CN110321594B - Reliability analysis method and device for aircraft mechanism with multiple failure modes - Google Patents
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Abstract
The present disclosure provides a method and apparatus for reliability analysis of an aircraft mechanism having multiple failure modes. Extracting N sample points according to an initial probability density function, and extracting N new sample points according to an intermediate sampling density function and the N sample points; determining N response values of each failure mode at N new sample points, and judging whether at least a preset number of response values in the response values of each failure mode are smaller than a preset value; determining the failure probability of failure modes with the response values of which the preset number are smaller than the preset value; and establishing a new intermediate sampling density function according to the initial sampling density function and the failure modes of which the failure probabilities are not determined, sampling again and determining response values until the failure probabilities of all the failure modes are determined. The present disclosure enables a determination of a failure probability for each of a plurality of failure modes.
Description
Technical Field
The present disclosure relates to the field of reliability detection technologies, and in particular, to a reliability analysis method for an aircraft mechanism with multiple failure modes and a reliability analysis device for an aircraft mechanism with multiple failure modes.
Background
In order to prolong the service life of the civil aircraft and improve the flight safety and the robustness of a mechanism system, the reliability analysis of the typical parts of the civil aircraft mechanism is of great significance.
The existing reliability analysis method performs taylor expansion on a limit state function at a design point, and performs reliability analysis based on the obtained taylor expansion. However, this method can only analyze a single failure mode, and is no longer applicable to components with multiple failure modes.
It is noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present disclosure and therefore may include information that does not constitute prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
The present disclosure is directed to a method for analyzing reliability of an aircraft mechanism having a plurality of failure modes and an apparatus for analyzing reliability of an aircraft mechanism having a plurality of failure modes, which are capable of determining a failure probability of each failure mode.
According to one aspect of the present disclosure, there is provided a method of reliability analysis of an aircraft mechanism having a plurality of failure modes, comprising:
s1, extracting N sample points according to an initial probability density function, wherein N is greater than 1;
s2, determining an intermediate sampling density function according to the initial probability density function and the limit state function corresponding to each failure mode, wherein the intermediate sampling density function is as follows:
wherein,
as a function of said intermediate sampling density, Z j For normalization constant, [ phi ] is the standard normal distribution function, g n (x) As a function of the extreme state corresponding to the nth failure mode, f X (x) The initial probability density function is represented by sigma which is a control factor, j is a positive integer greater than or equal to 2, and n is a positive integer greater than 0;
s3, enabling the value of j to be 2, and extracting N new sample points according to the N sample points and the intermediate sampling density function;
s4, determining N response values of each failure mode at N new sample points, and if at least a preset number of response values smaller than a preset value do not exist in the response values of each failure mode, turning to S5; if at least a preset number of response values in the response values of at least one failure mode are smaller than a preset value, turning to step S6;
s5, increasing the value of j by 1, extracting N new sample points according to the N sample points extracted last time and the intermediate sampling density function, and turning to the step S4;
s6, determining that at least a preset number of response values in the response values have failure probabilities of the failure modes with the response values smaller than a preset value;
s7, determining a new intermediate sampling density function according to the extreme state function corresponding to the failure modes of which at least the response values are smaller than the preset value and the number of the response values is not at least preset;
and S8, increasing the value of j by 1, extracting N new sample points according to the N sample points extracted last time and the new intermediate sampling density function, and turning to the step S4 until the failure probability of all failure modes is obtained.
In an exemplary embodiment of the present disclosure, the preset value is 0.
In an exemplary embodiment of the present disclosure, the preset number is N/3.
In an exemplary embodiment of the present disclosure, the failure probability may be determined by a first preset formula, where the first preset formula is:
wherein, P f To failure probability, Z j In order to be a normalization constant, the method comprises the following steps of,
for the ith sample point of the N sample points,
in order to indicate the function,
is a transition function in which, among other things,
in an exemplary embodiment of the present disclosure, determining a new intermediate sampling density function from the extreme state function corresponding to the absence of at least a preset number of failure modes of the response values being less than a preset value comprises:
and reserving the limit state functions corresponding to failure modes of which at least the response values are smaller than the preset value in the response values and the number of the response values is not at least preset, in the intermediate sampling density function determined last time, so as to obtain a new intermediate sampling density function.
According to one aspect of the present disclosure, there is provided a reliability analysis device for an aircraft mechanism having a plurality of failure modes, comprising:
the first extraction module is used for extracting N sample points according to the initial probability density function, wherein N is greater than 1;
a first determining module for determining an intermediate sampling density function based on the initial probability density function and the extreme state function corresponding to each of the failure modes, the intermediate sampling density function being:
wherein,
as a function of said intermediate sampling density, Z j For normalization constant, [ phi ] is the standard normal distribution function, g n (x) As a function of the extreme state corresponding to the nth failure mode, f X (x) Representing said initial probability density function, σ being controlFactor j is a positive integer greater than or equal to 2, n is a positive integer greater than 0;
a second extraction module, configured to make the value of j be 2, and extract N new sample points according to the N sample points and the intermediate sampling density function;
a determining module configured to execute a response value determining action, where the response value determining action includes: determining N response values of each failure mode at N new sample points, and judging whether at least a preset number of response values in the response values of each failure mode are smaller than a preset value;
a third extraction module, configured to increase the value of j by 1 when at least a preset number of response values smaller than a preset value do not exist in the response values of each failure mode, extract N new sample points according to N sample points extracted last time and an intermediate sampling density function, and execute the response value determination action;
a second determining module, configured to determine, when at least a preset number of response values in the response value of at least one of the failure modes are smaller than a preset value, a failure probability that at least a preset number of response values in the response value are smaller than a preset value;
a third determining module, configured to determine a new intermediate sampling density function according to a limit state function corresponding to no failure mode in which at least a preset number of response values are smaller than a preset value among the response values;
and the fourth extraction module is used for increasing the value of j by 1, extracting IV sample points according to the new sampling density function and executing the response value judgment action.
In an exemplary embodiment of the present disclosure, the preset value is 0.
In an exemplary embodiment of the present disclosure, the preset number is N/3.
In an exemplary embodiment of the present disclosure, the failure probability may be determined by a first preset formula, where the first preset formula is:
wherein, P f To failure probability, Z j In order to be a normalization constant, the method comprises the following steps of,
for the ith of the IV said sample points,
in order to indicate the function,
is a transition function in which, among other things,
in an exemplary embodiment of the disclosure, the third determining module is configured to retain a limit state function corresponding to no failure mode with at least a preset number of response values smaller than a preset value in the response values in the last determined intermediate sampling density function, so as to obtain a new intermediate sampling density function.
The reliability analysis method of the aircraft mechanism with the plurality of failure modes and the reliability analysis device of the aircraft mechanism with the plurality of failure modes extract IV sample points according to an initial probability density function, and extract IV new sample points according to an intermediate sampling density function and the IV sample points; determining IV response values of each failure mode at an IV sample point, and judging whether at least a preset number of response values in the response values of each failure mode are smaller than a preset value; determining the failure probability of failure modes with the response values of which the preset number are smaller than the preset value; and establishing a new intermediate sampling density function according to the initial sampling density function and the failure modes of which the failure probabilities are not determined, sampling again and determining response values until the failure probabilities of all the failure modes are determined.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
The above and other features and advantages of the present disclosure will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings. It should be apparent that the drawings in the following description are merely examples of the disclosure and that other drawings may be derived by those of ordinary skill in the art without inventive effort.
Fig. 1 is a schematic view of a spindle according to an embodiment of the present disclosure.
In the figure: 1. a first failure interface; 2. a second failure interface; 3. a third failure interface; 4. a fourth failure interface; 5. a fifth failure interface; 6. a rotating shaft.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the subject matter of the present disclosure can be practiced without one or more of the specific details, or with other methods, apparatus, etc.
Furthermore, the drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and a repetitive description thereof will be omitted. The terms "comprising" and "having" are intended to be inclusive and mean that there may be additional elements/components/etc. other than the listed elements/components/etc.
The disclosed embodiments provide a method for reliability analysis of an aircraft mechanism having multiple failure modes. The aircraft mechanism may be a rotating shaft of an aircraft horizontal tail, but the disclosure is not limited thereto. The method comprises the following steps:
s1, extracting N sample points according to an initial probability density function, wherein N is greater than 1;
s2, determining an intermediate sampling density function according to the initial probability density function and the limit state function corresponding to each failure mode, wherein the intermediate sampling density function is as follows:
wherein,
as a function of the intermediate sampling density, Z j For normalization constant, [ phi ] is the standard normal distribution function, g n (x) As a function of the extreme state corresponding to the nth failure mode, f X (x) Expressing an initial probability density function, wherein sigma is a control factor, j is a positive integer greater than or equal to 2, and n is a positive integer greater than 0;
s3, enabling the value of j to be 2, and extracting N new sample points according to the N sample points and the intermediate sampling density function;
s4, determining N response values of each failure mode at N new sample points, and if at least a preset number of response values smaller than a preset value do not exist in the response values of each failure mode, turning to S5; if at least a preset number of response values in the response values of at least one failure mode are smaller than a preset value, turning to step S6;
s5, increasing the value of j by 1, extracting N new sample points according to the N sample points extracted last time and the intermediate sampling density function, and turning to the step S4;
s6, determining the failure probability of failure modes with at least a preset number of response values smaller than a preset value in the response values;
s7, determining a new intermediate sampling density function according to the extreme state function corresponding to failure modes of which at least the response values are smaller than the preset value in the absence of at least preset number of response values;
and S8, increasing the value of j by 1, extracting N new sample points according to the N sample points extracted last time and the new intermediate sampling density function, and turning to the step S4 until the failure probabilities of all failure modes are obtained.
According to the reliability analysis method of the aircraft mechanism with the multiple failure modes, N sample points are extracted according to an initial probability density function, and N new sample points are extracted according to an intermediate sampling density function and the N sample points; determining N response values of each failure mode at N sample points, and judging whether at least a preset number of response values in the response values of each failure mode are smaller than a preset value; determining the failure probability of failure modes with the response values of which the preset number are smaller than the preset value; and establishing a new intermediate sampling density function according to the initial sampling density function and the failure modes of which the failure probabilities are not determined, sampling again and determining response values until the failure probabilities of all the failure modes are determined.
Embodiments of the disclosure are described in further detail below:
this step S1 is the first sampling. This step S3 is a second sub-sampling, which may be performed according to the markov chain-monte carlo method.
The preset value in step S4 may be 0. The predetermined number in step S4 may be N/3. In step S4, if at least N/3 response values among the response values at the N sample points extracted in step S3 of each failure mode are not less than 0, go to step S5 to extract N sample points again. In step S5, the value of j is increased by 1. Since j takes a value of 2 when the last time the iv sample points were extracted, j takes a value of 3 when this time the extraction was performed. And if at least N/3 response values in the response values of the IV sample points extracted at this time in each failure mode are not less than 0, increasing the value of j by 1, and continuously extracting the IV sample points, namely continuously extracting the IV sample points under the condition that j is equal to 4.
In step S4, if at least N/3 response values of the k-th failure mode of the plurality of failure modes exist in the response values at the iv sample points extracted in step S3, the process goes to step S6, i.e., the failure probability of the k-th failure mode is determined. The failure probability can be determined by a first preset formula, where the first preset formula is:
in the first predetermined formula, P f To failure probability, Z j In order to be a normalization constant, the method comprises the following steps of,
for the ith sample point of the iv sample points,
in order to indicate the function,
is a transition function in which, among other things,
the iv sample points in step S3 are extracted when the value of j is 2, and the failure probability of the kth failure mode can be calculated by the first preset attack when the value of j is 2. If the IV sample points are extracted under the condition that the value of j is 3, calculating the failure probability through a first preset formula under the condition that the value of j is 3.
Normalization constant Z in the first predetermined formula j May be determined by a second predetermined formula, which may be:
in the second predetermined formula, r m Is the ratio of adjacent normalization constants.
The ratio of the adjacent normalization constants can be determined by a third preset formula, where m is equal to j for example, the third preset formula can be:
wherein,
and
are all transition functions.
In step S7, a new intermediate sampling density function is determined based on the extreme state functions corresponding to the absence of at least a preset number of failure modes in which the response values are less than the preset value. Specifically, the limit state functions corresponding to failure modes of which at least a preset number of response values are smaller than a preset value do not exist in the response values in the intermediate sampling density function determined last time are reserved, and a new intermediate sampling density function is obtained. Taking the example that at least N/3 response values of the k-th failure mode in the response values of the N sample points extracted in step S3 are smaller than 0, the limit state function corresponding to the k-th failure mode in the intermediate sampling density function in step S2 is removed, and the obtained new intermediate sampling density function is:
in step S8, the sampling may also be performed according to the markov chain-monte carlo method.
In the related art, the failure probability of a plurality of failure modes can also be determined by using the monte carlo method. The method of the present disclosure is compared to the monte carlo method below. As shown in fig. 1, taking a rotating shaft 6 of a horizontal tail of an aircraft as an example, the rotating shaft comprises a first failure interface 1, a second failure interface 2, a third failure interface 3, a fourth failure interface 4 and a fifth failure interface 5. The input variable distribution of the rotating shaft is shown in table 1, and the results determined by the method of the present disclosure and the conventional method are shown in table 2.
TABLE 1
TABLE 2
| Failure mode | Computing item | Monte Carlo method | Methods of the present disclosure |
| g 1 (x) | Probability of failure | 0.0127 | 0.0115 |
| g 0 (x) | Probability of failure | 0.0405 | 0.0399 |
| g 3 (x) | Probability of failure | 0.0138 | 0.0124 |
| g 4 (x) | Probability of failure | 0.0986 | 0.0952 |
| g 5 (x) | Probability of failure | 0.0236 | 0.0218 |
| Total number of sample points | 10 6 | 4325 |
As can be seen from table 2, compared with the monte carlo method, the failure probability determined by the method of the present disclosure is similar to the failure probability determined by the monte carlo method, but the number of required total sample points is greatly reduced, and the efficiency of reliability analysis is improved.
The disclosed embodiments also provide a reliability analysis device for an aircraft mechanism with multiple failure modes. The reliability analysis device may include:
the first extraction module is used for extracting N sample points according to the initial probability density function, wherein N is greater than 1;
a first determining module for determining an intermediate sampling density function based on the initial probability density function and the extreme state function corresponding to each failure mode, the intermediate sampling density function being:
wherein,
as a function of the intermediate sampling density, Z j For normalization constant, [ phi ] is the standard normal distribution function, g n (x) Is composed ofExtreme state function, f, corresponding to the nth failure mode X (x) Expressing an initial probability density function, wherein sigma is a control factor, j is a positive integer greater than or equal to 2, and n is a positive integer greater than 0;
the second extraction module is used for enabling the value of j to be 2 and extracting N new sample points according to the N sample points and the intermediate sampling density function;
a determining module for performing a response value determining action, the response value determining action comprising: determining N response values of each failure mode at N new sample points, and judging whether at least a preset number of response values in the response values of each failure mode are smaller than a preset value;
the third extraction module is used for increasing the value of j by 1 under the condition that at least a preset number of response values smaller than a preset value do not exist in the response values of all failure modes, extracting N new sample points according to the N sample points extracted last time and the intermediate sampling density function, and executing response value judgment behaviors;
the second determining module is used for determining the failure probability of failure modes with at least a preset number of response values smaller than a preset value in the response values under the condition that at least a preset number of response values smaller than the preset value exist in the response values of at least one failure mode;
a third determining module, configured to determine a new intermediate sampling density function according to a limit state function corresponding to a failure mode in which at least a preset number of response values are smaller than a preset value among the response values;
and the fourth extraction module is used for increasing the value of j by 1, extracting N sample points according to the new intermediate sampling density function and executing response value judgment action.
The reliability analysis device of the aircraft mechanism with the multiple failure modes extracts N sample points according to an initial probability density function, and extracts N new sample points according to an intermediate sampling density function and the N sample points; determining N response values of each failure mode at N sample points, and judging whether at least a preset number of response values in the response values of each failure mode are smaller than a preset value; determining the failure probability of failure modes with the response values of which the preset number are smaller than the preset value; and establishing a new intermediate sampling density function according to the initial sampling density function and the failure modes of which the failure probabilities are not determined, sampling again and determining response values until the failure probabilities of all the failure modes are determined.
The preset value may be 0. The predetermined number may be N/3. The failure probability may be determined by a first preset formula, which is:
wherein, P f To failure probability, Z j In order to be a normalization constant, the method comprises the following steps of,
for the ith of the IV said sample points,
in order to indicate the function(s),
is a transition function in which, among other things,
the third determining module is configured to retain a limit state function corresponding to no failure mode with at least a preset number of response values smaller than a preset value in the response values in the previously determined intermediate sampling density function, so as to obtain a new intermediate sampling density function.
The embodiment of the disclosure also provides a storage medium. The storage medium is a computer-readable storage medium, such as a hard disk, but is not limited thereto, and may also be a Random Access Memory (RAM), a Read Only Memory (ROM), and the like. The storage medium has stored thereon a computer program. Which when executed by a processor implements a reliability analysis method according to any of the embodiments described above. Since the method for analyzing the dependency of the tail implemented by the computer program of the embodiment of the present disclosure when executed by the processor is the same as the method for analyzing the dependency of the embodiment described above, the same effects are obtained, and are not described herein again.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
Claims (8)
1. A method of reliability analysis of an aircraft mechanism having a plurality of failure modes, comprising:
s1, extracting N sample points according to an initial probability density function, wherein N is greater than 1;
s2, determining an intermediate sampling density function according to the initial probability density function and the limit state function corresponding to each failure mode, wherein the intermediate sampling density function is as follows:
wherein,
as a function of said intermediate sampling density, Z j Is a normalized constant, phi is a standard normal distribution function, g n (x) As a function of the extreme state corresponding to the nth failure mode, f X (x) The initial probability density function is defined, sigma is a control factor, j is a positive integer greater than or equal to 2, and n is a positive integer greater than 0;
s3, enabling the value of j to be 2, and extracting N new sample points according to the N sample points and the intermediate sampling density function;
s4, determining N response values of each failure mode at N new sample points, and if at least a preset number of response values smaller than a preset value do not exist in the response values of each failure mode, turning to S5; if at least a preset number of response values in the response values of at least one failure mode are smaller than a preset value, turning to step S6;
s5, increasing the value of j by 1, extracting N new sample points according to the N sample points extracted last time and the intermediate sampling density function, and turning to the step S4;
s6, determining that at least a preset number of response values are smaller than the failure probability of the failure mode in the response values; the failure probability is determined by a first preset formula, wherein the first preset formula is as follows:
wherein, P f To failure probability, Z j In order to be a normalization constant, the method comprises the following steps of,
for the ith sample point of the N sample points,
in order to indicate the function,
is a transition function in which, among other things,
wherein the normalization constant Z j The second preset formula is determined, and the second preset formula is as follows:
in the formula, r m Is the ratio of adjacent normalization constants;
the ratio of the adjacent normalization constants is determined by a third preset formula, wherein the third preset formula is as follows:
wherein,
and
are transition functions, m = j;
s7, determining a new intermediate sampling density function according to the extreme state function corresponding to the failure modes of which at least the response values are smaller than the preset value and the number of the response values is not at least preset;
and S8, increasing the value of j by 1, extracting N new sample points according to the N sample points extracted last time and the new intermediate sampling density function, and turning to the step S4 until the failure probability of all the failure modes is obtained.
2. The method of analyzing the reliability of an aircraft mechanism having multiple failure modes of claim 1, wherein the predetermined value is 0.
3. The method of analyzing the reliability of an aircraft mechanism having a plurality of failure modes of claim 1, wherein the predetermined number is N/3.
4. The method of analyzing the reliability of an aircraft mechanism having a plurality of failure modes according to claim 1, wherein determining a new intermediate sampling density function based on the extreme state functions corresponding to the absence of at least a preset number of failure modes in the response values that are less than a preset value comprises:
and reserving the limit state functions corresponding to failure modes of which at least the response values are smaller than the preset value in the response values and the number of the response values is not at least preset, in the intermediate sampling density function determined last time, so as to obtain a new intermediate sampling density function.
5. An apparatus for reliability analysis of an aircraft mechanism having a plurality of failure modes, comprising:
the first extraction module is used for extracting N sample points according to the initial probability density function, wherein N is greater than 1;
a first determining module for determining an intermediate sampling density function based on the initial probability density function and the extreme state function corresponding to each of the failure modes, the intermediate sampling density function being:
wherein,
as a function of said intermediate sampling density, Z j Is a normalized constant, phi is a standard normal distribution function, g n (x) As a function of the extreme state corresponding to the nth failure mode, f X (x) Expressing the initial probability density function, wherein sigma is a control factor, j is a positive integer greater than or equal to 2, and n is a positive integer greater than 0;
a second extraction module, configured to make the value of j be 2, and extract N new sample points according to the N sample points and the intermediate sampling density function;
a determining module configured to perform a response value determining action, where the response value determining action includes: determining N response values of each failure mode at N new sample points, and judging whether at least a preset number of response values in the response values of each failure mode are smaller than a preset value;
a third extraction module, configured to increase the value of j by 1 if at least a preset number of response values smaller than a preset value do not exist in the response values of each failure mode, extract N new sample points according to the N sample points extracted last time and an intermediate sampling density function, and execute the response value determination behavior;
a second determining module, configured to determine, when at least a preset number of response values in the response value of at least one of the failure modes are smaller than a preset value, a failure probability that at least a preset number of response values in the response value are smaller than a preset value; the failure probability is determined by a first preset formula, wherein the first preset formula is as follows:
wherein, P f To failure probability, Z j In order to be a normalization constant, the method comprises the following steps of,
for the ith sample point of the N sample points,
in order to indicate the function,
is a transition function in which, among other things,
wherein the normalization constant Z j The second preset formula is determined, and the second preset formula is as follows:
in the formula, r m Is the ratio of adjacent normalization constants;
ratio r of the neighboring normalization constants m The method is determined by a third preset formula, wherein the third preset formula is as follows:
wherein,
and
are transition functions, m = j;
a third determining module, configured to determine a new intermediate sampling density function according to a limit state function corresponding to a failure mode in which at least a preset number of response values are smaller than a preset value among the response values;
and the fourth extraction module is used for increasing the value of j by 1, extracting N sample points according to the new intermediate sampling density function, and executing the response value judgment action.
6. The reliability analysis device of an aircraft mechanism having multiple failure modes according to claim 5, wherein the preset value is 0.
7. The apparatus of claim 5, wherein the predetermined number is N/3.
8. The apparatus of claim 5, wherein the third determining module is configured to retain a new intermediate sampling density function from the previously determined intermediate sampling density function corresponding to the extreme state functions for which there are no failure modes with at least a predetermined number of response values less than a predetermined value from the response values.
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