AU2018374073B2 - 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
Correlation Modeling Method for Coupling Failure of Critical Components of Deep Well Hoist under Incomplete Information Condition
[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.
[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] [1]Noh Y, Choi K K, Du L. Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula[J].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.
Technical Solution
[0010] Embodiments of the present invention may 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. Embodiments of the method may 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] According to one aspect of the present invention , there is provided 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, wherein the function approximation method is a truncated Edgeworth series approximation method;
[0015] step 3: analyzing probability correlation attributes between each pair of failure modes by using a goodness-of-fit test criterion, wherein the goodness-of-fit test criterion is an Akaike information criterion (AIC), 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, wherein 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.
[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
E=g(Y)+ Var (Y)+ P4(Y)
[0018] 2a(yT)2 4!a()yT
1g(Y) 1a8yg+Y0) 2 g (Y-)p g(Y) Var- T Var(Y)+p.4(Y)- ~ 3!
[~l' ! ay)
[0019] VrLY
[0020] Tm2 1 Y a(Y y 2
[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,
3a
[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] pt4(Y) represents a fourth moment of the fault data sample vector,
[00291 . &('" is a Kronecker power of (*,and a symbol 0 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:
(Y) (D () (Y) Tm Y
[0031] 72 Var
[0032] where
[0033] 0 ( ' ) 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=-2InC(u,,v,;6) + 2
[0036]
[0037] where
[0038] C(ui, vi; 0) represents a known copula function;
[0039] ui and vi represent random variables subjected to statistical processing, specifically expressed as:
rank (y,) _ rank( v , N u,= , v,= (i=I,2,...,N)
[0040] N+1 N+1
[0041] where yii 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(yj) or rank(y2i) represents the ranks of the fault data samples of the hoist, namely {yii,.., y1N) or (Y21, ... , 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:
[00511 Cmix=wiC1(u, v; a)+w2C2(u, v; p)+w 3 C3 (u, v; 0)
[0052] where
[0053] C 1 , C 2 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] a, P and 0 respectively represent the undeterminedcoefficients of the best-fit copula functions C1, C 2 and C 3 in the hybrid copula function; and
[0056] wi, w2 and w3 represent weight coefficients of the best-fit copula functions C 1 , C 2 and C 3 in the hybrid copula function and are solved by using an image set method, where wI+w2+w3=1.
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.
[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.
[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
4 I E=g(Y)+ I .gyVar(Y)+- a g()~ (Y)
[0068] 2a(y 4!a(YT)
Var= LY T Var(Y)+p.,(Y)I 4L(y T )2 ., 3! OYT I ,(yT)
[00691
Tm= 3p., (Y)]a2g(Y) T
[0070] 2 .y 0a(yT)y
[0071] where E represents a mean value of random response in a failure mode,
[0072] Var represents a variance of random response in a failure mode,
[0073] 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] pt4(Y) represents a fourth moment of the fault data sample vector,
[00791 (k( I()(.)®(.)®'''G(') is a Kronecker power of (',and a symbol 0 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] 72 Var
[0082] where
[0083] ( * ) represents a cumulative probability distribution function of standard normal distribution; and
[0084] 9'(*) 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:
AIC=-2InC(ui,v,;O)+2
[00861
[0087] where
[0088] C(ui, vi; 0) represents a known copula function;
[0089] ui and vi represent random variables subjected to statistical processing, specifically expressed as:
=rank(y 1 ) =rank(y,)(i1 ui = ( ,an = rn 'vi (i =1, 2,..., N)
[0090] N+1 N+1
[0091] where yii 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(yi) or rank(y 2i) represents the ranks of the fault data samples of the hoist, namely {y, ... , y oN {y21, or ... , 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)+w 2 C2 (u, v; p)+w 3 C3 (u, v; 0)
[0102] where
[01031 C 1 , C 2 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] a, P and 0 respectively represent the undetermined coefficients of the best-fit copula functions C1, C 2 and C 3 in the hybrid copula function; and
[0106] w 1, w2 and w3 represent weight coefficients of the best-fit copula functions C 1 , C 2 and C 3 in the hybrid copula function and are solved by using an image set method, where wI+w2+w3=1.
[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) gig2 -346.52 -318.94 -311.55 -196.93 -318.94 -208.75 gig3 -345.08 -328.84 -378.88 -347.95 -191.63 -203.24 g29 3 -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] 72 a
[0115] 72 a
[0116] 72 3,
[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, t and
ai represent the mean value and standard deviation of stress response, p2 and G2 represent the mean value and standard deviation of strain response, and t3 and G3
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:
[01191 T12=0.769; T13=0.338; E23=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(p) t(O) Clayton(O) gig2 0.560 0.628 3.08 gig3 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] w 1=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] C12=wiCi(u, V, a)+w2C2(u, V, )+w 3C 3(u, V, 0)
[0126] =0. 6 8 CGaussian(P1, P2, 0.5 6 )+0. 2 3 CGumbe(P1, P2, 0.628)+0.09C(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] C 13=wiC 1(u, V, a)+w 2C 2(u, V, p)+w 3C 3(u, V, 0)
[0131] =0.51CGaussian(P1, P3, 0.5 9 4 )+0. 3 5CGumbei(P1, P3, 0.579)+0.1 4 Cciayton(pi, P3, 3.354)
[0132] Forg2g3,
[0133] w 1=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] C 23=wIC 1(u, V, a)+w2C2(u, V, p)+w 3C 3(u, V, 0)
[0136] =0.5 6 CGaussian(P2, P3, 0.5 8 9 )+0. 3 3 CGumbel(P2,P3,0.324)+0.11Ct(P2, P3, 2.81)
11A
[0137] Throughout the specification and the claims that follow, unless the context requires otherwise, the words "comprise" and "include" and variations such as "comprising" and "including" will be understood to imply the inclusion of a stated integer or group of integers, but not the exclusion of any other integer or group of integers.
[0138] The reference to any prior art in this specification is not, and should not be taken as, an acknowledgement of any form of suggestion that such prior art forms part
of the common general knowledge.
[0139] It will be appreciated by those skilled in the art that the disclosure is not restricted in its use to the particular application or applications described. Neither is the
present disclosure restricted in its preferred embodiment with regard to the particular
elements and/or features described or depicted herein. It will be appreciated that the
disclosure is not limited to the embodiment or embodiments disclosed, but is capable of
numerous rearrangements, modifications and substitutions without departing from the
scope as set forth and defined by the following claims.
Claims (5)
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, wherein the function approximation method is a truncated Edgeworth series approximation method;
step 3: analyzing probability correlation attributes between each pair of failure modes by using a goodness-of-fit test criterion, wherein the goodness-of-fit test criterion is an Akaike information criterion (AIC), 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, wherein 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.
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, namely
E=g(Y)+ -Var(Y)+ p(Y) 2 a(yT)' 4! a(yT)'
Var= (y) Var(Y)+g,(Y)(y) BY4 a (y') 3! 0 (yT)'
2 Tm2 Tm3pYag(Y) g(Y) YT a(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,
pt4 (Y) represents a fourth moment of the fault data sample vector,
(.)*1I9[*-J()()®..() is a Kronecker power of (,and a symbol 0 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
by combining the fault data samples and the statistical moment information obtained in the step 1, an approximation probability distribution function can be obtained:
PE () ( ((Y) Tm YT 72 Var3
wherein
(K )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 Akaike information criterion is expressed as: N AIC=-2EInC(u,,v,;O)+2
wherein
C(ui, vi; 0) represents a known copula function;
ui and vi represent random variables subjected to statistical processing, specifically expressed as:
=rank(y 1 ) _rank(y,)(2 N Ili = rn yj, v, = rn Y,)(i = 1, 2,..., N) N+1 N+1
wherein yi 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(y 2i) represents the ranks of the fault data samples of the hoist, namely {y11, .. , Y1N) or {y21,, Y2N).
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; and
4.4 determining that the form of the hybrid copula function for describing the correlation attributes between two failure modes is:
Cmix=wiC1(u, v; a)+w 2C 2(u,v; p)+w 3C 3(u, v; 0)
wherein
C1, C2 and C 3 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;
a, P and 0 respectively represent the undetermined coefficients of the best-fit copula functions C 1 , C2 and C 3 in the hybrid copula function; and
w 1, w2 and w 3 represent weight coefficients of the best-fit copula functions C 1, C2 and C 3 in the hybrid copula function and are solved by using an image set method, wherein wi+w2+w3=1.
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