CA3014415A1 - Reliability evaluation method for hoist main shaft of kilometer-deep mine considering multiple failure modes - Google Patents
Reliability evaluation method for hoist main shaft of kilometer-deep mine considering multiple failure modes Download PDFInfo
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Abstract
The present invention discloses a reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes. First, a parametrical three-dimensional model of the main shaft is established according to physical dimensions of the main shaft. Then, a sampling matrix for random variables of the main shaft is established according to probability types of the random variables, and strength and stiffness responses of the main shaft are solved using the sampling matrix with a finite element method. Afterwards, an explicit function defining a relationship between the responses and the matrix for the random variables is established using a neural network approach, and explicit performance functions in a strength failure mode and in a stiffness failure mode are separately established according to strength and stiffness design criteria; and then, probabilities of these two failures are calculated by means of a saddlepoint approximation method. Finally, a joint failure probability model combining the two failure modes is established using a Clayton copula function, and system reliability in the case of a joint failure is solved using a bound reliability method. The present invention considers probability correlation between a strength failure and a stiffness failure, and can more accurately and reasonably evaluate system reliability of the hoist main shaft.
Description
, RELIABILITY EVALUATION METHOD FOR HOIST MAIN SHAFT
OF KILOMETER-DEEP MINE CONSIDERING MULTIPLE FAILURE
MODES
BACKGROUND OF THE INVENTION
Technical Field The present invention relates to the field of technical research on reliability of a mechanical structure, and in particular, to a system reliability evaluation method for a mechanical product, especially, for a hoist main shaft of a kilometer-deep mine in the case of correlated probabilities of failure modes.
Background At present, most coal mines in China are shallow mines which are 500 to 800 meters deep. However, coal resources that account for 53% of the total reserves are hidden at the depth of 1000 to 2000 meters. Therefore, it is required to use a kilometer-deep mine hoisting system (including a hoist, a hoisting container, a hoisting rope, and the like). As a principal bearing part of a hoist, a main shaft takes all the torque for raising and lowering loads, and also withstands the tension force of the steel ropes on both sides. As the mine depth reaches above one kilometer, the maximum static tension of the hoist and the number of winding layers on a reel of the main shaft are greatly increased, such that the steel rope produces a winding pressure much greater than that of an existing structure on the reel, and the tension force and torque of the steel rope on the main shaft are further greatly increased. As the mine depth reaches two kilometers, the static load of a hoist terminal may reach 240 t or more, and an economic hoisting rate may reach 20 m/s or more. A huge dynamic load produced accordingly seriously affects the service life of the main shaft.
Therefore, a kilometer-deep mine hoist has extremely high requirement on the reliability of the main shaft.
The hoist main shaft of the kilometer-deep mine has a variety of fault modes of different forms, where a strength failure and a stiffness failure are the primary failure modes that affect safety and stability of the hoist. Due to homogeneity of stimuli and consistency in characterization of system characteristic parameters, the various faults of the hoist main shaft are generally correlated. If such a characteristic is neglected, it is difficult to acquire accurate failure data and reliability information.
SUMMARY OF THE INVENTION
Invention objective: An objective of the present invention is to provide a feasible probabilistic modeling and analysis method for system reliability evaluation in a state of a joint failure of multiple failure modes of a hoist main shaft of a kilometer-deep mine.
To achieve the foregoing objective, the present invention adopts the following technical solutions:
A reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes is provided. First, a parametrical three-dimensional model of the main shaft is established according to physical dimensions of the main shaft. Then, a sampling matrix for random variables of the main shaft is established according to probability types of the random variables, and strength and stiffness responses of the main shaft are solved using the sampling matrix with a finite element method. Afterwards, an explicit function defining a relationship between the responses and the matrix for the random variables is established using a neural network approach, and explicit performance functions in a strength failure mode and in a stiffness failure mode are separately established according to strength and stiffness design criteria; and then, probabilities of these two failures are calculated by means of a saddlepoint approximation method.
Finally, a joint failure probability model combining the two failure modes is established using Clayton copula function, and system reliability in the case of a joint failure is solved using a bound reliability method.
Comprising specifically steps as follows:
step 1: determining mean values and variances of dimension parameters, material attribute parameters, and loads in different working conditions, and determining distribution types of these parameters;
step 2: establishing a three-dimensional parametrical model of the main shaft
OF KILOMETER-DEEP MINE CONSIDERING MULTIPLE FAILURE
MODES
BACKGROUND OF THE INVENTION
Technical Field The present invention relates to the field of technical research on reliability of a mechanical structure, and in particular, to a system reliability evaluation method for a mechanical product, especially, for a hoist main shaft of a kilometer-deep mine in the case of correlated probabilities of failure modes.
Background At present, most coal mines in China are shallow mines which are 500 to 800 meters deep. However, coal resources that account for 53% of the total reserves are hidden at the depth of 1000 to 2000 meters. Therefore, it is required to use a kilometer-deep mine hoisting system (including a hoist, a hoisting container, a hoisting rope, and the like). As a principal bearing part of a hoist, a main shaft takes all the torque for raising and lowering loads, and also withstands the tension force of the steel ropes on both sides. As the mine depth reaches above one kilometer, the maximum static tension of the hoist and the number of winding layers on a reel of the main shaft are greatly increased, such that the steel rope produces a winding pressure much greater than that of an existing structure on the reel, and the tension force and torque of the steel rope on the main shaft are further greatly increased. As the mine depth reaches two kilometers, the static load of a hoist terminal may reach 240 t or more, and an economic hoisting rate may reach 20 m/s or more. A huge dynamic load produced accordingly seriously affects the service life of the main shaft.
Therefore, a kilometer-deep mine hoist has extremely high requirement on the reliability of the main shaft.
The hoist main shaft of the kilometer-deep mine has a variety of fault modes of different forms, where a strength failure and a stiffness failure are the primary failure modes that affect safety and stability of the hoist. Due to homogeneity of stimuli and consistency in characterization of system characteristic parameters, the various faults of the hoist main shaft are generally correlated. If such a characteristic is neglected, it is difficult to acquire accurate failure data and reliability information.
SUMMARY OF THE INVENTION
Invention objective: An objective of the present invention is to provide a feasible probabilistic modeling and analysis method for system reliability evaluation in a state of a joint failure of multiple failure modes of a hoist main shaft of a kilometer-deep mine.
To achieve the foregoing objective, the present invention adopts the following technical solutions:
A reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes is provided. First, a parametrical three-dimensional model of the main shaft is established according to physical dimensions of the main shaft. Then, a sampling matrix for random variables of the main shaft is established according to probability types of the random variables, and strength and stiffness responses of the main shaft are solved using the sampling matrix with a finite element method. Afterwards, an explicit function defining a relationship between the responses and the matrix for the random variables is established using a neural network approach, and explicit performance functions in a strength failure mode and in a stiffness failure mode are separately established according to strength and stiffness design criteria; and then, probabilities of these two failures are calculated by means of a saddlepoint approximation method.
Finally, a joint failure probability model combining the two failure modes is established using Clayton copula function, and system reliability in the case of a joint failure is solved using a bound reliability method.
Comprising specifically steps as follows:
step 1: determining mean values and variances of dimension parameters, material attribute parameters, and loads in different working conditions, and determining distribution types of these parameters;
step 2: establishing a three-dimensional parametrical model of the main shaft
2 according to structure parameters of the hoist main shaft, and importing the three-dimensional parametrical model of the main shaft into finite element software, to perform statics analysis;
step 3: establishing a random sampling matrix for the various basic parameters according to the mean values and variances of the basic parameters of the main shaft determined in step 1 by using a sampling method;
step 4: according to parameter values in each line of the random sampling matrix, repeatedly generating a new three-dimensional model of the main shaft and performing finite element analysis again, to obtain new stress-strain response samples;
step 5: fitting the random sampling matrix and the stress-strain values by using a neural network approach, to obtain a function relationship between a stress-strain response of the main shaft and a change in structural performance parameters;
step 6: separately establishing reliability performance functions in a strength failure mode and a stiffness failure mode according to strength and stiffness requirements on the hoist main shaft; calculating third and fourth order moments of the basic parameters according to their mean values and variances; then, calculating mean values, variances, third order moments and fourth order moments of the performance functions according to the established performance functions; and separately calculating a strength failure probability and a stiffness failure probability by means of the saddlepoint approximation method; and step 7: acquiring a correlation coefficient between the strength failure and the stiffness failure by means of a statistical method, establishing joint failure distribution combining the strength failure and stiffness failure by using Clayton copula function, and then calculating a system failure probability in the case of correlated failures by using the bound reliability method.
Step 1 specifically includes:
determining mean values and variances of physical dimensions and material attributes of the hoist main shaft;
determining working conditions of the hoist main shaft, and then determining mean values and variances of loads taken by the main shaft in the different working
step 3: establishing a random sampling matrix for the various basic parameters according to the mean values and variances of the basic parameters of the main shaft determined in step 1 by using a sampling method;
step 4: according to parameter values in each line of the random sampling matrix, repeatedly generating a new three-dimensional model of the main shaft and performing finite element analysis again, to obtain new stress-strain response samples;
step 5: fitting the random sampling matrix and the stress-strain values by using a neural network approach, to obtain a function relationship between a stress-strain response of the main shaft and a change in structural performance parameters;
step 6: separately establishing reliability performance functions in a strength failure mode and a stiffness failure mode according to strength and stiffness requirements on the hoist main shaft; calculating third and fourth order moments of the basic parameters according to their mean values and variances; then, calculating mean values, variances, third order moments and fourth order moments of the performance functions according to the established performance functions; and separately calculating a strength failure probability and a stiffness failure probability by means of the saddlepoint approximation method; and step 7: acquiring a correlation coefficient between the strength failure and the stiffness failure by means of a statistical method, establishing joint failure distribution combining the strength failure and stiffness failure by using Clayton copula function, and then calculating a system failure probability in the case of correlated failures by using the bound reliability method.
Step 1 specifically includes:
determining mean values and variances of physical dimensions and material attributes of the hoist main shaft;
determining working conditions of the hoist main shaft, and then determining mean values and variances of loads taken by the main shaft in the different working
3 i conditions, the loads including a static load, dynamic load, bending moment, torque, and the like; and determining distribution types of the foregoing parameters.
Step 2 specifically includes:
by a parametrical modeling of the hoist main shaft, generating a command flow file of the modeling, exporting an established model of the main shaft, and saving the model in a working directory;
by means of a finite element analysis of the hoist main shaft, generating a command flow file of the analysis process, exporting a text file containing an analysis result, and saving the file in the working directory; and establishing a finite element model of the main shaft according to material performance parameters of the main shaft, and imposing external loads such as the bending moment, torque, and maximum static load, where the physical parameters of the main shaft include the diameters and lengths of sections of the main shaft, and the diameters and lengths of reels; and the material performance parameters include the elastic modulus, Poisson's ratio, and density.
Step 4 specifically includes:
by using the set working directory, and according to the generated random sampling matrix, modifying variable values in a command flow file generated in a modeling process, and generating a new main shaft model;
analyzing the newly generated main shaft model by using a command flow of finite element analysis , to obtain a new stress-strain response value; and repeating the foregoing steps till a corresponding stress-strain response value is acquired for each set of random variable values in the matrix for the random variables.
Step 7 specifically includes:
performing random sampling according to distribution types of random variables of the main shaft, and acquiring calculated values between the strength failure and the stiffness failure by using the reliability performance functions established in step 6;
calculating a rank correlation coefficient of the two failure modes by means of a
Step 2 specifically includes:
by a parametrical modeling of the hoist main shaft, generating a command flow file of the modeling, exporting an established model of the main shaft, and saving the model in a working directory;
by means of a finite element analysis of the hoist main shaft, generating a command flow file of the analysis process, exporting a text file containing an analysis result, and saving the file in the working directory; and establishing a finite element model of the main shaft according to material performance parameters of the main shaft, and imposing external loads such as the bending moment, torque, and maximum static load, where the physical parameters of the main shaft include the diameters and lengths of sections of the main shaft, and the diameters and lengths of reels; and the material performance parameters include the elastic modulus, Poisson's ratio, and density.
Step 4 specifically includes:
by using the set working directory, and according to the generated random sampling matrix, modifying variable values in a command flow file generated in a modeling process, and generating a new main shaft model;
analyzing the newly generated main shaft model by using a command flow of finite element analysis , to obtain a new stress-strain response value; and repeating the foregoing steps till a corresponding stress-strain response value is acquired for each set of random variable values in the matrix for the random variables.
Step 7 specifically includes:
performing random sampling according to distribution types of random variables of the main shaft, and acquiring calculated values between the strength failure and the stiffness failure by using the reliability performance functions established in step 6;
calculating a rank correlation coefficient of the two failure modes by means of a
4 statistical method, and calculating undetermined parameters of the Clayton copula function;
calculating a joint failure probability of the strength and stiffness failure by using the Clayton copula function; and by using a second-order narrow-bound theory, substituting the strength failure probability and stiffness failure probability obtained in step 6, and the joint failure probability to calculate a system failure probability of the hoist main shaft.
The present invention has the following advantages and positive effects:
1) By use of a WSP (Wootton, Sergent, Phan-Tan-Luu) sampling method, a sampling matrix regarding multi-dimensional random variables of the hoist main shaft can be established, thus reducing the number of experiment designs based on finite element analysis on the premise of ensuring fitting precision of non-linear functions.
2) A correlation between the strength failure probability and the stiffness failure probability is considered, and therefore system reliability of the hoist main shaft can be more accurately and reasonably evaluated as compared with a failure independence assumption.
3) The strength failure and stiffness failure of the hoist main shaft highly positively correlate. By use of Clayton copula function, positively correlated probability models can be accurately established, thus overcoming a deficiency in Gaussian copula function that only symmetric correlations can be described.
Therefore, precision of system reliability evaluation for the hoist main shaft is improved.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. I is an implementation flowchart of a reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes according to the present invention;
FIG. 2 is a two-dimensional structure diagram of a main shaft of a hoist;
FIG. 3 is a diagram showing probability density of Clayton copula function;
and FIG. 4 is a scatter diagram of the Clayton copula function.
1.
In the drawings: DI indicates the diameter of a section of the main shaft fitted into a left bearing, L I indicates the length of the section of the main shaft fitted into the left bearing, D2 indicates the diameter of a section of the main shaft where a reel is mounted, D3 indicates the diameter of a section of the main shaft fitted into a right bearing, and L2 indicates the length of the section of the main shaft fitted into the right bearing.
DETAILED DESCRIPTION OF THE INVENTION
The present invention is further described below with reference to the accompanying drawings and embodiments.
As shown in FIG. 1, the present invention provides a system reliability evaluation method considering multiple failure modes, which includes the following steps:
Step 1: By surveying and mapping on the scene and with reference to a design drawing of a main shaft of a hoist, mean values and variances of dimension parameters, material attributes, and loads in different working conditions are acquired;
and distribution types of these parameters are determined.
Step 2: A three-dimensional parametrical model of the main shaft is established according to structure parameters of the hoist main shaft, and the three-dimensional parametrical model of the main shaft is imported into finite element software, to perform statics analysis.
Step 3: A random sampling matrix for the various basic parameters is established by using a WSP sampling method and according to the mean values and variances of the basic parameters of the main shaft determined in step I.
Step 4: Generation of a three-dimensional model of a new main shaft is repeated according to parameter values in each line of the random sampling matrix, and finite element analysis is performed again, to obtain new stress-strain response samples.
Step 5: The random sampling matrix (input samples) and the stress-strain values (response samples) are fitted by using a neural network approach, to obtain a function relationship between a stress-strain response of the main shaft and a change in structural performance parameters.
Step 6: Reliability performance functions in a strength failure mode and a stiffness failure mode are separately established according to strength and stiffness requirements on the hoist main shaft; third and fourth order moments of the basic parameters are calculated according to the mean values and variances thereof;
then, mean values, variances, third order moments and fourth order moments of the performance functions are calculated according to the established performance functions; and a strength failure probability and a stiffness failure probability are separately calculated by means of the saddlepoint approximation method.
Step 7: A correlation coefficient between the strength failure and the stiffness failure is acquired by means of a statistical method, joint failure distribution of the strength failure and stiffness failure is established by using Clayton copula function, and then a system failure probability in the case of correlated failures is calculated by using the bound reliability method.
Embodiment In order to fully understand the characteristics of the invention and its engineering applicability, the present invention solves system reliability related to strength and stiffness of a to-be-built main shaft structure of a kilometer-deep mine hoist shown in FIG. 2.
This main shaft structure bears moment and torque effects. By combining structure dimensions and load conditions of the main shaft, a random sampling matrix of the main shaft can be established, and a stress-strain response sample matrix of the main shaft can be acquired by using a finite element method. An explicit function relationship between the response and the input matrix is established according to a neural network approach, and then explicit limit state equations related to two failure modes, that is, a limit state equation related to a strength failure and a limit state equation related to a stiffness failure, are established according to a strength criterion and a stiffness criterion of the hoist main shaft. Table I shows probability information about random variables of the main shaft in this embodiment, where DI
indicates the diameter of a section of the main shaft fitted into a left bearing, LI
indicates the length of the section of the main shaft fitted into the left bearing, D2 indicates the diameter of a section of the main shaft where a reel is mounted, D3 indicates the diameter of a section of the main shaft fitted into a right bearing, and L2 indicates the length of the section of the main shaft fitted into the right bearing.
1, Table 1 Characteristics of probability statistics of random variables in the main shaft Variable Mean value Standard deviation Distribution type Di(mm) 710 21.3 Normal L1(mm) 315 9.45 Normal D2(mm) 800 23 Normal D3(mm) 710 21.3 Normal L2(mm) 315 9.45 Normal In this embodiment, by using the method for calculating a failure probability provided by the present invention, a failure probability in a strength failure mode is Pfi=0.003241, and a stiffness failure probability is Pf2=0.005173. n sample values of the random variables of the main shaft structure are randomly generated by using a random sampling method, and the n sample values are substituted into the explicit limit state equations combining the two failure modes, to obtain n response values through calculation. A correlation coefficient between a strength response vector and a stiffness response vector is calculated by using a command in MATLAB, and undetermined parameters of the Clayton copula function are estimated. The failure probabilities Pfi and Pf2 are substituted into the following equation:
.l+ Zniax( Pfl ZP.0) Pft EPfl - ElinaX(Pft ) In the equation, m indicates the number of failure modes of the hoist main shaft, P11 indicates the maximum failure probability in the failure modes of the hoist main shaft, Pfi indicates a failure probability of the ith failure mode, Pfij indicates a joint failure probability of the ith and jth failure mode, and pfs indicates a system failure probability related to a failure of the hoist main shaft.
A failure probability obtained in consideration of correlation between the strength failure and the stiffness failure of the main shaft structure is Pfs=0.008536.
A system failure probability calculated using a simulation method is Pfsm=0.008746.
To sum up, for a hoist main shaft of a kilometer-deep mine, this method provides a method for solving system reliability in consideration of correlation between a strength failure and a stiffness failure. First, a parametrical three-dimensional model of the main shaft is established according to physical dimensions of the main shaft.
Then, a sampling matrix for random variables of the main shaft is established according to probability types of the random variables, and strength and stiffness responses of the main shaft are solved using the sampling matrix with a finite element method. Afterwards, an explicit function defining a relationship between the responses and the matrix for the random variables is established using a neural network approach, and explicit performance functions in a strength failure mode and in a stiffness failure mode are separately established according to strength and stiffness design criteria; and then, probabilities of these two failures are calculated by means of the saddlepoint approximation method. Finally, a joint failure probability model combining the two failure modes is established using Clayton copula function, and system reliability in the case of a joint failure is solved using the bound reliability method.
The part not described in detail in the present invention belongs to technologies knows to researchers in this field.
calculating a joint failure probability of the strength and stiffness failure by using the Clayton copula function; and by using a second-order narrow-bound theory, substituting the strength failure probability and stiffness failure probability obtained in step 6, and the joint failure probability to calculate a system failure probability of the hoist main shaft.
The present invention has the following advantages and positive effects:
1) By use of a WSP (Wootton, Sergent, Phan-Tan-Luu) sampling method, a sampling matrix regarding multi-dimensional random variables of the hoist main shaft can be established, thus reducing the number of experiment designs based on finite element analysis on the premise of ensuring fitting precision of non-linear functions.
2) A correlation between the strength failure probability and the stiffness failure probability is considered, and therefore system reliability of the hoist main shaft can be more accurately and reasonably evaluated as compared with a failure independence assumption.
3) The strength failure and stiffness failure of the hoist main shaft highly positively correlate. By use of Clayton copula function, positively correlated probability models can be accurately established, thus overcoming a deficiency in Gaussian copula function that only symmetric correlations can be described.
Therefore, precision of system reliability evaluation for the hoist main shaft is improved.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. I is an implementation flowchart of a reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes according to the present invention;
FIG. 2 is a two-dimensional structure diagram of a main shaft of a hoist;
FIG. 3 is a diagram showing probability density of Clayton copula function;
and FIG. 4 is a scatter diagram of the Clayton copula function.
1.
In the drawings: DI indicates the diameter of a section of the main shaft fitted into a left bearing, L I indicates the length of the section of the main shaft fitted into the left bearing, D2 indicates the diameter of a section of the main shaft where a reel is mounted, D3 indicates the diameter of a section of the main shaft fitted into a right bearing, and L2 indicates the length of the section of the main shaft fitted into the right bearing.
DETAILED DESCRIPTION OF THE INVENTION
The present invention is further described below with reference to the accompanying drawings and embodiments.
As shown in FIG. 1, the present invention provides a system reliability evaluation method considering multiple failure modes, which includes the following steps:
Step 1: By surveying and mapping on the scene and with reference to a design drawing of a main shaft of a hoist, mean values and variances of dimension parameters, material attributes, and loads in different working conditions are acquired;
and distribution types of these parameters are determined.
Step 2: A three-dimensional parametrical model of the main shaft is established according to structure parameters of the hoist main shaft, and the three-dimensional parametrical model of the main shaft is imported into finite element software, to perform statics analysis.
Step 3: A random sampling matrix for the various basic parameters is established by using a WSP sampling method and according to the mean values and variances of the basic parameters of the main shaft determined in step I.
Step 4: Generation of a three-dimensional model of a new main shaft is repeated according to parameter values in each line of the random sampling matrix, and finite element analysis is performed again, to obtain new stress-strain response samples.
Step 5: The random sampling matrix (input samples) and the stress-strain values (response samples) are fitted by using a neural network approach, to obtain a function relationship between a stress-strain response of the main shaft and a change in structural performance parameters.
Step 6: Reliability performance functions in a strength failure mode and a stiffness failure mode are separately established according to strength and stiffness requirements on the hoist main shaft; third and fourth order moments of the basic parameters are calculated according to the mean values and variances thereof;
then, mean values, variances, third order moments and fourth order moments of the performance functions are calculated according to the established performance functions; and a strength failure probability and a stiffness failure probability are separately calculated by means of the saddlepoint approximation method.
Step 7: A correlation coefficient between the strength failure and the stiffness failure is acquired by means of a statistical method, joint failure distribution of the strength failure and stiffness failure is established by using Clayton copula function, and then a system failure probability in the case of correlated failures is calculated by using the bound reliability method.
Embodiment In order to fully understand the characteristics of the invention and its engineering applicability, the present invention solves system reliability related to strength and stiffness of a to-be-built main shaft structure of a kilometer-deep mine hoist shown in FIG. 2.
This main shaft structure bears moment and torque effects. By combining structure dimensions and load conditions of the main shaft, a random sampling matrix of the main shaft can be established, and a stress-strain response sample matrix of the main shaft can be acquired by using a finite element method. An explicit function relationship between the response and the input matrix is established according to a neural network approach, and then explicit limit state equations related to two failure modes, that is, a limit state equation related to a strength failure and a limit state equation related to a stiffness failure, are established according to a strength criterion and a stiffness criterion of the hoist main shaft. Table I shows probability information about random variables of the main shaft in this embodiment, where DI
indicates the diameter of a section of the main shaft fitted into a left bearing, LI
indicates the length of the section of the main shaft fitted into the left bearing, D2 indicates the diameter of a section of the main shaft where a reel is mounted, D3 indicates the diameter of a section of the main shaft fitted into a right bearing, and L2 indicates the length of the section of the main shaft fitted into the right bearing.
1, Table 1 Characteristics of probability statistics of random variables in the main shaft Variable Mean value Standard deviation Distribution type Di(mm) 710 21.3 Normal L1(mm) 315 9.45 Normal D2(mm) 800 23 Normal D3(mm) 710 21.3 Normal L2(mm) 315 9.45 Normal In this embodiment, by using the method for calculating a failure probability provided by the present invention, a failure probability in a strength failure mode is Pfi=0.003241, and a stiffness failure probability is Pf2=0.005173. n sample values of the random variables of the main shaft structure are randomly generated by using a random sampling method, and the n sample values are substituted into the explicit limit state equations combining the two failure modes, to obtain n response values through calculation. A correlation coefficient between a strength response vector and a stiffness response vector is calculated by using a command in MATLAB, and undetermined parameters of the Clayton copula function are estimated. The failure probabilities Pfi and Pf2 are substituted into the following equation:
.l+ Zniax( Pfl ZP.0) Pft EPfl - ElinaX(Pft ) In the equation, m indicates the number of failure modes of the hoist main shaft, P11 indicates the maximum failure probability in the failure modes of the hoist main shaft, Pfi indicates a failure probability of the ith failure mode, Pfij indicates a joint failure probability of the ith and jth failure mode, and pfs indicates a system failure probability related to a failure of the hoist main shaft.
A failure probability obtained in consideration of correlation between the strength failure and the stiffness failure of the main shaft structure is Pfs=0.008536.
A system failure probability calculated using a simulation method is Pfsm=0.008746.
To sum up, for a hoist main shaft of a kilometer-deep mine, this method provides a method for solving system reliability in consideration of correlation between a strength failure and a stiffness failure. First, a parametrical three-dimensional model of the main shaft is established according to physical dimensions of the main shaft.
Then, a sampling matrix for random variables of the main shaft is established according to probability types of the random variables, and strength and stiffness responses of the main shaft are solved using the sampling matrix with a finite element method. Afterwards, an explicit function defining a relationship between the responses and the matrix for the random variables is established using a neural network approach, and explicit performance functions in a strength failure mode and in a stiffness failure mode are separately established according to strength and stiffness design criteria; and then, probabilities of these two failures are calculated by means of the saddlepoint approximation method. Finally, a joint failure probability model combining the two failure modes is established using Clayton copula function, and system reliability in the case of a joint failure is solved using the bound reliability method.
The part not described in detail in the present invention belongs to technologies knows to researchers in this field.
Claims (6)
1. A reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes, characterized in that, comprising: first, a parametrical three-dimensional model of the main shaft is established according to physical dimensions of the main shaft; then, a sampling matrix for random variables of the main shaft is established according to probability types of the random variables, and strength and stiffness responses of the main shaft are solved using the sampling matrix with a finite element method; afterwards, an explicit function defining a relationship between the responses and the matrix for the random variables is established using a neural network approach, and explicit performance functions in a strength failure mode and in a stiffness failure mode are separately established according to strength and stiffness design criteria; and then, probabilities of these two failures are calculated by means of a saddlepoint approximation method; and finally, a joint failure probability model combining the two failure modes is established using a Clayton copula function, and system reliability in the case of a joint failure is solved using a bound reliability method.
2. The reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes according to claim 1, characterized in that, comprising specifically steps as follows:
step 1: determining mean values and variances of dimension parameters, material attribute parameters, and loads in different working conditions of the hoist main shaft of the kilometer-deep mine, and determining distribution types of these parameters;
step 2: establishing a three-dimensional parametrical model of the main shaft according to structure parameters of the hoist main shaft, and importing the three-dimensional parametrical model of the main shaft into a finite element software, to perform statics analysis;
step 3: establishing a random sampling matrix for the various basic parameters according to the mean values and variances of the basic parameters of the main shaft determined in step 1 by using a sampling method;
step 4: according to parameter values in each line of the random sampling matrix, repeatedly generating a new three-dimensional model of the main shaft and performing finite element analysis again, to obtain new stress-strain response samples;
step 5: fitting the random sampling matrix and the stress-strain values by using a neural network approach, to obtain a function relationship between a stress-strain response of the main shaft and a change in structural performance parameters;
step 6: separately establishing reliability performance functions in a strength failure mode and a stiffness failure mode according to strength and stiffness requirements on the hoist main shaft; calculating third and fourth order moments of the basic parameters according to the mean values and variances thereof; then, calculating mean values, variances, third order moments, and fourth order moments of the performance functions according to the established performance functions; and separately calculating a strength failure probability and a stiffness failure probability by means of the saddlepoint approximation method; and step 7: acquiring a correlation coefficient between the strength failure and the stiffness failure by means of a statistical method, establishing a joint failure distribution combining the strength failure and stiffness failure by using the Clayton copula function, and then calculating a system failure probability in the case of correlated failures by using the bound reliability method.
step 1: determining mean values and variances of dimension parameters, material attribute parameters, and loads in different working conditions of the hoist main shaft of the kilometer-deep mine, and determining distribution types of these parameters;
step 2: establishing a three-dimensional parametrical model of the main shaft according to structure parameters of the hoist main shaft, and importing the three-dimensional parametrical model of the main shaft into a finite element software, to perform statics analysis;
step 3: establishing a random sampling matrix for the various basic parameters according to the mean values and variances of the basic parameters of the main shaft determined in step 1 by using a sampling method;
step 4: according to parameter values in each line of the random sampling matrix, repeatedly generating a new three-dimensional model of the main shaft and performing finite element analysis again, to obtain new stress-strain response samples;
step 5: fitting the random sampling matrix and the stress-strain values by using a neural network approach, to obtain a function relationship between a stress-strain response of the main shaft and a change in structural performance parameters;
step 6: separately establishing reliability performance functions in a strength failure mode and a stiffness failure mode according to strength and stiffness requirements on the hoist main shaft; calculating third and fourth order moments of the basic parameters according to the mean values and variances thereof; then, calculating mean values, variances, third order moments, and fourth order moments of the performance functions according to the established performance functions; and separately calculating a strength failure probability and a stiffness failure probability by means of the saddlepoint approximation method; and step 7: acquiring a correlation coefficient between the strength failure and the stiffness failure by means of a statistical method, establishing a joint failure distribution combining the strength failure and stiffness failure by using the Clayton copula function, and then calculating a system failure probability in the case of correlated failures by using the bound reliability method.
3. The reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes according to claim 2, characterized in that, step 1 specifically comprises:
determining the mean values and variances of physical dimensions and material attributes of the hoist main shaft;
determining the working conditions of the hoist main shaft, and then determining mean values and variances of loads, such as a static load, dynamic load, bending moment and torque experienced by the main shaft in the different working conditions;
and determining the distribution types of the foregoing parameters.
determining the mean values and variances of physical dimensions and material attributes of the hoist main shaft;
determining the working conditions of the hoist main shaft, and then determining mean values and variances of loads, such as a static load, dynamic load, bending moment and torque experienced by the main shaft in the different working conditions;
and determining the distribution types of the foregoing parameters.
4. The reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes according to claim 2, characterized in that, step 2 specifically comprises:
by a parametrical modeling of the hoist main shaft, generating a command flow file of the modeling, exporting an established model of the main shaft, and saving the established model in a working directory;
by means of a finite element analysis of the hoist main shaft, generating a command flow file of the finite element analysis process, exporting a text file containing an analysis result, and saving the text file in the working directory; and establishing a finite element model of the main shaft according to material performance parameters of the main shaft, and imposing external loads such as the bending moment, torque, and maximum static load, wherein the physical parameters of the main shaft comprise diameters and lengths of sections of the main shaft, and diameters and lengths of reels; and the material performance parameters comprise a elastic modulus, Poisson's ratio, and density.
by a parametrical modeling of the hoist main shaft, generating a command flow file of the modeling, exporting an established model of the main shaft, and saving the established model in a working directory;
by means of a finite element analysis of the hoist main shaft, generating a command flow file of the finite element analysis process, exporting a text file containing an analysis result, and saving the text file in the working directory; and establishing a finite element model of the main shaft according to material performance parameters of the main shaft, and imposing external loads such as the bending moment, torque, and maximum static load, wherein the physical parameters of the main shaft comprise diameters and lengths of sections of the main shaft, and diameters and lengths of reels; and the material performance parameters comprise a elastic modulus, Poisson's ratio, and density.
5. The reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes according to claim 2, characterized in that, step 4 specifically comprises:
modifying values of variables in a command flow file of a modeling process in the set working directory according to the established random sampling matrix, and generating a new main shaft model;
analyzing the newly generated main shaft model by using a command flow of finite element analysis , to obtain a new stress-strain response value; and repeating the foregoing steps till a corresponding stress-strain response value is acquired for each set of random variable values in the matrix for the random variables.
modifying values of variables in a command flow file of a modeling process in the set working directory according to the established random sampling matrix, and generating a new main shaft model;
analyzing the newly generated main shaft model by using a command flow of finite element analysis , to obtain a new stress-strain response value; and repeating the foregoing steps till a corresponding stress-strain response value is acquired for each set of random variable values in the matrix for the random variables.
6. The reliability evaluation method for a hoist main shaft of a kilometer-deep mine considering multiple failure modes according to claim 2, characterized in that, step 7 specifically comprises:
performing random sampling according to distribution types of the random variables of the main shaft, and acquiring calculated values between the strength failure and the stiffness failure by using the reliability performance functions established in step 6;
calculating a rank correlation coefficient of the two failure modes by means of a statistical method, and calculating undetermined parameters of the Clayton copula function;
calculating a joint failure probability of the strength and stiffness failure by using the Clayton copula function; and by using a second-order narrow-bound theory, substituting the strength failure probability and the stiffness failure probability obtained in step 6, and the joint failure probability, to calculate a system failure probability of the hoist main shaft.
performing random sampling according to distribution types of the random variables of the main shaft, and acquiring calculated values between the strength failure and the stiffness failure by using the reliability performance functions established in step 6;
calculating a rank correlation coefficient of the two failure modes by means of a statistical method, and calculating undetermined parameters of the Clayton copula function;
calculating a joint failure probability of the strength and stiffness failure by using the Clayton copula function; and by using a second-order narrow-bound theory, substituting the strength failure probability and the stiffness failure probability obtained in step 6, and the joint failure probability, to calculate a system failure probability of the hoist main shaft.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710377138.7A CN107291989B (en) | 2017-05-25 | 2017-05-25 | Km deep-well main shaft of hoister multi-invalidation mode reliability estimation method |
| CN201710377138.7 | 2017-05-25 | ||
| PCT/CN2017/102000 WO2018214348A1 (en) | 2017-05-25 | 2017-09-18 | Reliability assessment method for main shaft of kilometer-deep well elevator under multiple failure modes |
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| CA3014415A1 true CA3014415A1 (en) | 2018-11-25 |
| CA3014415C CA3014415C (en) | 2020-12-01 |
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| CN (1) | CN107291989B (en) |
| AU (1) | AU2017396541B9 (en) |
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- 2017-05-25 CN CN201710377138.7A patent/CN107291989B/en active Active
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| CN112685825A (en) * | 2021-01-22 | 2021-04-20 | 西安航空职业技术学院 | Optimization method of stepwise equivalent plane method |
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| WO2018214348A1 (en) | 2018-11-29 |
| AU2017396541A1 (en) | 2018-12-13 |
| AU2017396541B9 (en) | 2019-09-26 |
| AU2017396541B2 (en) | 2019-05-23 |
| RU2682821C1 (en) | 2019-03-21 |
| CN107291989B (en) | 2018-09-14 |
| CN107291989A (en) | 2017-10-24 |
| CA3014415C (en) | 2020-12-01 |
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