CN111783239B - Fuzzy reliability analysis method for turbine tenon connection structure - Google Patents
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- 238000004458 analytical method Methods 0.000 title claims abstract description 36
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Abstract
The disclosure relates to the technical field of reliability analysis, and provides a fuzzy reliability analysis method for a turbine tenon connection structure, which is characterized by comprising the following steps: dividing a grid in a three-dimensional model of a turbine dovetail connection structure to establish a finite element model of the turbine dovetail connection structure; determining a functional function of the turbine dovetail connection structure according to the finite element model; on the basis of the function, adding an auxiliary random variable to establish a generalized function, wherein the auxiliary random variable obeys standard normal distribution; constructing a Kriging model according to the generalized function; and solving the fuzzy failure probability of the turbine tenon connection structure based on the Kriging model. The method can be used for efficiently and accurately analyzing the fuzzy reliability of the turbine tenon connecting structure.
Description
Technical Field
The disclosure relates to the technical field of reliability analysis, in particular to a fuzzy reliability analysis method for a turbine tenon connection structure.
Background
In conventional reliability analysis, the limit state as a means of distinguishing the structural failure state from the safety state is a clear boundary, and is referred to as a dual state. However, in practical engineering problems, the limits of the safe state and the disabled state are often not clear, there is a transition between the safe state and the disabled state, which is neither completely safe nor completely disabled, but rather is subject to a certain degree of safety and failure, respectively, called fuzzy state.
At present, the Monte Carlo method is generally adopted to analyze the fuzzy reliability of the structure, but the method has low analysis efficiency and cannot meet the requirement of engineering.
The above information disclosed in the background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute prior art that is known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to provide a fuzzy reliability analysis method for a turbine tenon connecting structure, which can be used for efficiently and accurately analyzing the fuzzy reliability of the turbine tenon connecting structure.
Additional aspects and advantages of the disclosure will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the disclosure.
According to one aspect of the disclosure, a fuzzy reliability analysis method of a turbine dovetail connection structure includes:
dividing a grid in a three-dimensional model of a turbine dovetail connection structure to establish a finite element model of the turbine dovetail connection structure;
determining a functional function of the turbine dovetail connection structure according to the finite element model;
on the basis of the function, adding an auxiliary random variable to establish a generalized function, wherein the auxiliary random variable obeys standard normal distribution;
constructing a Kriging model according to the generalized function;
and solving the fuzzy failure probability of the turbine tenon connection structure based on the Kriging model.
In an exemplary embodiment of the disclosure, the determining a functional function of the turbine dovetail connection structure according to the finite element model includes:
determining a dangerous part of the turbine tenon connecting structure according to the finite element model;
determining a failure mode of the hazardous location based on the hazardous location;
and establishing a function of the turbine tenon connection structure according to the failure mode.
In an exemplary embodiment of the disclosure, the adding, on the basis of the function, an auxiliary random variable to establish a generalized function includes:
acquiring a random input variable of the turbine tenon connecting structure;
according to the function, establishing a membership function of the function in the failure mode;
adding the auxiliary random variable, and determining a distribution function of the auxiliary random variable according to the auxiliary random variable;
and establishing the generalized function according to the function, the membership function and the distribution function.
In an exemplary embodiment of the present disclosure, the generalized function is:
wherein,
for the generalized function, g (x)1,x2,x3,…,xn) For said function, x1,x2,x3,…,xnA random input variable, x, for the turbine dovetail connectionn+1For the auxiliary random variable, Φ (x)n+1) Is a function of the distribution of the auxiliary random variables,
and taking the distribution function of the auxiliary random variable as an inverse function of the variable for the membership function.
In an exemplary embodiment of the present disclosure, the constructing a Kriging model according to the generalized function includes:
obtaining a design point of the generalized function by using a first-order second-order moment method, wherein the design point has a plurality of dimensions;
establishing a sampling density function according to the design point;
generating a sample pool of the important samples in the random input variable according to the sampling density function and by using a random sampling method;
constructing the Kriging model based on the sample pool;
wherein the sample cell comprises a plurality of sample points.
In an exemplary embodiment of the disclosure, the establishing a sampling density function according to the design point includes:
according to the design point, constructing a probability density function of each dimension of the design point;
and establishing the sampling density function based on the probability density function of each dimension of the design point.
In an exemplary embodiment of the present disclosure, the constructing the Kriging model based on the sample pool includes:
randomly selecting at least one sample point from the sample pool, and constructing a training sample pool;
constructing an initial Kriging model according to the training sample pool;
establishing a learning function according to the initial Kriging model;
and constructing the Kriging model based on the learning function.
In an exemplary embodiment of the present disclosure, the constructing the Kriging model based on the learning function includes:
setting a lower bound value of the learning function;
substituting the remaining sample points in the sample pool into the learning function to obtain a learning function value of each remaining sample point in the sample pool;
acquiring the minimum value of the learning function value;
when the minimum value is smaller than the lower bound value, adding the sample point corresponding to the minimum value into the training sample pool to update the training sample pool, and updating the initial Kriging model according to the updated training sample pool;
when the minimum value is larger than or equal to the lower bound value, stopping updating the initial Kriging model to construct the Kriging model.
In an exemplary embodiment of the disclosure, the determining the probability of the fuzzy failure of the turbine dovetail connection structure based on the Kriging model includes:
constructing an indication function according to the Kriging model;
obtaining a value of the Kriging model corresponding to each sample point;
obtaining an indication function value of each sample point based on the indication function and the value of the Kriging model corresponding to each sample point;
and solving the fuzzy failure probability of the turbine tenon connecting structure according to the indication function value of each sample point.
In an exemplary embodiment of the present disclosure, the fuzzy failure probability is:
wherein N isISIs the number of said sample points in said sample cell,
for the probability density function of the jth of said sample points,
for the value of the sampling density function corresponding to the jth of the sample points,
an indicator function value for the jth said sample point;
the value of the indicator function for the jth of the sample points is:
wherein,
for the jth of said sample points,
is the value of the Kriging model corresponding to the jth sample point, SISIs the sample cell.
According to the technical scheme, the method has at least one of the following advantages and positive effects:
the fuzzy reliability analysis method of the turbine tenon connection structure provided by the present disclosure establishes a finite element model of the turbine tenon connection structure by dividing a mesh in a three-dimensional model of the turbine tenon connection structure; determining a functional function of the turbine tenon connecting structure according to the finite element model; and then, on the basis of the function, adding an auxiliary random variable to establish a generalized function, wherein the auxiliary random variable obeys standard normal distribution. According to the generalized function, a Kriging model can be constructed. And finally, based on the Kriging model, obtaining the fuzzy failure probability of the turbine tenon connecting structure. According to the fuzzy reliability analysis method of the turbine tenon connection structure, the problem of fuzzy reliability analysis can be converted into the problem of traditional reliability analysis by adding the auxiliary random variable. Thus, the present disclosure can apply the Kriging model to address the fuzzy reliability analysis of the turbine dovetail connection structure. And then the efficiency and the accuracy of the fuzzy reliability analysis are improved, and the requirements of engineering can be met.
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.
FIG. 1 is a schematic flow diagram of a method for fuzzy reliability analysis of a turbine dovetail connection structure according to an embodiment of the present disclosure;
FIG. 2 is a two-dimensional structural schematic of a turbine dovetail connection structure according to an embodiment of the present disclosure;
FIG. 3 is a three-dimensional structural schematic of a turbine dovetail connection structure according to an embodiment of the present disclosure;
FIG. 4 is a schematic representation of a meshing of a turbine dovetail connection structure according to an embodiment of the present disclosure;
FIG. 5 is a schematic illustration of a temperature distribution cloud of a turbine dovetail connection in accordance with an embodiment of the present disclosure;
FIG. 6 is a schematic illustration of a stress distribution cloud of a turbine dovetail connection structure according to an embodiment of the present disclosure;
FIG. 7 is a schematic illustration of a strain distribution cloud for a turbine dovetail connection structure according to an embodiment of the present disclosure.
Description of the reference numerals:
1. a turbine blade; 2. a turbine disk; 11. a tenon first tooth root; 12. a tenon second tooth root; 21. a tongue-and-groove first tooth root; 22. the root of the second tooth of the mortise.
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 embodiments 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 same reference numerals in the drawings denote the same or similar structures, and thus their detailed description will be omitted.
The fuzzy reliability analysis method for the turbine tenon connection structure can convert a fuzzy reliability analysis problem into a traditional reliability analysis problem by adding an auxiliary random variable. Thus, the present disclosure can apply the Kriging model (Kriging model) to solve the fuzzy reliability analysis of the turbine dovetail connection structure. And then the efficiency and the accuracy of the fuzzy reliability analysis are improved, and the requirements of engineering can be met.
As shown in fig. 1, the fuzzy reliability analysis method of the turbine dovetail connection structure may include the steps of:
step S10, dividing grids in the three-dimensional model of the turbine tenon connecting structure to establish a finite element model of the turbine tenon connecting structure;
step S20, determining a functional function of the turbine tenon connecting structure according to the finite element model;
step S30, on the basis of the function, adding an auxiliary random variable to establish a generalized function, wherein the auxiliary random variable obeys standard normal distribution;
step S40, constructing a Kriging model according to the generalized function;
and step S50, based on the Kriging model, obtaining the fuzzy failure probability of the turbine tenon connection structure.
The above steps will be described in detail below.
In step S10, a finite element model of the turbine dovetail connection structure may be built by meshing the three-dimensional model of the turbine dovetail connection structure.
As shown in fig. 2 to 4, a three-dimensional model of the turbine dovetail connection structure may be provided, a mesh may be divided in the three-dimensional model of the turbine dovetail connection structure by using finite element software, and the three-dimensional model of the turbine dovetail connection structure may be parameterized to establish the finite element model of the turbine dovetail connection structure. As shown in fig. 5 to 7, the temperature distribution cloud of the turbine dovetail connection structure, the stress distribution cloud of the turbine dovetail connection structure, and the strain distribution cloud of the turbine dovetail connection structure can be obtained by the finite element model of the turbine dovetail connection structure, but not limited thereto, and other parameter maps of the turbine dovetail connection structure can be obtained by the finite element model of the turbine dovetail connection structure. The finite element model of the turbine dovetail connection structure can be obtained by combining MATLAB software and Abaqus software, but is not limited thereto, and can also be obtained by other numerical calculation software and finite element modeling software, which are within the protection scope of the present disclosure.
Specifically, since the turbine is composed of the turbine blade 1 and the turbine disk 2, the performance of the turbine dovetail connection structure of the present disclosure may be affected by the performance of the turbine blade 1 and the turbine disk 2. The turbine blade 1 may be made of nickel-based superalloy DZl25, and may have a density ρ of 8.56g/cm3However, the material of the turbine blade 1 may be other materials. Since the temperature has an influence on the properties of the nickel-base superalloy DZl25, the properties of the turbine blade 1 at different temperatures are different, which is expressed as: temperature effects on the elastic modulus, poisson's ratio, thermal yield strength, material tensile limit, and material coefficient of thermal expansion of the nickel-base superalloy DZl 25.
As shown in table 1 below, is the modulus of elasticity of the nickel-base superalloy DZl25 at various temperatures.
TABLE 1
As shown in table 2 below, is the poisson ratio of the nickel-base superalloy DZl25 at different temperatures.
TABLE 2
| Temperature of | 20 | 250 | 500 | 600 | 700 | 800 | 900 | 1000 |
| Poisson ratio | 0.335 | 0.333 | 0.340 | 0.343 | 0.360 | 0.360 | 0.368 | 0.380 |
The thermal yield strength of the nickel-base superalloy DZl25 at different temperatures is shown in table 3 below.
TABLE 3
As shown in table 4 below, the tensile limit for nickel-base superalloy DZl25 at various temperatures.
TABLE 4
As shown in table 5 below, is the coefficient of thermal expansion of the nickel-base superalloy DZl25 at various temperatures.
TABLE 5
Table 6 below shows the thermal conductivity of the nickel-base superalloy DZl25 at different temperatures.
TABLE 6
The material of the turbine disk 2 may be a nickel-based superalloy FGH96, and the density thereof may be ρ 8.32g/cm3However, the material of the turbine disk 2 may be other materials. Since the temperature has an influence on the performance of the nickel-based superalloy FGH96, the performance of the turbine disk 2 at different temperatures is different, which is expressed as: the influence of temperature on the elastic modulus, Poisson's ratio, thermal yield strength, material tensile limit and material thermal expansion coefficient of the nickel-base superalloy FGH 96.
As shown in table 7 below, the modulus of elasticity of the nickel-base superalloy FGH96 at different temperatures.
TABLE 7
Table 8 below shows the poisson ratio of the nickel-base superalloy FGH96 at different temperatures.
TABLE 8
| Temperature of | 20 | 450 | 650 | 750 |
| Poisson ratio | 0.31 | 0.31 | 0.31 | 0.31 |
Table 9 below shows the thermal yield strength of the nickel-base superalloy FGH96 at various temperatures.
TABLE 9
As shown in table 10 below, is the tensile limit of the nickel-base superalloy FGH96 at various temperatures.
Watch 10
Table 11 below shows the coefficients of thermal expansion of the nickel-base superalloy FGH96 at various temperatures.
TABLE 11
Table 12 below shows the thermal conductivity of the nickel-base superalloy FGH96 at various temperatures.
TABLE 12
The data in tables 1 to 12 may be input into the finite element software and the numerical calculation software, so as to obtain the finite element model of the turbine dovetail connection structure, the temperature distribution cloud chart of the turbine dovetail connection structure, the stress distribution cloud chart of the turbine dovetail connection structure, and the strain distribution cloud chart of the turbine dovetail connection structure.
In step S20, a functional function of the turbine dovetail connection may be determined based on the finite element model.
In detail, the dangerous part of the turbine tenon connecting structure can be determined according to the finite element model. Specifically, the dangerous portions of the turbine dovetail connection structure may be determined according to the temperature distribution cloud chart of the turbine dovetail connection structure, the stress distribution cloud chart of the turbine dovetail connection structure, and the strain distribution cloud chart of the turbine dovetail connection structure, but the method is not limited thereto, and the dangerous portions of the turbine dovetail connection structure may be determined in other manners, and this is within the scope of the disclosure. According to the temperature distribution cloud picture, the stress distribution cloud picture and the strain distribution cloud picture of the turbine tenon connecting structure, the dangerous parts of the turbine tenon connecting structure can be determined to be a mortise first tooth root part 21, a mortise second tooth root part 22, a tenon first tooth root part 11 and a tenon second tooth root part 12.
After the critical section of the turbine dovetail connection is determined, a failure mode of the critical section may be determined based on the critical section. Since the critical locations may be the first slot root 21, the second slot root 22, the first tenon root 11, and the second tenon root 12, the failure mode may be that the life (i.e., the length of use) of the critical locations exceeds the specified "start-max-start" cycle life. The lifetime under this cycling regime may be 10000 h. It should be noted that, when the dangerous locations are different, the failure modes may be different, and the life time in the above cycle state may not be 10000h, and may be determined according to practical situations, for example: the number of "start-max-start" cycles in engine 750h is 1100. The cyclic fatigue life N of the dangerous part of the turbine tenon connecting structure is calculated by a Morrow elastic stress linear correction model:
in the formula, N is the fatigue life of the turbine tenon connecting structure; sigma'fFatigue strength coefficient of the turbine tenon connecting structure; epsilon'fFatigue ductility coefficient of the turbine tenon connecting structure; b is a fatigue strength index of the turbine tenon connecting structure; c is the fatigue ductility index of the turbine tenon connecting structure; sigmamThe average stress at the strain concentration of the turbine dovetail connection is, and Δ ε is the strain amplitude of the turbine dovetail connection. Fatigue performance parameters of the turbine dovetail connection structure can be consulted according to aviation material manuals and test data.
Based on the failure modes described above, a functional function of the turbine dovetail connection structure may be established. The function may be:
g(x)＝N(x)-N0
wherein N (x) is the life of the dangerous part, N0The life in the cycle state.
In step S30, an auxiliary random variable is added on the basis of the function to establish a generalized function, wherein the auxiliary random variable follows a standard normal distribution.
First, as shown in fig. 2, random input variables of the turbine dovetail connection structure and distribution parameters of the random input variables are acquired. As shown in table 13, the random input variables are parameters of each random input variable, but it should be noted that the random input variables described in the present disclosure are not limited to the random input variables shown in table 13, and may also include other random input variables, all of which are within the protection scope of the present disclosure.
Watch 13
| Random input variable | The physical significance | Mean value | Standard deviation of |
| X1 | Wedge angle phi | 12.23 | 0.00244 |
| X2 | Upper side angle beta | 30.5 | 0.00610 |
| X3 | Lower flank angle alpha | 30.5 | 0.00610 |
| X4 | Inclination angle delta of groove bottom | 77.5 | 0.01550 |
| X5 | Intertooth transition radius r | 0.67 | 0.00013 |
| X6 | Maximum speed n1(rad/s) | 2189 | 43.78 |
Secondly, a membership function of the function in the failure mode can be established according to the function. Common membership functions are: linear type membership functions, normal type membership functions, and cauchy type membership functions. Wherein, the linear type membership function may be:
wherein, a1And a2Position parameters and shape parameters of linear type membership functions, and g (x) is a function.
The normal type membership function may be:
wherein, b1And b2Position parameters and shape parameters of normal type membership functions, and g (x) is a function.
The Cauchy-type membership functions may be:
wherein, c1And c2Position parameters and shape parameters of the Cauchy-type membership functions, and g (x) is a function.
Preferably, the failure mode of the turbine dovetail connection is that the life of the critical part exceeds the life of the specified "start-max-start" cycle. Therefore, in order to ensure the accuracy of the fuzzy reliability analysis, the membership function of the turbine dovetail connection structure may be a linear type membership function, but is not limited thereto, and two other membership functions may also be adopted, and are within the scope of the present disclosure.
Further, the position parameter of the linear type membership function may be 500, and the shape parameter may be-500, but is not limited thereto, and other parameters may be included within the scope of the present disclosure.
Further, a secondary random variable may be added and a distribution function of the random variables is determined based on the secondary random variable, wherein the secondary random variable follows a standard normal distribution. According to the function, the membership function and the distribution function of the auxiliary random variable, the generalized function of the turbine tenon connection structure can be established. Thus, the fuzzy reliability analysis problem is converted into the traditional reliability analysis problem by adding the auxiliary random variable. The generalized function may be:
wherein,
for the generalized function, g (x)1,x2,x3,…,xn) For said function, x1,x2,x3,…,xnRandom input for the turbine dovetail connectionVariable, xn+1For the auxiliary random variable, Φ (x)n+1) Is a function of the distribution of the auxiliary random variables,
and taking the distribution function of the auxiliary random variable as an inverse function of the variable for the membership function.
Thus, under the condition of the generalized function, the expression of the fuzzy failure probability of the turbine tenon connection structure can be as follows:
wherein,
is the generalized function.
In step S40, a Kriging model is constructed according to the generalized function, which may include:
obtaining a design point of the generalized function by a first-order second-order moment method, wherein the design point can be xMPPAnd the design point has multiple dimensions, i.e.
But is not limited thereto, and other methods may be utilized to obtain the design point, all of which are within the scope of the present disclosure.
The sampling density function may be established based on the obtained design point. Specifically, a probability density function of each dimension of the design point can be constructed according to the design point; the sampling density function may be established based on a probability density function for each dimension of the design point. The probability density function may be a normal distribution
The density function of (a), wherein,
to be provided withThe ith dimension of the point is counted,
is the standard deviation of the ith random input variable. Multiplying the probability density function of each dimension of the design point to obtain a sampling density function; the sampling density function may be:
wherein, f (x)i) The probability density function of the ith dimension of the design point is obtained.
Further, a sample pool, which may include a plurality of sample points, may be generated in the random input variable according to the sampling density function and using a random sampling method. The random sampling method may be, but is not limited to, a latin hypercube method, and other sampling methods may be used. The sampling efficiency can be obviously improved by using the hyper-Latin cube method, so that the fuzzy reliability analysis efficiency is obviously improved, and the actual engineering requirements can be met.
Based on the sample pool, a Kriging model can be constructed. Specifically, at least one sample point may be randomly selected from the sample pool to construct a training sample pool, and an initial Kriging model may be constructed according to the training sample pool, and a learning function may be established according to the initial Kriging model. Wherein, the learning function can be:
wherein,
for the predicted value of the Kriging model at the sample point,
is the predicted standard deviation of the Kriging model at the sample point.
Further, based on the learning function, a Kriging model can be constructed. Specifically, a lower bound value of the learning function may be preset, the lower bound value may be 2, and when the lower bound value is 2, the probability that the predicted symbol (i.e., the sign of the functional function) is incorrect is Φ (-2) ═ 0.023, but the present disclosure is not limited thereto, and other values may also be used, and all values are within the protection scope of the present disclosure.
The remaining sample points in the sample pool (i.e. the sample points that are not selected into the training sample pool) can be substituted into the learning function to obtain a learning function value of each remaining sample point in the sample pool; and comparing the learning function values of the sample points to obtain the minimum value of the learning function. When the minimum value of the learning function is smaller than the lower bound value, the sample point corresponding to the minimum value is obtained, where the sample point may be:
wherein,
is the minimum value of the learning function and,
is the sample point corresponding to the minimum value.
The sample point corresponding to the minimum value may be added to the training sample pool to update the training sample pool, and the initial Kriging model may be updated according to the updated training sample pool. And when the minimum value of the learning function is larger than or equal to the lower bound value, stopping updating the initial Kriging model to construct the Kriging model.
It can be understood that the learning function can be updated by the updated initial Kriging model, and the remaining sample points of the sample pool (i.e. the sample points that are not selected in the training sample pool) can be brought into the updated learning function to obtain the learning function value corresponding to each sample point, then the minimum learning function value is compared with the lower bound value of the learning function, if the minimum learning function value is smaller than the lower bound value, the sample point corresponding to the minimum learning function value is added into the training sample, the updated initial Kriging model is updated again, and the cycle is repeated. And stopping updating the initial Kriging model of the cycle until the minimum learning function value is greater than or equal to the lower limit value. The initial Kriging model is continuously updated in a circulating mode, so that the finally constructed Kriging model can be more accurate, and the fuzzy reliability analysis method is more accurate.
In step S50, based on the Kriging model, the probability of the fuzzy failure of the turbine dovetail joint structure can be obtained.
Specifically, an indication function can be constructed according to a Kriging model; the value of the Kriging model corresponding to each sample point can be obtained; the indicating function value of each sample point can be obtained based on the indicating function and the value of the Kriging model corresponding to each sample point; and solving the fuzzy failure probability of the turbine tenon connecting structure according to the indication function value of each sample point. By means of the fuzzy failure probability, the fuzzy reliability of the turbine tenon connection structure can be analyzed.
For example, the fuzzy failure probability may be:
wherein N isISIs the number of said sample points in said sample cell,
for the probability density function of the jth of said sample points,
for the value of the sampling density function corresponding to the jth of the sample points,
an indicator function value for the jth said sample point;
the value of the indicator function for the jth of the sample points is:
wherein,
for the jth of said sample points,
is the value of the Kriging model corresponding to the jth sample point, SISIs the sample cell.
The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, and the features discussed in connection with the embodiments are interchangeable, if possible. In the above 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, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the disclosure.
In this specification, the terms "a", "an", "the", "said" and "at least one" are used to indicate the presence of one or more elements/components/etc.; the terms "comprising," "including," 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 terms "first," "second," and the like are used merely as labels, and are not limiting on the number of their objects.
It is to be understood that the disclosure is not limited in its application to the details of construction and the arrangements of the components set forth in the specification. The present disclosure is capable of other embodiments and of being practiced and carried out in various ways. The foregoing variations and modifications are within the scope of the present disclosure. It should be understood that the disclosure disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or evident from the text and/or drawings. All of these different combinations constitute various alternative aspects of the present disclosure. The embodiments described herein explain the best modes known for practicing the disclosure and will enable others skilled in the art to utilize the disclosure.
Claims (8)
1. A fuzzy reliability analysis method of a turbine tenon connecting structure is characterized by comprising the following steps:
dividing grids in the three-dimensional model of the turbine tenon connection structure to establish a finite element model of the turbine tenon connection structure;
determining a functional function of the turbine dovetail connection structure according to the finite element model;
on the basis of the function, adding an auxiliary random variable to establish a generalized function, wherein the auxiliary random variable obeys standard normal distribution;
constructing a Kriging model according to the generalized function;
based on the Kriging model, solving the fuzzy failure probability of the turbine tenon connecting structure;
wherein, according to the generalized function, constructing a Kriging model, comprising:
obtaining a design point of the generalized function by using a first-order second-order moment method, wherein the design point has multiple dimensions;
establishing a sampling density function according to the design point;
generating a sample pool in a random input variable of the turbine tenon connecting structure according to the sampling density function and by using a random sampling method;
constructing the Kriging model based on the sample pool;
wherein the sample cell comprises a plurality of sample points;
the generalized function is:
wherein,
for the purpose of the generalized function in question,
in order to be a function of the function,
is a random input variable of the turbine dovetail connection structure,
in order to assist in the random variation,
in order to assist the distribution function of the random variable,
and taking the distribution function of the auxiliary random variable as an inverse function of the variable.
2. The fuzzy reliability analysis method of claim 1 wherein said determining a functional function of said turbine dovetail connection structure from said finite element model comprises:
determining a dangerous part of the turbine tenon connecting structure according to the finite element model;
determining a failure mode of the hazardous location based on the hazardous location;
and establishing a function of the turbine tenon connection structure according to the failure mode.
3. The fuzzy reliability analysis method according to claim 2, wherein said adding an auxiliary random variable on the basis of the function to establish a generalized function comprises:
acquiring a random input variable of the turbine tenon connecting structure;
according to the function, establishing a membership function of the function in the failure mode;
adding the auxiliary random variable, and determining a distribution function of the auxiliary random variable according to the auxiliary random variable;
and establishing the generalized function according to the function, the membership function and the distribution function.
4. The fuzzy reliability analysis method of claim 1 wherein said establishing a sampling density function based on said design point comprises:
according to the design point, constructing a probability density function of each dimension of the design point;
and establishing the sampling density function based on the probability density function of each dimension of the design point.
5. The fuzzy reliability analysis method of claim 4, wherein said constructing the Kriging model based on the sample pool comprises:
randomly selecting at least one sample point from the sample pool, and constructing a training sample pool;
constructing an initial Kriging model according to the training sample pool;
establishing a learning function according to the initial Kriging model;
and constructing the Kriging model based on the learning function.
6. The fuzzy reliability analysis method of claim 5, wherein said constructing said Kriging model based on said learning function comprises:
setting a lower bound value of the learning function;
substituting the remaining sample points in the sample pool into the learning function to obtain a learning function value of each remaining sample point in the sample pool;
acquiring the minimum value of the learning function value;
when the minimum value is smaller than the lower bound value, adding the sample point corresponding to the minimum value into the training sample pool to update the training sample pool, and updating the initial Kriging model according to the updated training sample pool;
when the minimum value is larger than or equal to the lower bound value, stopping updating the initial Kriging model to construct the Kriging model.
7. The fuzzy reliability analysis method of claim 6, wherein the step of obtaining the fuzzy failure probability of the turbine dovetail connection structure based on the Kriging model comprises:
constructing an indication function according to the Kriging model;
obtaining a value of the Kriging model corresponding to each sample point;
obtaining an indication function value of each sample point based on the indication function and the Kriging model value corresponding to each sample point;
and solving the fuzzy failure probability of the turbine tenon connecting structure according to the indication function value of each sample point.
8. The fuzzy reliability analysis method of claim 7, wherein the fuzzy failure probability is:
wherein,
the number of the sample points in the sample pool,
as a function of the probability density of the jth of said sample points,
for the value of the sampling density function corresponding to the jth of the sample points,
an indicated function value for the j-th sample point;
the value of the indicator function for the j-th sample point is:
wherein,
for the j-th one of said sample points,
is the value of the Kriging model corresponding to the jth sample point,
is the sample cell.
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| CN110096796A (en) * | 2019-04-29 | 2019-08-06 | 电子科技大学 | The analysis method for reliability of industrial robot RV retarder under a kind of multi-invalidation mode |
| CN110532723A (en) * | 2019-09-06 | 2019-12-03 | 北京航空航天大学 | A kind of turbine disk multi-invalidation mode reliability optimization method based on EGRA |
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