CN113011043A - Saddle point approximation-based wind power gear box reliability design optimization method - Google Patents
Saddle point approximation-based wind power gear box reliability design optimization method Download PDFInfo
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Abstract
The invention discloses a saddle point approximation-based wind power gear box reliability design optimization method; the method comprises the steps of constructing a reliability design optimization model, introducing a saddle point approximation method to construct a reliability design optimization model based on saddle point approximation, applying a reliability design optimization project based on saddle point approximation to a wind power gear box, constructing a reliability design optimization model based on saddle point approximation of the wind power gear box, analyzing inherent-operation coupling reliability of a transmission system of the wind power gear box, and finally performing design optimization. According to the invention, by combining the uncertain theory, the reliability theory and the saddle point approximation theory, the problem that the first-order/second-order reliability method in the traditional design method is subjected to normal conversion to increase the non-linearity degree of the wind power gear box is solved, so that the requirement of high product quality and reliability of the wind power gear box is met.
Description
Technical Field
The invention belongs to the technical field of reliability design optimization of mechanical products, and particularly relates to a saddle point approximation-based reliability design optimization method for a wind power gear box.
Background
Reliability is one of the important indexes for measuring the quality characteristics of mechanical products, and the reliability runs through all stages in the whole life cycle of mechanical parts, complex mechanical equipment and large-scale infrastructure, including design, manufacture, test, use, maintenance and the like. The reliability of large-scale complex mechanical equipment and an industrial system is accurately evaluated, the operation safety of the whole equipment and the system can be guaranteed, and information guidance can be provided for the formulation of a maintenance plan so as to reduce the cost of the whole life cycle. The rapid development of science and technology and the rapid progress of society make the structure of mechanical products more complex, the use places more extensive and the working environment more severe, so the reliability is more prominent in the quality characteristics of the mechanical products. Therefore, the reliability analysis method and the reliability optimization design method for researching the mechanical system are significant.
Reliability-Based Design Optimization (RBDO) is a powerful tool, which can fully consider the influence of uncertainty on constraints during Optimization to obtain an Optimization result meeting Reliability requirements, thereby achieving a good balance between Reliability and economy. The motivation for RBDO is to ensure that the inherent failure probability of a designed system is below an acceptable level, thereby reducing the likelihood of an accident. This goal is achieved by using uncertainty constraints in the RBDO.
Compared with common mechanical equipment, the wind turbine generator transmission system is more complex in load state, operation condition, environmental condition, structural layout and the like, and the damage process of the mechanical structure is a dynamic process of continuously accumulating multiple damages, continuously degrading material properties and redistributing stress. The failure mechanism, the failure development mode and the like of main parts such as gears, bearings and the like in a transmission chain have the particularity of multi-failure-mode coupling, and the failure rate of the transmission chain is higher than that of similar equipment in other industries. In addition, uncertainties can accumulate as the coupling design information is propagated, ultimately affecting the reliability and safety of the wind turbine transmission structure. Therefore, for the transmission structure of the wind turbine generator, reliability analysis is very important.
The conventional RBDO usually uses a first order/second order approximation reliability analysis method to perform reliability analysis. The basic idea is to evaluate the reliability of the respective approximating function after approximating the respective extreme state function. However, both of the above methods require conversion of random variables having an arbitrary distribution into random variables having a standard normal distribution. This conversion is a non-linear process when the random variables involved follow a particular non-normal distribution. It will increase the degree of non-linearity of the original problem. The design result is inaccurate, and the requirement of high reliability of the modern complex wind power gear box cannot be met.
Disclosure of Invention
The invention aims to: the invention provides a saddle point approximation-based wind power gear box reliability design optimization method, aiming at solving the problems of increased non-linear degree, lowered precision, inaccurate design result and the like caused by the fact that a first-order/second-order approximation reliability analysis method is used for reliability analysis in the traditional RBDO.
The technical scheme of the invention is as follows: a wind power gear box reliability design optimization method based on saddle point approximation comprises the following steps:
s1, constructing a reliability design optimization model related to the traditional uncertain factors;
s2, introducing the saddle point approximate reliability index and the approximate calculation method of the sensitivity thereof into the traditional reliability design optimization model to obtain a reliability design optimization model based on saddle point approximation;
s3, applying the saddle point approximation-based reliability design optimization model engineering constructed in the step S2 to the wind power gear box, constructing a saddle point approximation-based reliability design optimization model of the wind power gear box, analyzing inherent-operation coupling reliability of a transmission system of the wind power gear box, and finally performing design optimization;
further, the step S1 is to construct a reliability design optimization model related to the traditional uncertain factor, specifically: considering various uncertain factors, regarding the uncertain factors as random variables, and establishing a reliability optimization design model accompanied with the random variables, wherein the reliability optimization design model is expressed as follows:
in the formula: d is a deterministic design variable; x is the number ofrIs a continuous type random design variable; p is a radical ofrIs a continuous design parameter: pr (g)i(d,xr,pr)＞0)≤Φ(-βt) Is a probabilistic reliability constraint; gi(d,xr,pr) Is the limit state function of the optimization problem, and the corresponding failure mode is gi(d,xr,pr)＞0；Φ(-βt) The probability of failure allowed by the extreme state function; beta is atGenerally, β is taken as a target reliability index (target reliability index)t＝3.0，Φ(-βt) 0.0013(Φ is the cumulative distribution function of the standard normal variable); gj(d,xr,pr) Less than or equal to 0 is a deterministic design constraint, and n and m respectively represent the number of the probabilistic reliability constraint and the deterministic design constraint; superscripts U and L represent the upper and lower bounds of the design variable, respectively.
Further, the step S2 introduces the saddle point approximation reliability index and the approximation calculation method of the sensitivity thereof into the conventional reliability design optimization model to obtain a reliability design optimization model based on saddle point approximation, which specifically includes the following sub-steps:
s21, performing second-order Taylor expansion on the limit state function at the mean value of the random variable to obtain a second-order expansion function of the limit state function, wherein the second-order expansion function is as follows:
the following simplification is made:
then
Namely, it is
Y＝gL(X)＝XTAX+bTX+c。
S22, calculating a moment mother function according to the unfolded limit state function:
MY(t)＝|B|-1/2exp[t(μTAμ+bTμ+c)+(t2/2)dTB-1d]
s23, calculating the accumulated quantity mother function of the limit state function by using the following formula:
s24, finding the saddle point according to the following equation
S25, obtaining a probability density function of Y according to the obtained saddle point:
and S26, combining the step S1 to obtain a reliability design optimization model based on saddle point approximation.
And S27, carrying out inherent-operation coupling reliability analysis on the wind turbine transmission system under the mixed uncertainty.
Further, the step S3 applies the reliability design optimization model engineering based on saddle point approximation, which is constructed in S2, to the wind power gearbox, constructs a reliability design optimization model based on saddle point approximation for the wind power gearbox, and performs design optimization, specifically including the following sub-steps:
and S31, carrying out uncertain factor analysis on the wind power gear box, and selecting design variables and random parameters.
And S32, making assumptions about the working environment of the wind power gearbox.
S33, considering yield failure of each failure point on the wind power gear box, introducing axial force N and bending moment M into the RBDO. And (5) combining the steps S1 and S2 to construct a wind power gear box reliability design optimization model aiming at minimizing the volume of the platform, analyzing the inherent-operation coupling reliability of the transmission system of the wind power gear box, and finally performing design optimization.
The invention has the beneficial effects that: the method comprises the steps of constructing a reliability design optimization model; a saddle point approximation method is introduced to replace a first-order/second-order reliability method in the traditional design method to construct a reliability design optimization model based on saddle point approximation; applying a saddle point approximation-based reliability design optimization project to the wind power gear box, constructing a saddle point approximation-based reliability design optimization model of the wind power gear box, analyzing inherent-operation coupling reliability of a transmission system of the wind power gear box, and finally performing design optimization; according to the invention, by combining the uncertain theory, the reliability theory and the saddle point approximation theory, the problem that the first-order/second-order reliability method in the traditional design method is subjected to normal conversion to increase the non-linearity degree of the wind power gear box is solved, so that the requirement of high product quality and reliability of the wind power gear box is met.
Drawings
FIG. 1 is a schematic flow chart of a method for optimizing reliability design of a wind power gearbox based on saddle point approximation.
FIG. 2 is a technical roadmap for analyzing the intrinsic-operational coupling reliability of a wind turbine generator drive system under mixed uncertainty according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in FIG. 1, a schematic flow chart of a method for optimizing the reliability design of a wind power gearbox based on saddle point approximation is shown. A wind power gear box reliability design optimization method based on saddle point approximation comprises the following steps:
s1, constructing a reliability design optimization model related to the traditional uncertain factors;
s2, introducing the saddle point approximate reliability index and the approximate calculation method of the sensitivity thereof into the traditional reliability design optimization model to obtain a reliability design optimization model based on saddle point approximation;
s3, applying the saddle point approximation-based reliability design optimization model engineering constructed in the step S2 to the wind power gear box, constructing a saddle point approximation-based reliability design optimization model of the wind power gear box, analyzing inherent-operation coupling reliability of a transmission system of the wind power gear box, and finally performing design optimization;
in step S1, a reliability design optimization model related to the conventional uncertain factor is constructed, specifically: considering various uncertain factors, regarding the uncertain factors as random variables, and establishing a reliability optimization design model accompanied with the random variables, wherein the reliability optimization design model is expressed as follows:
in the formula: d is a deterministic design variable; x is the number ofrIs a continuous type random design variable; p is a radical ofrIs a continuous design parameter: pr (g)i(d,xr,pr)＞0)≤Φ(-βt) Is a probabilistic reliability constraint; gi(d,xr,pr) Is the limit state function of the optimization problem, and the corresponding failure mode is gi(d,xr,pr)＞0；Φ(-βt) The probability of failure allowed by the extreme state function; beta is atGenerally, β is taken as a target reliability index (target reliability index)t＝3.0，Φ(-βt) 0.0013(Φ is the cumulative distribution function of the standard normal variable); gj(d,xr,pr) Less than or equal to 0 is a deterministic design constraint, and n and m respectively represent the number of the probabilistic reliability constraint and the deterministic design constraint; superscripts U and L represent the upper and lower bounds of the design variable, respectively.
In step S2, introducing the saddle point approximation reliability index and the approximation calculation method for the sensitivity thereof into the conventional reliability design optimization model to obtain a reliability design optimization model based on saddle point approximation, specifically including the following sub-steps:
s21, performing second-order Taylor expansion on the limit state function at the mean value of the random variable to obtain a second-order expansion function of the limit state function, wherein the second-order expansion function is as follows:
the following simplification is made:
then Y is equal to gL(X)＝XTAX+bTX+c。
S22, calculating a moment mother function according to the unfolded limit state function:
MY(t)＝|B|-1/2exp[t(μTAμ+bTμ+c)+(t2/2)dTB-1d]
s23, calculating the accumulated quantity mother function of the limit state function by using the following formula:
s24, finding the saddle point according to the following equation
S25, obtaining a probability density function of Y according to the obtained saddle point:
and S26, combining the step S1 to obtain a reliability design optimization model based on saddle point approximation.
In step S3, the saddle point approximation-based reliability design optimization model engineering constructed in step S2 is applied to the wind power gearbox, a saddle point approximation-based reliability design optimization model of the wind power gearbox is constructed, the inherent-operational coupling reliability of the transmission system of the wind power gearbox is analyzed, and finally, design optimization is performed, specifically including the following sub-steps:
and S31, carrying out uncertain factor analysis on the wind power gear box, and selecting design variables and random parameters.
And S32, making assumptions about the working environment of the wind power gearbox.
S33, considering yield failure of each failure point on the wind power gear box, introducing axial force N and bending moment M into the RBDO. And (5) combining the steps S1 and S2 to construct a wind power gear box reliability design optimization model aiming at minimizing the volume of the platform, analyzing the inherent-operation coupling reliability of the transmission system of the wind power gear box, and finally performing design optimization.
In order to enable those skilled in the art to more clearly understand the method for constructing the reliability design optimization model of the wind power gearbox, the invention will be further described in detail with reference to specific embodiments.
FIG. 2 is a schematic diagram of an analysis technique for reliability of intrinsic-operational coupling of a wind turbine generator system under mixed uncertainty according to an embodiment of the present invention. Aiming at the reliability data characteristics of the wind turbine generator, a mixed uncertainty unified quantification frame based on an inaccurate probability theory is established by a unified quantification method of multiple uncertainties such as random uncertainty, fuzzy uncertainty and unacknowledged property and by the aid of the advantages of the inaccurate probability theory in processing mixed uncertainty problems; meanwhile, the coupling between the inherent reliability and the use reliability of the transmission system of the wind turbine generator is considered. In the design and manufacture stage, the transmission system is subjected to the repeated processes of design-test-improvement-redesign-retest, development-test-improvement-redevelopment-retest, the reliability of the transmission system is continuously increased, and the reliability increase information of the transmission system is more sufficient in the stage. Therefore, the method establishes an inaccurate reliability growth model based on an inaccurate Dirichlet prior distribution family by means of the advantages of the inaccurate Dirichlet model in representing edge information and hierarchical information and researching the reliability growth rule of a mechanical system in a design and development stage based on the inaccurate Dirichlet model; and (3) establishing an inherent-operational coupling reliability evaluation model by taking the inherent reliability related information as prior information and by means of a Bayesian method, and finally forming an inherent-operational coupling reliability analysis technology of the wind turbine generator system under the mixed uncertainty as shown in FIG. 2.
Consider wind power gearYield failure at each point of failure on the tank introduces axial force N and bending moment M into the RBDO. And building a wind power gearbox reliability design optimization model aiming at minimizing the volume of the platform by combining the steps S1 and S2. For each uncertainty constraint, a reliability index β for each fault pointmShould be greater than 4.0.
According to the invention, by combining the uncertain theory, the reliability theory and the saddle point approximation theory, the problem that the first-order/second-order reliability method in the traditional design method is subjected to normal conversion to increase the non-linearity degree of the wind power gear box is solved, so that the requirement of high product quality and reliability of the wind power gear box is met.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (4)
1. A wind power gear box reliability design optimization method based on saddle point approximation is characterized by comprising the following steps:
s1, constructing a reliability design optimization model related to the traditional uncertain factors;
s2, introducing the saddle point approximate reliability index and the approximate calculation method of the sensitivity thereof into a traditional reliability design optimization model to obtain a reliability design optimization method based on saddle point approximation;
s3, applying the reliability design optimization model engineering based on the saddle point approximation and constructed in the step S2 to the wind power gear box, constructing a wind power gear box reliability design optimization model based on the saddle point approximation, analyzing inherent-operation coupling reliability of a transmission system of the wind power gear box, and finally performing design optimization.
2. The saddle point approximation-based wind power gearbox reliability design optimization method as claimed in claim 1, wherein said step S1 is to construct a reliability design optimization model related to traditional uncertain factors, specifically: considering various uncertain factors, regarding the uncertain factors as random variables, and establishing a reliability optimization design model accompanied with the random variables, wherein the reliability optimization design model is expressed as follows:
in the formula: d is a deterministic design variable; x is the number ofrIs a continuous type random design variable; p is a radical ofrIs a continuous design parameter: pr (g)i(d,xr,pr)＞0)≤Φ(-βt) Is a probabilistic reliability constraint; gi(d,xr,pr) Is the limit state function of the optimization problem, and the corresponding failure mode is gi(d,xr,pr)＞0；Φ(-βt) The probability of failure allowed by the extreme state function; beta is atGenerally, β is taken as a target reliability index (target reliability index)t＝3.0，Φ(-βt) 0.0013(Φ is the cumulative distribution function of the standard normal variable); gj(d,xr,pr) Less than or equal to 0 is a deterministic design constraint, and n and m respectively represent the number of the probabilistic reliability constraint and the deterministic design constraint; superscripts U and L represent the upper and lower bounds of the design variable, respectively.
3. The method for optimizing the reliability design of the wind power gearbox based on the saddle point approximation as claimed in claim 2, wherein the step S2 introduces the saddle point approximation reliability index and the approximation calculation method of the sensitivity thereof into the traditional reliability design optimization model to obtain the reliability design optimization model based on the saddle point approximation, and specifically comprises the following sub-steps:
s21, performing second-order Taylor expansion on the limit state function at the mean value of the random variable to obtain a second-order expansion function of the limit state function, wherein the second-order expansion function is as follows:
the following simplification is made:
then
Namely, it is
Y＝gL(X)＝XTAX+bTX+c。
S22, calculating a moment mother function according to the unfolded limit state function:
MY(t)＝|B|-1/2exp[t(μTAμ+bTμ+c)+(t2/2)dTB-1d]
s23, calculating the accumulated quantity mother function of the limit state function by using the following formula:
s24, finding the saddle point according to the following equation
S25, obtaining a probability density function of Y according to the obtained saddle point:
and S26, combining the step S1 to obtain a reliability design optimization model based on saddle point approximation.
4. The method for optimizing the reliability design of the wind power gearbox based on the saddle point approximation as claimed in claim 3, wherein the step S3 applies the reliability design optimization model engineering based on the saddle point approximation constructed in the step S2 to the wind power gearbox, constructs a reliability design optimization model of the wind power gearbox based on the saddle point approximation, performs the intrinsic-operational coupling reliability analysis of the transmission system of the wind power gearbox, and finally performs the design optimization, and specifically comprises the following steps:
and S31, carrying out uncertain factor analysis on the wind power gearbox.
And S32, making assumptions about the working environment of the wind power gearbox.
S33, considering yield failure of each failure point on the wind power gear box, introducing axial force N and bending moment M into the RBDO. And (5) constructing a wind power gear box reliability design optimization model aiming at minimizing the volume of the wind power gear box by combining the steps S1 and S2, analyzing the inherent-operation coupling reliability of the transmission system of the wind power gear box, and finally performing design optimization.
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| US20060064288A1 (en) * | 2004-09-22 | 2006-03-23 | Liem Ferryanto | System and method of interactive design of a product |
| US20190362041A1 (en) * | 2017-10-31 | 2019-11-28 | China University Of Mining And Technology | Reliability robust design method for multiple failure modes of ultra-d eep well hoisting container |
| CN108763707A (en) * | 2018-05-21 | 2018-11-06 | 电子科技大学 | The approximate Analysis of structural reliability method of second order saddle point is based under Hybrid parameter matrix |
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| DEBIAO MENG等: "Uncertainty-based design and optimization using first order saddlepoint approximation method for multidisciplinary engineering systems.", 《JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS》 * |
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