AU2018374073A1 - Correlation modeling method for coupling failure of critical components of deep well hoist under incomplete information condition - Google Patents
Correlation modeling method for coupling failure of critical components of deep well hoist under incomplete information condition Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B19/00—Handling rods, casings, tubes or the like outside the borehole, e.g. in the derrick; Apparatus for feeding the rods or cables
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Abstract
The present invention discloses a correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition. The method includes the following steps: 1) acquiring fault data samples of the critical components of the hoist in different failure modes, and collecting statistics about statistical moment information of random response in each failure mode in the incomplete information condition; 2) obtaining a marginal probability distribution function of each failure mode by using a function approximation method; 3) analyzing probability correlation attributes between each pair of failure modes by using a goodness-offit test criterion, and determining best-fit copula functions for describing different correlation attributes of part failure; and 4) establishing a hybrid copula function model by combining the marginal probability distribution function of each failure mode with each best-fit copula function. By means of the present invention, an accurate marginal probability density function can be established in a small sample condition, and symmetric correlation, and upper tail correlation and lower tail correlation attributes possibly existing between failure modes are considered, thereby enhancing the flexibility and applicability of correlation modeling for coupling failure of critical components of an ultra-deep well hoist.
Description
[0001] The present invention relates to the technical field of mine hoisting, and particularly relates to a correlation modeling method for coupling failure of critical components of a main shaft of a deep well hoist.
DESCRIPTION OF RELATED ART [0002] The development and utilization of deep resources are development strategies of the country. Ultra-deep mine large-scale hoisting equipment is critical equipment for implementing the development of deep resources, and the safe and effective operation of the equipment is of great significance to the development of the national economy. The ultra-deep well hoisting equipment undergoes complicated operating conditions and extremely severe working conditions and easily causes serious accidents, therefore, accurate and reasonable evaluation and prediction of the reliability of the hoisting equipment are of great significance to ensure the safe operation of the equipment and improve the economic benefit. With the increase of the well depth, the payload of the traditional mine hoisting equipment is greatly increased, so that the hoisting efficiency, the safety and the like of the equipment are quickly reduced, and then, the equipment cannot be used for hoisting in an ultra-deep well. Therefore, it is necessary to carry out reliability research on the hoisting equipment in the severe environment of the ultra-deep well. Due to the homology of structural parameters and external excitation, the failure modes of the critical components of the main shaft of the deep well hoist have different degrees of correlation. When the system reliability analysis of the critical components of the hoist is performed, ignoring these potential correlation properties will cause deviation in reliability estimation and affect reliability evaluation of the hoist. Based on a hybrid copula function, the present invention provides a multivariate probabilistic correlated modeling method aiming at multi-failure mode coupling properties of the ultra-deep well hoisting equipment.
[0003] In the following literatures:
[0004] [l]Noh Y, Choi K K, Du L. Reliability-based design optimization of problems with correlated input variables using a Gaussian CopulafJ],Structural and multidisciplinary optimization, 2009, 38 (1):1-16.
[0005] [2]Tang X S, Li D Q, Zhou C B, et al. Impact of copulas for modeling bivariate distributions on system reliability [J], Structural safety, 2013, 44: 80-90.
[0006] [3]Multi-wind field output prediction method based on hybrid Copula function [P], invention patent, CN201710485692.7.
[0007] In the literature 1, a Gaussian copula function is used for performing correlation modeling between failure modes. However, when the failure modes are in asymmetric correlation, the modeling accuracy is poor.
[0008] In the literature 2, correlation attributes between the failure modes are described by selecting an best-fit copula function from a plurality of candidate copula functions. However, a single copula function cannot describe complete correlation attributes in most cases.
[0009] The literature 3 provides a hybrid copula function to establish a wind correlated model. The model is established on the premise of a large capacity of data samples by using an ergodic statistical method, has poor applicability to the deep well hoisting equipment lacking fault data, and cannot solve the modeling problem of a marginal probability function in a small sample condition.
SUMMARY OF THE INVENTION
Technical Solution [0010] One of the objectives of the present invention is to at least provide a correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition aiming at the problems existing in the prior art. The method can more accurately describe the probability correlation between failure modes of the critical components of the hoist in the condition that component fault information is lacking, thereby improving the accuracy of joint probability modeling of multiple failure modes of the deep well hoist.
[0011] In order to realize the above objective, the present invention uses the following technical solution:
[0012] A correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition includes the following steps:
[0013] step 1: acquiring fault data samples of the critical components of the hoist in different failure modes, and collecting statistics about statistical moment information of random response in each failure mode in the incomplete information condition;
[0014] step 2: obtaining a marginal probability distribution function of each failure mode by using a function approximation method;
[0015] step 3: analyzing probability correlation attributes between each pair of failure modes by using a goodness-of-fit test criterion, and determining best-fit copula functions for describing different correlation attributes of part failure; and [0016] step 4: establishing a hybrid copula function model by combining the marginal probability distribution function of each failure mode obtained in the step 2 with each best-fit copula function determined in the step 3.
[0017] The fault data samples of the critical components of the hoist in different failure modes in the step 1 include stress, strain, frequency response, wearing capacity and temperature variation of the critical components of the hoist; and the statistical moment information of random response in each failure mode in an incomplete information condition is solved by using a random perturbation method, namely [0018]
[0019]
d(yT); [0020] <?rT [0021] where E represents a mean value of random response in a failure mode, [0022] Var represents a variance of random response in a failure mode, [0023] Tm represents a third moment of random response in a failure mode, [0024] Y represents a fault data sample vector, [0025] YT represents a transposed vector of the fault data sample vector,
| [0026] | g(Y) represents a random response function, |
| [0027] | Var(Y) represents a variance of the fault data sample vector, |
| [0028] | P4(Y) represents a fourth moment of the fault data sample vector, |
| [0029] | (.)[]_(.)[' 1®(-)-(·)®(·)®···®(·) ·§ a Kj.onecker pOwer of (·), and a |
symbol ® represents a Kronecker product.
| [0030] | The function approximation method in the step 2 is a truncated Edgeworth |
series approximation method, and by combining the fault data samples and the statistical moment information obtained in the step 1, an approximation probability distribution function can be obtained:
| [0031] | Ρ.ΙΟ-ΦΙΟ-”1’'’ Tm. r’ v v ’ 72 Var |
| [0032] | where |
| [0033] | Φ () represents a cumulative probability distribution function of standard |
normal distribution; and
| [0034] | represents a probability density function of standard normal |
distribution.
[0035] The goodness-of-fit test criterion in the step 3 is an Akaike information criterion, specifically expressed as:
AIC = -2XlnC(n,.,v,.;i?) + 2 [0036] [0037] where [0038] C(ui, Vj; Θ) represents a known copula function;
[0039] u; and Vi represent random variables subjected to statistical processing, specifically expressed as:
rank (yh ) rank (v,() [0040] Y + l ’ Y + >
[0041] where yn and y2i respectively represent fault data samples in two failure modes, [0042] i represents the number of samples, [0043] N represents the capacity of the fault data samples, [0044] and rank(yii) or rank(y2i) represents the ranks of the fault data samples of the hoist, namely {yn, ..., yiN} or {y2i, ··., Y2n}; and [0045] the best-fit copula function refers to a copula function with a minimum AIC value in copula functions for describing the same type of correlation attributes.
[0046] The step 4 specifically includes:
[0047] 4.1 normalizing the fault data samples of the critical components of the hoist in different failure modes;
[0048] 4.2 calculating rank correlation coefficients among the fault data samples of the critical components of the hoist in different failure modes;
[0049] 4.3 respectively substituting each obtained rank correlation coefficient into each best-fit copula function obtained in the step 3 so as to determine a undetermined coefficient in each best-fit copula function; and [0050] 4.4 determining that the form of the hybrid copula function for describing the correlation attributes between two failure modes is:
[0051] Cmix=wiCi(u, v; a)+w2C2(u, v; 3)+w3C3(u, v; 0) [0052] where [0053] Ci, C2 and C3 represent the best-fit copula functions determined in the step 3, and are used for respectively describing symmetric correlation, upper tail correlation and lower tail correlation properties between two failure modes;
[0054] u and v represent marginal distribution functions of each failure mode;
[0055] α, β and 0 respectively represent the undeterminedcoefficients of the best-fit copula functions Ci, C2 and C3 in the hybrid copula function; and [0056] wi, w2 and w3 represent weight coefficients of the best-fit copula functions Ci, C2 and C3 in the hybrid copula function and are solved by using an image set method, where wi+w2+w3=l.
Advantageous Effect [0057] In conclusion, by using the above technical solution, the present invention at least has the following advantageous effects:
[0058] (1) in the method, for the condition of lack of the capacity of the fault data samples of the critical components of the deep well hoist, the probability distribution function of random response in each failure mode can be approximated in a small sample condition, thereby providing an accurate marginal probability density function for a copula function, and improving the modeling accuracy of the copula function; and [0059] (2) in the present invention, for the rigid-flexible coupling characteristic of the deep well hoist, the symmetric correlation, upper tail correlation and lower tail correlation attributes possibly existing between failure modes of mechanical components are fully considered, and best-fit copula functions are selected from alternative copula functions to model a hybrid copula function, thereby providing a more suitable modeling tool for characterizing the true failure correlation of the critical components of the deep well hoist.
BRIEF DESCRIPTION OF THE DRAWINGS [0060] Fig. 1 is a flowchart of the present invention; and [0061] Fig. 2 is a structural schematic diagram of a main shaft of a deep well hoist according to an embodiment of the present invention.
DETAILED DESCRIPTION OF THE INVENTION [0062] A correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition includes the following steps:
[0063] step 1: acquiring fault data samples of the critical components of the hoist in different failure modes, and collecting statistics about statistical moment information of random response in each failure mode in the incomplete information condition;
[0064] step 2: obtaining a marginal probability distribution function of each failure mode by using a function approximation method;
[0065] step 3: analyzing probability correlation attributes between each pair of failure modes by using a goodness-of-fit test criterion, and determining best-fit copula functions for describing different correlation attributes of part failure; and [0066] step 4: establishing a hybrid copula function model by combining the marginal probability distribution function of each failure mode obtained in the step 2 with each best-fit copula function determined in the step 3.
[0067] The fault data samples of the critical components of the hoist in different failure modes in the step 1 include stress, strain, frequency response, wearing capacity and temperature variation of the critical components of the hoist; and the statistical moment information of random response in each failure mode in the incomplete information condition is solved by using a random perturbation method, namely [0068]
Var = [0069]
| f 1 | [2’ , | |
| 4 | 3! <?Fr |
[0070] [0071] [0072] [0073] where E represents a mean value of random response in a failure mode,
Var represents a variance of random response in a failure mode,
Tm represents a third moment of random response in a failure mode, [0074] Y represents a fault data sample vector, [0075] YT represents a transposed vector of the fault data sample vector, [0076] g(Y) represents a random response function, [0077] Var(Y) represents a variance of the fault data sample vector, [0078] μ4(Υ) represents a fourth moment of the fault data sample vector, [0079] ]®(·)_(·)®(·)®”·®(·) js a Kronecker power of (’), and a symbol ® represents a Kronecker product.
[0080] The function approximation method in the step 2 is a truncated Edgeworth series approximation method, and by combining the fault data samples and the statistical moment information obtained in the step 1, an approximation probability distribution function can be obtained:
[0081] ρε(Γ)«Φ(Γ)y) Tm y
Var3 [0082] where [0083] ® (·) represents a cumulative probability distribution function of standard normal distribution; and [0084] «Ή represents a probability density function of standard normal distribution.
[0085] The goodness-of-fit test criterion in the step 3 is an Akaike information criterion, specifically expressed as:
AlC = -2\ lnC(w.,v-0) + 2 [0086] '[0087] where [0088] C(ui, Vj; Θ) represents a known copula function;
[0089] u; and Vi represent random variables subjected to statistical processing, specifically expressed as:
[0090]
[0091] where yb and y2i respectively represent fault data samples in two failure modes, [0092] i represents the number of samples, [0093] N represents the capacity of the fault data samples, [0094] rank(yii) or rank(y2i) represents the ranks of the fault data samples of the hoist, namely {ylb ..., yiN} or {y2b ..., y2N}; and [0095] the best-fit copula function refers to a copula function with the minimum AIC value in copula functions for describing the same type of correlation attributes.
[0096] The step 4 specifically includes:
[0097] 4.1 normalizing the fault data samples of the critical components of the hoist in different failure modes;
[0098] 4.2 calculating rank correlation coefficients among the fault data samples of the critical components of the hoist in different failure modes;
[0099] 4.3 respectively substituting each obtained rank correlation coefficient into each best-fit copula function obtained in the step 3 so as to determine the undetermined coefficient in each best-fit copula function; and [0100] 4.4 determining that the form of the hybrid copula function for describing the correlation attributes between two failure modes is:
[0101] Cmix=wiCi(u, v; a)+w2C2(u, v; p)+w3C3(u, v; 0) [0102] where [0103] Ci, C2 and C3 represent the best-fit copula functions determined in the step 3, and are used for respectively describing symmetric correlation, upper tail correlation and lower tail correlation properties between two failure modes;
[0104] u and v represent marginal distribution functions of each failure mode;
[0105] α, β and Θ respectively represent the undetermined coefficients of the best-fit copula functions Ci, C2 and C3 in the hybrid copula function; and [0106] wi, w2 and w3 represent weight coefficients of the best-fit copula functions Ci, C2 and C3 in the hybrid copula function and are solved by using an image set method, where wi+w2+w3=l.
[0107] Embodiment:
[0108] In the present invention, in order to more fully understand the characteristics and engineering applicability of the present invention, joint probability modeling in three failure modes of strength failure, stiffness failure and resonance failure is performed for the to-be-modeled structure of the main shaft of the deep well hoist as shown in Fig. 2.
[0109] (1) Three groups of fault data samples of stress, strain and frequency response of the main shaft of the hoist in fault conditions are obtained by site tests. In order to facilitate statistical analysis of the three groups of fault data samples, obtained sample values are normalized.
[0110] (2) According to the Akaike information criterion, AIC index values of each pair of failure modes under six candidate copula functions are respectively calculated, and results are as shown in table 1.
[0111] Table 1 AIC values of six candidate copula functions
| Gaussian(AIC) | Frank(AIC) | Gumbel(AIC) | CClayton(AIC) | t(AIC) | Clayton(AIC) | |
| glg2 | -346.52 | -318.94 | -311.55 | -196.93 | -318.94 | -208.75 |
| glg3 | -345.08 | -328.84 | -378.88 | -347.95 | -191.63 | -203.24 |
| g2g3 | -1426.24 | -1301.4 | -1298.38 | -912.62 | -1301.4 | -924.43 |
[0112] In three pairs of copula function groups, namely Gaussian copula and Frank copula, Gumbel copula and CClayton copula, as well as t copula and Clayton copula, copula functions with smaller AIC values are respectively selected to serve as best-fit copula functions.
[0113] (3) According to the three groups of fault data samples of stress, strain and frequency response of the main shaft of the hoist, the first three orders of statistical moments, mean value, variance and third moment of each group of failure data are obtained by using a statistical method. The truncated Edgeworth series is used to approximate the marginal probability distribution functions of all failure modes, and the marginal probability distribution functions are respectively as follows:
[0114]
Pi (.^)-^(.^) + ^(>ί)αΓ s σ,6 · '
Ρ3(ν3)~Φ(.ν3) + σ3 6 [0115] [0116] [0117] where pi(yi), P2(y2) and P3(y3) respectively represent marginal probability distribution functions of stress, strain and frequency response, yl, y2 and y3 respectively represent sample vectors of stress, strain and frequency response, μι and σι represent the mean value and standard deviation of stress response, μ2 and 02 represent the mean value and standard deviation of strain response, and μ3 and 03 represent the mean value and standard deviation of frequency response.
[0118] (4) According to the three groups of fault data samples of stress, strain and frequency response of the main shaft of the hoist, rank correlation coefficients between each pair of failure modes are solved, and the rank correlation coefficients are respectively as follows:
[0119] Ti2=0.769; n3=0.338; τ23=0.542 [0120] Then, the undetermined coefficients of all best-fit copula functions are solved, and the undetermined coefficients are as shown in table 2.
[0121] Table 2 Parameter values of best-fit copula functions
| Gaussian(a) | Gumbel(3) | t(0) | Clayton(O) | |
| glg2 | 0.560 | 0.628 | 3.08 | - |
| glg3 | 0.594 | 0.579 | - | 3.354 |
| g2g3 | 0.589 | 0.324 | 2.81 | - |
[0122] (5) According to the three groups of fault data samples of stress, strain and frequency response of the main shaft of the hoist, weight coefficients of three best-fit copula functions are calculated by an image set method. For gig2, [0123] wi=0.68; W2=0.23; W3=0.09 [0124] In combination with a preferred best-fit copula function, a joint probability model for stress and strain failure is:
[0125] Ci2=wiCi(u, v, a)+w2C2(u, v, P)+w3C3(u, v, 0) [0126] =0.68CGaussian(pi, P2, 0.56)+0.23CGumbei(pi, P2, 0.628)+0.09Ct(pi, p2, 3.08) [0127] For gig3, [0128] wi=0.51; W2=0.35; w3=0.14 [0129] In combination with a preferred best-fit copula function, a joint probability model for stress and frequency failure is:
[0130] Ci3=wiCi(u, v, a)+w2C2(u, v, P)+w3C3(u, v, 0) [0131] =0.51CGaUssian(pi, P3, 0.594)+0.35CGumbel(pi, P3, 0.579)+0.14Cciayton(pi, P3, 3.354) [0132] For g2g3, [0133] wi=0.56; W2=0.33; w3=0.11 [0134] In combination with a preferred best-fit copula function, a joint probability model for stress and frequency failure is:
[0135] C23=wiCi(u, v, a)+w2C2(u, v, P)+w3C3(u, v, 0) [0136] =0.56CGaussian(p2, p3, 0.589)+0.33CGumbei(P2, P3, 0.324)+0.HCt(p2, p3, 2.81)
Claims (5)
- What is claimed is:1. A correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition, wherein the method comprises the following steps:step 1: acquiring fault data samples of the critical components of the hoist in different failure modes, and collecting statistics about statistical moment information of random response in each failure mode in the incomplete information condition;step 2: obtaining a marginal probability distribution function of each failure mode by using a function approximation method;step 3: analyzing probability correlation attributes between each pair of failure modes by using a goodness-of-fit test criterion, and determining best-fit copula functions for describing different correlation attributes of part failure; and step 4: establishing a hybrid copula function model by combining the marginal probability distribution function of each failure mode obtained in the step 2 with each best-fit copula function determined in the step 3.
- 2. The correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition according to claim 1, wherein the fault data samples of the critical components of the hoist in different failure modes in the step 1 comprise stress, strain, frequency response, wearing capacity and temperature variation of the critical components of the hoist; and the statistical moment information of random response in each failure mode in the incomplete information condition is solved by using a random perturbation method, namelyVar =Ίμι • Var(K) i1 ^g(y)4!β(Γη4
/ 1 4 [*)2 ^(F)a3g(F) - 3! cU5(yT): wherein, E represents a mean value of random response in a failure mode, Var represents a variance of random response in a failure mode, Tm represents a third moment of random response in a failure mode, Y represents a fault data sample vector,YT represents a transposed vector of the fault data sample vector, g(Y) represents a random response function,Var(Y) represents a variance of the fault data sample vector, g4(Y) represents a fourth moment of the fault data sample vector, is a Kronecker power of (*), and a symbol ® represents a Kronecker product.3. The correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition according to claim 1, wherein the function approximation method in the step 2 is a truncated Edgeworth series approximation method, and by combining the fault data samples and the statistical moment information obtained in the step 1, an approximation probability distribution function can be obtained:whereinΦ ( ’ ) represents a cumulative probability distribution function of standard normal distribution; and represents a probability density function of standard normal distribution.
- 4. The correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition according to claim 1, wherein the goodness-of-fit test criterion in the step 3 is an Akaike information criterion, specifically expressed as:AIC = -2^ In vs;0) + 2 whereinC(ui, ν;; Θ) represents a known copula function;U; and V; represent random variables subjected to statistical processing, specifically expressed as:wherein yu and y2i respectively represent fault data samples in two failure modes, i represents the number of samples, N represents the capacity of the fault data samples, and rank(yii) or rank(y2i) represents the ranks of the fault data samples of the hoist, namely {yn, ..., yiN} or {y2i, ···, y2x}; and the best-fit copula function refers to a copula function with a minimum AIC value in copula functions for describing the same type of correlation attributes.
- 5. The correlation modeling method for coupling failure of critical components of a deep well hoist in an incomplete information condition according to claim 1, wherein the step 4 specifically comprises:4.1 normalizing the fault data samples of the critical components of the hoist in different failure modes;4.2 calculating rank correlation coefficients among the fault data samples of the critical components of the hoist in different failure modes;4.3 respectively substituting each obtained rank correlation coefficient into each best-fit copula function obtained in the step 3 so as to determine a undetermined coefficient in each best-fit copula function; and4.4 determining that the form of the hybrid copula function for describing the correlation attributes between two failure modes is:Cmix=wiCi(u, v; a)+w2C2(u, v; P)+w3C3(u, v; Θ) whereinCi, C2 and C3 represent the best-fit copula functions determined in the step 3, and are used for respectively describing symmetric correlation, upper tail correlation and lower tail correlation properties between two failure modes;u and v represent marginal distribution functions of each failure mode;α, β and Θ respectively represent the undetermined coefficients of the best-fit copula functions Ci, C2 and C3 in the hybrid copula function; and wi, w2 and w3 represent weight coefficients of the best-fit copula functions Ci, C2 and C3 in the hybrid copula function and are solved by using an image set method, wherein wi+w2+w3=l.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201810087587.2A CN108345731A (en) | 2018-01-30 | 2018-01-30 | Deep-well elevator critical component couples failure correlation modeling method under a kind of incomplete information condition |
| CN201810087587.2 | 2018-01-30 | ||
| PCT/CN2018/106892 WO2019148857A1 (en) | 2018-01-30 | 2018-09-21 | Coupling failure correlation modeling method for key component of deep well hoist under incomplete information condition |
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| CN112100929A (en) * | 2020-11-09 | 2020-12-18 | 西南交通大学 | Dynamic fine adjustment method for track based on particle swarm algorithm |
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| CN108345731A (en) * | 2018-01-30 | 2018-07-31 | 中国矿业大学 | Deep-well elevator critical component couples failure correlation modeling method under a kind of incomplete information condition |
| CN110362858B (en) * | 2019-06-05 | 2021-10-22 | 徐州圣邦机械有限公司 | Reliability evaluation method for high-pressure internal gear pump gear pair |
| CN112685915B (en) * | 2021-01-18 | 2023-06-30 | 重庆大学 | Wind power output condition probability distribution modeling method |
| CN113239641A (en) * | 2021-03-30 | 2021-08-10 | 湖北工业大学 | Prediction method for maximum drift distance of debris flow |
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| RU2098630C1 (en) * | 1995-08-02 | 1997-12-10 | Открытое акционерное общество Фирма "Геомар" | Station for monitoring shaft guide parameters |
| US7689394B2 (en) * | 2003-08-26 | 2010-03-30 | Siemens Industry, Inc. | System and method for remotely analyzing machine performance |
| US20160283621A1 (en) * | 2010-01-06 | 2016-09-29 | Sas Institute Inc. | Hybrid Simulation Methodologies |
| WO2016091198A1 (en) * | 2014-12-11 | 2016-06-16 | 冯春魁 | Method and system for parameter acquisition, control, operation and load monitoring for elevator |
| CN104914775B (en) * | 2015-06-12 | 2017-05-31 | 华东理工大学 | Multi-modal procedure failure testing method and system based on the description of vine copula correlations |
| CN105117550B (en) * | 2015-08-26 | 2017-12-26 | 电子科技大学 | A kind of modeling method towards product multidimensional correlation degradation failure |
| CN106650204A (en) * | 2016-09-27 | 2017-05-10 | 北京航空航天大学 | Product failure behavior coupling modeling and reliability evaluation method |
| CN106548256B (en) * | 2016-12-05 | 2020-05-08 | 西南石油大学 | Method and system for modeling time-space dynamic correlation of wind power plant |
| CN107291989B (en) * | 2017-05-25 | 2018-09-14 | 中国矿业大学 | Km deep-well main shaft of hoister multi-invalidation mode reliability estimation method |
| CN107274028A (en) * | 2017-06-23 | 2017-10-20 | 国网山东省电力公司经济技术研究院 | A kind of many wind fields based on mixing Copula functions are exerted oneself Forecasting Methodology |
| CN107577896B (en) * | 2017-09-22 | 2020-08-14 | 国网江苏省电力公司电力科学研究院 | Wind power plant multi-machine aggregation equivalent method based on hybrid Copula theory |
| CN108345731A (en) * | 2018-01-30 | 2018-07-31 | 中国矿业大学 | Deep-well elevator critical component couples failure correlation modeling method under a kind of incomplete information condition |
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| CN112100929A (en) * | 2020-11-09 | 2020-12-18 | 西南交通大学 | Dynamic fine adjustment method for track based on particle swarm algorithm |
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