.40，0.30≤h2≤0.70，0.0≤h3≤0.40
0≤h1≤0.50，0≤h2≤0.70，0.20≤h3≤1.0
0≤h1≤0.60，0≤h2≤0.70，0.10≤h3≤1.0
in the formula (25), the formula (26) and the formula (27),the interval of the original k-th order origin moment,the interval of the original q-th order central moment; superscripts L and R represent the lower and upper boundaries of the interval, respectively;as a constraint condition of the moment of origin,the two moment constraint conditions are used for ensuring the consistency of the cumulative distribution function;andthe shape constraint condition is used for ensuring the effectiveness of the cumulative distribution function; objective functionFor obtaining probability box variablesThe maximum entropy of the cumulative distribution function is ensured;
and 7: converting the uncertainty optimization problem shown in formula (25), formula (26) and formula (27) into an unconstrained certainty optimization problem;
the conversion of the uncertainty optimization problem shown in the formula (25), the formula (26) and the formula (27) into an unconstrained certainty optimization problem comprises the following sub-steps:
step 71: processing the constraint function by using the interval possibility degree;
constraint moment condition g for equations in uncertainty optimization problem equation (25), equation (26), and equation (27)rkDescribing the interval uncertainty constraint using the interval likelihood level can be converted into a deterministic equation constraint as shown in equation (28):
in the formula (28), the first and second groups,representing probability box variables made up of new focal elementsOf the kth origin moment, and similarly, the equation constraint moment conditionDescribing the interval uncertainty constraint with the interval likelihood level can be converted to a deterministic equality constraint as shown in equation (29):
in the formula (29), the reaction is carried out,representing probability box variables made up of new focal elementsThe interval of the qth order central moment of (a);
step 72: obtaining an unconstrained deterministic optimization problem by using a penalty function method;
constraining equations (28), (29) and (29) using penalty function methodAndprocessing can further be achieved by taking the following penalty functionThe expressed unconstrained deterministic optimization problem:
in the formula (30), λ, Φ and ∈ are penalty factors, and λ ═ Φ ═ ε ═ 1000;τk，ξq，ψqtheta and η are
The penalty function can be obtained by the following formula:
and 8: solving the unconstrained deterministic optimization problem formula (30) by using an alternate mapping genetic algorithm to obtain the probability box variables shown in the graph (3), the graph (4) and the graph (5)A cumulative distribution function;
and step 9: the maximum impact acceleration a (X, Y) borne by the landing impact of the air-drop equipment cannot exceed amax＝250m/s2Therefore, a limit state function of the air-bag damper equipped is constructed as shown in equation (37): g (X, Y) ═ 250-a (X, Y) formula (37)
The random vector X is (X) according to equation (38) and equation (39)1,X2,X3) And probability box vector Y ═ Y (Y)1,Y2,Y3) Mapping to standard normal space U to obtain new extreme state function G (U)X,UY) Wherein, UXFor vectors in which the random vector X is mapped to a standard normal space, UYMapping the probability box vector Y to a vector under a standard normal space;
in equations (38) and (39), Φ is a cumulative distribution function of the normal distribution, Φ-1Which is the cumulative distribution inverse of a standard normal distribution,is a random variable XμThe cumulative distribution function of (a) is,as a probability box variableThe lower boundary of the cumulative distribution function of (c),as a probability box variableUpper boundary of the cumulative distribution function of (1);is a random variable XμA variable mapped to a standard normal space,as a probability box variableMaps to the lower boundary of the variable under the standard normal space,as a probability box variableMapping to the upper boundary of the variable under the standard normal space;
step 10, establishing an optimization problem shown as a formula (40) and a formula (41), and solving a minimum reliability index β of the air-drop airbag buffer device by adopting an alternate mapping genetic algorithmLAnd a maximum reliability index βR。
Wherein,
wherein,
in this example, the minimum reliability index β of the airborne airbag cushion systemLAnd a maximum reliability index βRThe final solution results are shown in table (7).
TABLE 7 reliability solving results for airborne airbag buffering device
The above detailed description is specific to possible embodiments of the present invention, and the embodiments are not intended to limit the scope of the present invention, and all equivalent implementations or modifications that do not depart from the scope of the present invention are intended to be included within the scope of the present invention.
Claims (3)
1. A design method for non-precise probability reliability of an air-drop airbag buffer device is characterized by comprising the following steps:
step 1: analyzing uncertainty factors in the air-drop airbag buffering process, and dividing uncertainty vectors into random vectors and probability box vectors according to the information of the sample points; random vector X ═ X1,Xμ,...,XW) 1,2, W is described using a probability model, a probability box vectorDescribing by adopting a probability box model; probability box variablesIs composed of n focal elements in formula (1):
in the formula (1), yiThe (i) th focal element is shown,an interval representing the ith focal element, aiAnd biThe interval end point of the ith focal element is shown,representing the mass of the ith focal element;
step 2: calculating probability box variables based on equations (2) and (3)Origin moment and center moment of (c):
in the formula (2) and the formula (3),representing probability box variablesThe s-th order origin moment of (c),representing probability box variablesThe s-th central moment of (a);
and step 3: to probability box variableDividing contribution degree units;
the pair probability box variableThe division of the contribution degree unit comprises the following sub-steps:
step 31: variable of probability boxOrdering the endpoints of all included focal elements from small to large { d1,d2,...,de}；
Step 32: grouping every two adjacent end points into a group, and respectively forming a new section of contribution degree unit { [ d { [ D ]1,d2],[d2,d3],[d3,d4],...,[de-1,de]}；
Step 33: superposing the original focal element quality in each contribution degree unit interval to form the quality of a new contribution degree unit, and forming a new contribution degree unit as shown in formula (4):
in the formula (4), crDenotes the r-th contribution unit, drAnd dr+1Represents the interval end point of the r-th contribution degree unit,representing the quality of the r-th contribution unit;
and 4, step 4: each contribution degree unit can move up and down according to the mass of the previous contribution degree unit to determine the position of the previous contribution degree unit in the cumulative distribution function, and the distance h for moving up and down of the contribution degree unit is selected as a design variable as shown in formula (5):
wherein,
and 5: sorting the upper and lower boundaries of the unit mass of each contribution degree from small to largeWherein, F1 new＝0，Then, every two adjacent boundaries are grouped, new focal element quality is formed according to the difference between the upper boundary and the lower boundary of the two adjacent boundaries, and the end points corresponding to the upper boundary and the lower boundary of the new focal element are selected as the interval of the new focal element, so as to form a new contribution degree unit as shown in formula (6):
z＝1,...,v-1
in the formula (6), the first and second groups,the z-th new focal element is represented,andthe interval end point of the z-th new focal element is shown,representing the mass of the z-th new focal element;
step 6: the uncertainty optimization problem shown in equation (7) is established to obtain the probability box variablesCumulative distribution function of (2):
wherein,
in the formula (7), the first and second groups,the interval of the original k-th order origin moment,the interval of the original q-th order central moment; superscripts L and R represent the lower and upper boundaries of the interval, respectively;as a constraint condition of the moment of origin,the two moment constraint conditions are used for ensuring the consistency of the cumulative distribution function;andthe shape constraint condition is used for ensuring the effectiveness of the cumulative distribution function; objective function f (Y) for obtaining probability box variablesThe maximum entropy of the cumulative distribution function is ensured;
and 7: converting the uncertainty optimization problem shown in formula (7) into an unconstrained certainty optimization problem;
the conversion of the uncertainty optimization problem shown in the formula (7) into an unconstrained certainty optimization problem comprises the following sub-steps:
step 71: processing the constraint function by using the interval possibility degree;
moment condition of equality constraint in equation (7) for uncertainty optimization problemThe description of the interval uncertainty constraint by using the interval probability level can be converted into the certainty shown in the formula (8) and the likeThe constraint condition of the formula:
in the formula (8), the first and second groups,representing probability box variables made up of new focal elementsOf the kth origin moment, and similarly, the equation constraint moment conditionDescribing the interval uncertainty constraint with the interval likelihood level can be converted to a deterministic equality constraint as shown in equation (9):
in the formula (9), the reaction mixture,representing probability box variables made up of new focal elementsThe interval of the qth order central moment of (a);
step 72: obtaining an unconstrained deterministic optimization problem by using a penalty function method;
constraining equations (8), (9) and (9) by penalty function methodAndprocessing can further be achieved as follows with a penalty function fp(Y) an unconstrained deterministic optimization problem:
in the formula (10), λ, φ and ε are penalty factors;τk，ξq，ψqθ and η are penalty functions, which can be obtained by the following equations:
and 8: genetic algorithm pair adopting generation-alternate mappingThe unconstrained deterministic optimization problem equation (10) is solved to obtain the probability box variablesA cumulative distribution function;
and step 9: constructing a limit state function g (X, Y) of the air-drop air bag buffer device, and setting a random vector X as (X)1,Xμ,...,XW) And probability box vectorMapping to standard normal space U to obtain new extreme state function G (U)X,UY) Wherein, UXFor vectors in which the random vector X is mapped to a standard normal space, UYMapping the probability box vector Y to a vector under a standard normal space;
step 10, establishing an optimization problem shown as a formula (17) and a formula (18) so as to solve the minimum reliability index β of the air-bag buffer device for air-drop equipmentLAnd a maximum reliability index βR。
Wherein,
wherein,
2. the design method of the inaccurate probability reliability of the air-drop bag buffer device is characterized in that: in step 9, the random vector X may be (X) according to equation (19) and equation (20)1,Xμ,...,XW) And probability box vectorMapping to the standard normal space U:
in equations (19) and (20), Φ is a cumulative distribution function of the normal distribution, Φ-1Which is the cumulative distribution inverse of a standard normal distribution,is a random variable XμThe cumulative distribution function of (a) is,as a probability box variableThe lower boundary of the cumulative distribution function of (c),as a probability box variableUpper boundary of the cumulative distribution function of (1);is a random variable XμA variable mapped to a standard normal space,as a probability box variableMaps to the lower boundary of the variable under the standard normal space,as a probability box variableMapping to the upper boundary of the variable under the standard normal space.
3. The method for designing the inaccurate probability reliability of the air bag buffer device for equipment airborne according to claim 1, wherein the step 10 is to use an alternate mapping genetic algorithm to solve the minimum reliability index β of the air bag buffer device for equipment airborneLAnd a maximum reliability index βR。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910449281.1A CN110162898A (en) | 2019-05-28 | 2019-05-28 | A kind of non-precision probabilistic reliability design method for equipping airborne air bag buffer |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910449281.1A CN110162898A (en) | 2019-05-28 | 2019-05-28 | A kind of non-precision probabilistic reliability design method for equipping airborne air bag buffer |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN110162898A true CN110162898A (en) | 2019-08-23 |
Family
ID=67629294
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910449281.1A Withdrawn CN110162898A (en) | 2019-05-28 | 2019-05-28 | A kind of non-precision probabilistic reliability design method for equipping airborne air bag buffer |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110162898A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110851975A (en) * | 2019-11-06 | 2020-02-28 | 长沙理工大学 | Non-probability reliability assessment method for gear transmission device |
-
2019
- 2019-05-28 CN CN201910449281.1A patent/CN110162898A/en not_active Withdrawn
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110851975A (en) * | 2019-11-06 | 2020-02-28 | 长沙理工大学 | Non-probability reliability assessment method for gear transmission device |
| CN110851975B (en) * | 2019-11-06 | 2021-03-16 | 长沙理工大学 | Non-probability reliability assessment method for gear transmission device |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Xiao et al. | A simple algebraic interface capturing scheme using hyperbolic tangent function | |
| CN101697006B (en) | Target identification method based on data fusion of airborne radar and infrared imaging sensor | |
| CN109635685A (en) | Target object 3D detection method, device, medium and equipment | |
| CN109117876A (en) | A kind of dense small target deteection model building method, model and detection method | |
| CN110009037B (en) | Short-term engineering wind speed prediction method and system based on physical information coupling | |
| CN113538391A (en) | Photovoltaic defect detection method based on Yolov4 and thermal infrared image | |
| CN109376403B (en) | Two-dimensional icing numerical simulation method based on Cartesian self-adaptive reconstruction technology | |
| CN108876799A (en) | A kind of real-time step detection method based on binocular camera | |
| CN110070025A (en) | Objective detection system and method based on monocular image | |
| CN109375252A (en) | Consider the ground motion parameter evaluation method of different seismic structure maximum credible earthquakes | |
| CN110175391B (en) | Accelerometer uncertainty analysis method based on arbitrary chaotic polynomial | |
| CN108460176A (en) | A method of it improving satellite orbit perturbation power model and indicates precision | |
| Mignac et al. | Argo data assimilation into HYCOM with an EnOI method in the Atlantic Ocean | |
| CN103093243B (en) | The panchromatic remote sensing image clouds of high-resolution sentences method | |
| CN102298728B (en) | Method for evaluating target threat degree | |
| CN113239884A (en) | Method for recognizing human body behaviors in elevator car | |
| CN110162898A (en) | A kind of non-precision probabilistic reliability design method for equipping airborne air bag buffer | |
| Yin et al. | An enhanced lightweight convolutional neural network for ship detection in maritime surveillance system | |
| CN117390498A (en) | Flight capability assessment method of fixed wing cluster unmanned aerial vehicle based on Transformer model | |
| CN117853955A (en) | Unmanned aerial vehicle small target detection method based on improved YOLOv5 | |
| CN116503765A (en) | Engineering scale wave identification method based on machine vision | |
| CN116503798A (en) | Telegraph pole tower inclination monitoring method based on rotation target detection | |
| KR102411074B1 (en) | Devices and Methods for Detection and Prediction of Cold Water Mass Using Artificial Intelligence and Satellite Imaging | |
| Xu et al. | Key issues in developing numerical models for artificial weather modification | |
| CN112327317B (en) | Convolution neural network-based spatial non-cooperative target angular velocity measurement method |
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 | ||
| WW01 | Invention patent application withdrawn after publication | ||
| WW01 | Invention patent application withdrawn after publication |
Application publication date: 20190823 |