CN112070413A - Reliability research method of traction power supply system based on small sample condition - Google Patents

Reliability research method of traction power supply system based on small sample condition Download PDF

Info

Publication number
CN112070413A
CN112070413A CN202010979983.3A CN202010979983A CN112070413A CN 112070413 A CN112070413 A CN 112070413A CN 202010979983 A CN202010979983 A CN 202010979983A CN 112070413 A CN112070413 A CN 112070413A
Authority
CN
China
Prior art keywords
power supply
reliability
supply system
traction power
traction
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010979983.3A
Other languages
Chinese (zh)
Other versions
CN112070413B (en
Inventor
张海刚
陈璇
刘飘
王步来
张文
解嘉懿
陈湘女
罗俊
赵德成
徐兵
储雷
童中祥
杨俊�
孙平飞
王燕锋
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shanghai Jiudao Information Technology Co ltd
Original Assignee
Shanghai Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shanghai Institute of Technology filed Critical Shanghai Institute of Technology
Priority to CN202010979983.3A priority Critical patent/CN112070413B/en
Publication of CN112070413A publication Critical patent/CN112070413A/en
Application granted granted Critical
Publication of CN112070413B publication Critical patent/CN112070413B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0639—Performance analysis of employees; Performance analysis of enterprise or organisation operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Energy or water supply

Landscapes

  • Business, Economics & Management (AREA)
  • Engineering & Computer Science (AREA)
  • Human Resources & Organizations (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Economics (AREA)
  • Strategic Management (AREA)
  • Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Development Economics (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Marketing (AREA)
  • General Health & Medical Sciences (AREA)
  • Tourism & Hospitality (AREA)
  • Educational Administration (AREA)
  • General Business, Economics & Management (AREA)
  • Biophysics (AREA)
  • Operations Research (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Biomedical Technology (AREA)
  • Game Theory and Decision Science (AREA)
  • Computational Linguistics (AREA)
  • Data Mining & Analysis (AREA)
  • Evolutionary Computation (AREA)
  • Quality & Reliability (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Public Health (AREA)
  • Water Supply & Treatment (AREA)
  • Primary Health Care (AREA)
  • Supply And Distribution Of Alternating Current (AREA)

Abstract

The invention discloses a reliability research method of a traction power supply system based on a small sample condition, which is used for virtually augmenting small sample data by applying a Bootstrap method and effectively solving the problem of poor fitting effect on Weibull distribution caused by small actual sample amount of related fault data in the prior art. Compared with the traditional SVM algorithm, the LSSVM algorithm simplifies the complexity of calculation and improves the convergence precision of the algorithm. And the particle swarm algorithm is combined, so that the method has the advantages of easiness in realization, high precision, quick convergence and the like. And optimizing LSSVM model parameters by applying a designed PSO-LSSVM algorithm, and selecting the optimal parameters of the LSSVM for configuration. And effectively predicting the traction power supply system model established by adopting a fault tree analysis method and a BDD algorithm. And the reliability and the average failure time of the traction power supply system equipment are obtained, and a reliable scientific basis is provided for the maintenance plan of the whole equipment of the traction power supply system.

Description

Reliability research method of traction power supply system based on small sample condition
Technical Field
The invention relates to the field of railway traction power supply, in particular to a reliability research method of a traction power supply system based on a small sample condition.
Background
The traction power supply system is a key part of a high-speed railway system, and the acceleration of the train puts higher requirements on the traction power supply system. The conventional railway traction power supply system integration scheme (including technical specifications) cannot meet the requirement of safe operation of the system, the reliable and safe operation of the traction power supply system is very important for a high-speed passenger special line, and the reliable and reliable operation of a train is directly influenced. The traction power supply system comprises a large number of contact networks, cables, transformers, circuit breakers, isolating switches, transformers, lightning arresters, secondary equipment and the like, but the highest failure rate is that the traction substation and the contact networks are two major systems, wherein equipment failures comprise multiple factors, such as equipment performance reasons, accidental factors, common cause failures and the like, which can cause equipment failures.
In the existing traction power supply fault analysis theory, a Weibull distribution model is generally used as a fault fitting model of traction power supply equipment, and reliability analysis is performed on a system on the basis. However, the weibull distribution is based on a model over a large sample, a large sample is needed as a basis for analysis, fault analysis data of train traction power supply is obtained, partial input variables are lost due to various reasons in an experiment, and the available 'sample size' of the fault data is small. To address the limitations in the prior art, improvements in the prior art and methods are needed. The Bootstrap method is applied to virtually augment the data of the 'small samples', so that the problem that the fitting effect on Weibull distribution is poor due to the fact that the actual sample amount of relevant fault data is small in the prior art is effectively solved. Compared with the traditional SVM algorithm, the LSSVM algorithm simplifies the complexity of calculation and improves the convergence precision of the algorithm. And the PSO particle swarm algorithm is combined, so that the method has the advantages of easiness in realization, high precision, quick convergence and the like.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a reliability research method of a traction power supply system based on a small sample condition, a Bootstrap method is applied to virtually augment the data of the small sample, and the problem of poor fitting effect on Weibull distribution caused by small actual sample amount of related fault data in the prior art is effectively solved. The PSO-LSSVM intelligent fitting algorithm optimizes LSSVM model parameters by applying a particle swarm algorithm, and selects the optimal parameters of the LSSVM for configuration. And effectively predicting the traction power supply system model established by adopting a fault tree analysis method and a BDD algorithm. And the reliability and the average failure time of the traction power supply system equipment are obtained, and a reliable scientific basis is provided for the maintenance plan of the whole equipment of the traction power supply system.
In order to achieve the above purpose, the technical solution for solving the technical problem is as follows:
a reliability research method of a traction power supply system based on a small sample condition comprises the following steps:
step 1: according to the fault type and fault rate actual conditions of main equipment of a traction power supply system, under the condition that fault data is a 'small sample', a Bootstrap method is adopted, original sample data is resampled by a computer to generate a regeneration sample, and the fault rate data of the total sample is used as input;
step 2: establishing a fused particle swarm-least square support vector machine regression algorithm, performing reliability fitting on each device of the traction power supply system, and fitting to obtain optimal estimation parameters of the characteristic service life alpha and the shape parameter beta based on Weibull distribution;
and step 3: completion K, W2Detecting the goodness of fit, and performing reliability modeling on each device of the traction power supply system according to the obtained optimal parameters;
and 4, step 4: the traction power supply system is subdivided into two subsystems according to structure and function: a traction substation subsystem and a contact network subsystem;
and 5: on the basis of analyzing the reliability of a subsystem or equipment, a fault tree analysis method is applied to respectively establish a fault tree model of a traction substation subsystem and a fault tree model of a contact network subsystem, and further an overall reliability model of a traction power supply system is established;
step 6: and (3) combining the Weibull distribution model of each device of the traction power supply system, carrying out reliability analysis on the fault tree models of the two subsystems, finally summarizing to obtain an integral reliability model of the traction power supply system, and calculating the integral reliability and the average service life of the system.
Further, in step 1, the main devices of the traction power supply system include a traction transformer, an isolating switch, a current transformer, a contact wire, a catenary cable and an insulator, wherein the frequency of the contact wire having a fault in actual operation is highest, and for the fault rate of the contact wire and related devices, a common weibull distribution method is adopted to estimate the reliability parameters of the traction power supply device on the basis of collecting a sufficient number of device failure data, and in actual operation, the number of fault data is small, or the number of failure data is large, and the collection of a sufficient number of sample quantities cannot be met, so that a boottrap method is introduced to perform virtual augmentation on small sample data, thereby meeting the analysis requirement:
in step 1, the method specifically comprises the following steps:
step 11: generating random numbers S uniformly distributed among [0, 1] by using a computer;
step 12: let xi ═ S, i ═ floor (xi) +1, where floor (xi) denotes xi rounded down;
step 13: let x*＝xi+(ξ-i+1)(xi+1-xi) Where x*Namely the regeneration sample data;
step 14: repeating the above steps n times to obtain a set of resampled samples x*＝(x*1,x*2,…,x*n)。
Further, in step 2, the method specifically comprises the following steps:
step 21: carrying out normalization preprocessing on the faults of the total fault sample data, wherein the formula is as follows:
Figure BDA0002687180370000031
step 22: initializing PSO parameters and LSSVM model key parameters and xi, and training the model;
step 23: in order to evaluate the quality of PSO optimization LSSVM model parameters, a K-fold cross validation mode is adopted, the mean value of the root mean square errors of K times is used as an evaluation reference, and the calculation formula is as follows:
Figure BDA0002687180370000032
wherein F is the mean value of the root mean square error of the K times, y is the true value,
Figure BDA0002687180370000033
is a predicted value, n is the prediction times, k is the iteration algebra;
step 24: judging whether the condition of terminating iteration is met, if not, returning to the step 22 to continue iteration;
step 25: and obtaining optimal values of key parameters and xi of the LSSVM after iteration is finished, substituting the optimal parameters into the LSSVM for retraining, and obtaining optimal fitting parameters based on Weibull.
Further, in step 22, the PSO-LSSVM is initialized as follows:
setting the learning factor C1 to 1.6 and the learning factor C2 to 1.8; the population scale M is 30; the population iteration algebra is 300; the inertial weight ω is 0.8, and the optimization interval is as follows: not less than 0.01 and not more than 10, not less than 1 and not more than xi and not more than 1000.
Further, in step 24:
the judgment basis is that when the mean value F of the root mean square error of the sample is minimum, the corresponding xi value is the optimal parameter.
Further, the LSSVM is an improvement of the support vector machine, which converts inequality constraints into equality constraints on the basis of the support vector machine, and simultaneously, the least square linear system error sum of squares is used as a loss function, thereby simplifying the quadratic programming problem into a solution problem of a linear equation set, simplifying the complexity of calculation, improving the convergence accuracy of the algorithm, and the SVR algorithm in step 25 specifically comprises:
the optimization problem of the LSSVM algorithm can be expressed by equation (3):
Figure BDA0002687180370000041
the above expression is satisfied under the following formula:
Figure BDA0002687180370000042
wherein x isiFor input samples, xi∈Rn；yiAs the output type, yi∈RnN is the number of samples; ω is a weight vector, eiIs an error variable, and eta is a deviation value;
the Lagrange function is introduced, and the optimization problem can be converted into a solution square multiplication set problem by utilizing the KKT condition for simplification:
Figure BDA0002687180370000043
where ξ is a normalization parameter, In＝[1，1，...，1]T,
Figure BDA0002687180370000044
a＝[a1，a2，...，an]T，y＝[y1，y2，...，yn]T
Figure BDA0002687180370000045
Wherein x is an input variable, ai、
Figure BDA0002687180370000046
Is a Lagrangian multiplier, ai、
Figure BDA0002687180370000047
Eta is the offset, and eta is the offset,
Figure BDA0002687180370000048
is a mapping function;
to avoid high-dimensional inner product operation, a kernel function k (x) is introducediX) substitution
Figure BDA0002687180370000051
Equation (6) is updated as:
Figure BDA0002687180370000052
selecting a Gaussian radial basis kernel function, wherein the expression is as follows:
k(xi，x)＝exp[-γ||xi-x||2],γ＞0 (8)
where γ is 1/σ 2, σ is a width parameter of the radial basis function, affects the range of influence of the sample selected as the support vector, | | xi-x | | is the euclidean distance between the sample point and any point in space.
Further, in step 5, the method specifically comprises the following steps:
step 51: carrying out quantitative analysis on the fault tree by adopting a BDD algorithm;
step 52: the BDD algorithm can be used for analyzing and modeling the subsystem of the traction substation:
the minimum cut set for powering up (G, M) up and down on the left side is:
{(E1,E2),(E4,E6),(E1,E3,E6),(E2,E3,E4)}
the minimum cut set for powering up and down (H, N) to the right is:
{(E1,E2),(E5,E7),(E1,E3,E7),(E2,E3,E5)}；
step 53: the fault of the power supply subsystem of the traction substation is represented as follows:
FTS＝F GM +F HN (9)
wherein, the subscript _ indicates the abnormal event corresponding to the normal event, i.e. the fault state;
step 54: the minimum cut set corresponding to the fault model of the traction substation is as follows:
{(E1,E2),(E4,E6),(E5,E7),(E1,E3,E6),(E2,E3,E4),(E1,E3,E7),(E2,E3,E5)}；
step 55: the failure rate of the traction substation is as follows:
λTS＝λE1λE2+λE4λE6+λE5λE7+λE1λE3λE6+λE2λE3λE4+λE1λE3λE7+λE2λE3λE5 (10)。
further, in step 6, the method specifically includes the following steps:
step 61: the contact net mainly comprises a contact line, a catenary, an insulator, a central anchor section joint and a compensator, so that the reliability of a contact net subsystem can be expressed as follows:
Rc(t)＝∏Ri(t)(i＝1,2,3,4,5) (11)
wherein R isc(t) contact network subsystem reliability, Ri(t) reliability of main parts of the contact network subsystem;
step 62: from step 55, the failure rate of the traction substation subsystem is obtained, and then from the weibull distribution, the reliability r (t) and the failure rate λ (t) of the equipment are:
R(t)＝exp[-(t/α)β] (12)
Figure BDA0002687180370000061
wherein alpha is the characteristic life of the Weibull distribution, and beta is a shape parameter;
and step 63: reliability R of traction substation subsystemT(t) can be derived from the following formula:
Figure BDA0002687180370000062
step 64: because the traction substation is in series connection with the contact network, the reliability R of the traction power supply systemTS(t) can be expressed as:
RTS(t)＝RT(t)·Rc(t) (15)
wherein R isT(t) reliability of traction substation subsystem, Rc(t) contact network subsystem reliability;
step 65: the non-intermittency of railway transportation requires that the power supply system has only 2 states: and (3) normal operation or complete failure, wherein the average failure time of the power supply system is the average service life MTTF:
Figure BDA0002687180370000063
due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects:
1. the invention discloses a reliability research method of a traction power supply system, which solves the problem that the quantity of actually available samples is small due to the loss of partial input variables caused by various reasons in the collection process of data samples. A Bootstrap self-service sampling method is applied to 'small sample' fault data, and samples are virtually augmented, so that the condition of enough data volume can be met. Therefore, the fitting effect is better, and the reliability of the equipment can be more accurately predicted;
2. the method integrates the LSSVM-PSO (particle swarm optimization), selects the optimal parameters by utilizing the characteristics of easy realization, high precision, fast convergence and the like, and solves the problem of poor fitting effect caused by inappropriate selection of the key parameters of the LSSVM algorithm;
3. the traction power supply system adopts a traction power supply system model established by a fault tree analysis method and a BDD algorithm, so that the reliability and the average failure time of equipment of the traction power supply system are effectively predicted, and a reliable scientific basis is provided for the maintenance plan of the whole equipment of the traction power supply system;
4. the method has the advantages of low cost, quick fitting intelligent algorithm, high fitting precision, easy realization and the like.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:
FIG. 1 is an overall flow chart of a method for researching the reliability of a traction power supply system based on a small sample condition according to the invention;
FIG. 2 is a diagram of the steps performed by the traction power supply system based on a small sample condition according to the present invention;
FIG. 3 is a detailed flowchart of step 1 in the method for researching the reliability of the traction power supply system based on the small sample condition according to the present invention;
FIG. 4 is a particle swarm algorithm (PSO) schematic diagram involved in the reliability research method of the traction power supply system based on the small sample condition;
FIG. 5 is a block diagram of a PSO-LSSVM (particle swarm least squares support vector machine) algorithm fitting process in the reliability research method of the traction power supply system based on the small sample condition;
FIG. 6 is a detailed flowchart of step 2 in the method for researching the reliability of the traction power supply system based on the small sample condition according to the present invention;
FIG. 7 is a simplified model of a fault tree analysis-based fault in a traction substation in the reliability research method of a traction power supply system based on a small sample condition according to the present invention;
fig. 8 is a specific flowchart of step 5 in the reliability research method for the traction power supply system based on the small sample condition according to the present invention.
Detailed Description
While the embodiments of the present invention will be described and illustrated in detail with reference to the accompanying drawings, it is to be understood that the invention is not limited to the specific embodiments disclosed, but is intended to cover various modifications, equivalents, and alternatives falling within the scope of the invention as defined by the appended claims.
Referring to fig. 1 and 4, the technical scheme provided by the invention is to fit a traction power supply system fault model based on Weibull distribution by adopting a PSO-LSSVM algorithm. The PSO-LSSVM algorithm comprises the advantages of easy realization, high precision, fast convergence and the like of the particle swarm algorithm, and the optimal parameters of the LSSVM are selected for configuration. Under the condition that the sample size of the fault data is small, the small sample of the fault data can be virtually augmented. Under the condition of obtaining a sufficient amount of sample analysis, the PSO-LSSVM algorithm performs better fitting on a fault model. Therefore, reliability analysis is carried out on the traction power supply system, average life estimation is obtained, and reference is provided for later-stage traction power supply system equipment maintenance planning.
Referring to fig. 2, the present embodiment discloses a method for researching reliability of a traction power supply system based on a small sample condition, including the following steps:
step 1: according to the fault type and fault rate actual conditions of main equipment of a traction power supply system, under the condition that fault data is a 'small sample', a Bootstrap method is adopted, original sample data is resampled by a computer to generate a regeneration sample, and the fault rate data of the total sample is used as input;
step 2: establishing a fused particle swarm-least square support vector machine regression algorithm, performing reliability fitting on each device of the traction power supply system, and fitting to obtain optimal estimation parameters of the characteristic service life alpha and the shape parameter beta based on Weibull distribution;
and step 3: completion K, W2Detecting the goodness of fit, and performing reliability modeling on each device of the traction power supply system according to the obtained optimal parameters;
and 4, step 4: the traction power supply system is subdivided into two subsystems according to structure and function: a traction substation subsystem and a contact network subsystem;
and 5: on the basis of analyzing the reliability of a subsystem or equipment, a fault tree analysis method is applied to respectively establish a fault tree model (as shown in figure 7) of a traction substation subsystem and a contact network subsystem, and further an overall reliability model of a traction power supply system is established;
step 6: and (3) combining the Weibull distribution model of each device of the traction power supply system, carrying out reliability analysis on the fault tree models of the two subsystems, finally summarizing to obtain an integral reliability model of the traction power supply system, and calculating the integral reliability and the average service life of the system.
Further, in step 1, the main devices of the traction power supply system include a traction transformer, a disconnector, a current transformer, a contact wire, a catenary cable, and an insulator, where a frequency of a fault occurring in the contact wire during actual operation is highest, and for a fault rate of the contact wire and related devices, on the basis of collecting a sufficient number of device failure data, a common weibull distribution method is used to estimate reliability parameters of the traction power supply device, and a weibull distribution model is generally used as a fault fitting model of the traction power supply device, and reliability analysis is performed on the system on the basis of the failure data. As fault analysis data of train traction power supply, on-site data collection and arrangement are difficult due to long service life and limited conditions of traction power supply equipment, and in order to guarantee system reliability, a plurality of equipment are replaced or maintained in advance before reaching the service life, statistical accuracy is difficult to guarantee, unreliable data exist, and available data are few. Therefore, a Bootstrap method is introduced to virtually augment small sample data so as to meet the analysis requirement, the method can accept a small sample with the sample volume n being more than or equal to 10 as input, and can well complete the virtual augmentation of the sample.
Referring to fig. 3, in step 1, the method specifically includes the following steps:
step 11: generating random numbers S uniformly distributed among [0, 1] by using a computer;
step 12: let xi ═ S, i ═ floor (xi) +1, where floor (xi) denotes xi rounded down;
step 13: let x*＝xi+(ξ-i+1)(xi+1-xi) Where x*Namely the regeneration sample data;
step 14: repeating the above steps n times to obtain a set of resampled samples x*＝(x*1,x*2,…,x*n)。
With further reference to fig. 5 and 6, in step 2, the following steps are specifically included:
step 21: carrying out normalization preprocessing on the faults of the total fault sample data, wherein the formula is as follows:
Figure BDA0002687180370000091
step 22: initializing PSO parameters and LSSVM model key parameters and xi, and training the model;
step 23: in order to evaluate the quality of PSO optimization LSSVM model parameters, a K-fold cross validation mode is adopted, the mean value of the root mean square errors of K times is used as an evaluation reference, and the calculation formula is as follows:
Figure BDA0002687180370000101
wherein F is the mean value of the root mean square error of the K times, y is the true value,
Figure BDA0002687180370000102
is a predicted value, n is the prediction times, k is the iteration algebra;
step 24: judging whether the condition of terminating iteration is met, if not, returning to the step 22 to continue iteration;
step 25: and obtaining optimal values of key parameters and xi of the LSSVM after iteration is finished, substituting the optimal parameters into the LSSVM for retraining, and obtaining optimal fitting parameters based on Weibull.
In step 21, in some cases, it is difficult to obtain "large enough" large sample experimental data:
(1) due to the fact that the service life of the traction power supply equipment is long and the conditions are limited, field data collection and arrangement work is difficult, replacement or maintenance work is carried out in advance when the service life of a plurality of equipment is short of the reliability of the system, and the statistical accuracy is difficult to guarantee.
(2) The electrified railway has complex geographical conditions and different transportation load conditions, particularly the traction contact network system has the defects of high cost and long time by simulating actual data through a test environment, and meanwhile, whether the test data is accurate or not is difficult to ensure.
Further, in step 22, the PSO-LSSVM is initialized as follows:
setting the learning factor C1 to 1.6 and the learning factor C2 to 1.8; the population scale M is 30; the population iteration algebra is 300; the inertial weight ω is 0.8, and the optimization interval is as follows: not less than 0.01 and not more than 10, not less than 1 and not more than xi and not more than 1000.
Further, in step 24:
the judgment basis is that when the mean value F of the root mean square error of the sample is minimum, the corresponding xi value is the optimal parameter.
Further, the LSSVM is an improvement of the support vector machine, which converts inequality constraints into equality constraints on the basis of the support vector machine, and simultaneously, the least square linear system error sum of squares is used as a loss function, thereby simplifying the quadratic programming problem into a solution problem of a linear equation set, simplifying the complexity of calculation, improving the convergence accuracy of the algorithm, and the SVR algorithm in step 25 specifically comprises:
the optimization problem of the LSSVM algorithm can be expressed by equation (3):
Figure BDA0002687180370000103
the above expression is satisfied under the following formula:
Figure BDA0002687180370000111
wherein x isiFor input samples, xi∈Rn；yiAs the output type, yi∈RnN is the number of samples; ω is a weight vector, eiIs an error variable, and eta is a deviation value;
the Lagrange function is introduced, and the optimization problem can be converted into a solution square multiplication set problem by utilizing the KKT condition for simplification:
Figure BDA0002687180370000112
where ξ is a normalization parameter, In＝[1，1，...，1]T,
Figure BDA0002687180370000113
a＝[a1，a2，...，an]T，y＝[y1，y2，...，yn]T
Figure BDA0002687180370000114
Wherein x is an input variable, ai、
Figure BDA0002687180370000115
Is a Lagrangian multiplier, ai
Figure BDA0002687180370000116
Eta is the offset, and eta is the offset,
Figure BDA0002687180370000117
is a mapping function;
to avoid high-dimensional inner product operation, a kernel function k (x) is introducediX) substitution
Figure BDA0002687180370000118
Equation (6) is updated as:
Figure BDA0002687180370000119
selecting a Gaussian radial basis kernel function, wherein the expression is as follows:
k(xi，x)＝exp[-γ||xi-x||2],γ＞0 (8)
where γ is 1/σ 2, σ is a width parameter of the radial basis function, affects the range of influence of the sample selected as the support vector, | | xi-x | | is the euclidean distance between the sample point and any point in space.
With further reference to fig. 8, in step 5, the method specifically includes the following steps:
step 51: carrying out quantitative analysis on the fault tree by adopting a BDD algorithm;
step 52: the BDD algorithm can be used for analyzing and modeling the subsystem of the traction substation:
the minimum cut set for powering up (G, M) up and down on the left side is:
{(E1,E2),(E4,E6),(E1,E3,E6),(E2,E3,E4)}
the minimum cut set for powering up and down (H, N) to the right is:
{(E1,E2),(E5,E7),(E1,E3,E7),(E2,E3,E5)}；
step 53: the fault of the power supply subsystem of the traction substation is represented as follows:
FTS＝F GM +F HN (9)
wherein, the subscript _ indicates the abnormal event corresponding to the normal event, i.e. the fault state;
step 54: the minimum cut set corresponding to the fault model of the traction substation is as follows:
{(E1,E2),(E4,E6),(E5,E7),(E1,E3,E6),(E2,E3,E4),(E1,E3,E7),(E2,E3,E5)}；
step 55: the failure rate of the traction substation is as follows:
λTS＝λE1λE2+λE4λE6+λE5λE7+λE1λE3λE6+λE2λE3λE4+λE1λE3λE7+λE2λE3λE5 (10)。
further, in step 6, the method specifically includes the following steps:
step 61: the contact net mainly comprises a contact line, a catenary, an insulator, a central anchor section joint and a compensator, so that the reliability of a contact net subsystem can be expressed as follows:
Rc(t)＝∏Ri(t)(i＝1,2,3,4,5) (11)
wherein R isc(t) contact network subsystem reliability, Ri(t) reliability of main parts of the contact network subsystem;
step 62: from step 55, the failure rate of the traction substation subsystem is obtained, and then from the weibull distribution, the reliability r (t) and the failure rate λ (t) of the equipment are:
R(t)＝exp[-(t/α)β] (12)
Figure BDA0002687180370000121
wherein alpha is the characteristic life of the Weibull distribution, and beta is a shape parameter;
and step 63: reliability R of traction substation subsystemT(t) can be derived from the following formula:
Figure BDA0002687180370000131
step 64: because the traction substation is in series connection with the contact network, the reliability R of the traction power supply systemTS(t) can be expressed as:
RTS(t)＝RT(t)·Rc(t) (15)
wherein R isT(t) reliability of traction substation subsystem, Rc(t) contact network subsystem reliability;
step 65: the non-intermittency of railway transportation requires that the power supply system has only 2 states: and (3) normal operation or complete failure, wherein the average failure time of the power supply system is the average service life MTTF:
Figure BDA0002687180370000132
the above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A reliability research method of a traction power supply system based on a small sample condition is characterized by comprising the following steps:
step 1: according to the fault type and fault rate actual conditions of main equipment of a traction power supply system, under the condition that fault data is a 'small sample', a Bootstrap method is adopted, original sample data is resampled by a computer to generate a regeneration sample, and the fault rate data of the total sample is used as input;
step 2: establishing a fused particle swarm-least square support vector machine regression algorithm, performing reliability fitting on each device of the traction power supply system, and fitting to obtain optimal estimation parameters of the characteristic service life alpha and the shape parameter beta based on Weibull distribution;
and step 3: completion K, W2Detecting the goodness of fit, and performing reliability modeling on each device of the traction power supply system according to the obtained optimal parameters;
and 4, step 4: the traction power supply system is subdivided into two subsystems according to structure and function: a traction substation subsystem and a contact network subsystem;
and 5: on the basis of analyzing the reliability of a subsystem or equipment, a fault tree analysis method is applied to respectively establish a fault tree model of a traction substation subsystem and a fault tree model of a contact network subsystem, and further an overall reliability model of a traction power supply system is established;
step 6: and (3) combining the Weibull distribution model of each device of the traction power supply system, carrying out reliability analysis on the fault tree models of the two subsystems, finally summarizing to obtain an integral reliability model of the traction power supply system, and calculating the integral reliability and the average service life of the system.
2. The method for researching the reliability of the traction power supply system based on the small sample condition as claimed in claim 1, wherein in step 1, the main devices of the traction power supply system include a traction transformer, a disconnector, a current transformer, a contact wire, a catenary and an insulator, wherein the frequency of the contact wire having a fault in actual operation is the highest, and for the fault rate of the contact wire and the related devices, a common weibull distribution method is adopted to estimate the reliability parameters of the traction power supply device on the basis of collecting a sufficient amount of device failure data, and in actual operation, the failure data is less or more, and the acquisition of a sufficient amount of samples cannot be satisfied, so that a boottrap method is introduced to virtually augment the small sample data, thereby satisfying the analysis requirement:
in step 1, the method specifically comprises the following steps:
step 11: generating random numbers S uniformly distributed among [0, 1] by using a computer;
step 12: let xi ═ S, i ═ floor (xi) +1, where floor (xi) denotes xi rounded down;
step 13: let x*＝xi+(ξ-i+1)(xi+1-xi) Where x*Namely the regeneration sample data;
step 14: repeating the above steps n times to obtain a set of resampled samples x*＝(x*1,x*2,…,x*n)。
3. The method for researching the reliability of the traction power supply system based on the small sample condition as claimed in claim 1, wherein in the step 2, the method specifically comprises the following steps:
step 21: carrying out normalization preprocessing on the faults of the total fault sample data, wherein the formula is as follows:
Figure FDA0002687180360000021
step 22: initializing PSO parameters and LSSVM model key parameters and xi, and training the model;
step 23: in order to evaluate the quality of PSO optimization LSSVM model parameters, a K-fold cross validation mode is adopted, the mean value of the root mean square errors of K times is used as an evaluation reference, and the calculation formula is as follows:
Figure FDA0002687180360000022
wherein F is the mean value of the root mean square error of the K times, y is the true value,
Figure FDA0002687180360000023
is a predicted value, n is the prediction times, k is the iteration algebra;
step 24: judging whether the condition of terminating iteration is met, if not, returning to the step 22 to continue iteration;
step 25: and obtaining optimal values of key parameters and xi of the LSSVM after iteration is finished, substituting the optimal parameters into the LSSVM for retraining, and obtaining optimal fitting parameters based on Weibull.
4. The method for researching the reliability of the traction power supply system based on the small sample condition as claimed in claim 3, wherein in step 22, the PSO-LSSVM is initialized as follows:
setting the learning factor C1 to 1.6 and the learning factor C2 to 1.8; the population scale M is 30; the population iteration algebra is 300; the inertial weight ω is 0.8, and the optimization interval is as follows: not less than 0.01 and not more than 10, not less than 1 and not more than xi and not more than 1000.
5. The method for researching the reliability of the traction power supply system under the condition of the small sample according to claim 3, wherein in the step 24:
the judgment basis is that when the mean value F of the root mean square error of the sample is minimum, the corresponding xi value is the optimal parameter.
6. The method for researching the reliability of the traction power supply system based on the small sample condition as claimed in claim 3, wherein the LSSVM is an improvement of a support vector machine, and converts inequality constraints into equality constraints on the basis of the support vector machine, and simultaneously adopts least square linear system error sum of squares as a loss function, thereby simplifying a quadratic programming problem into a solving problem of a linear equation set, simplifying the complexity of calculation, and improving the convergence accuracy of the algorithm, wherein the SVR algorithm in step 25 specifically comprises:
the optimization problem of the LSSVM algorithm can be expressed by equation (3):
Figure FDA0002687180360000031
the above expression is satisfied under the following formula:
Figure FDA0002687180360000032
wherein x isiFor input samples, xi∈Rn；yiAs the output type, yi∈RnN is the number of samples; ω is a weight vector, eiIs an error variable, and eta is a deviation value;
the Lagrange function is introduced, and the optimization problem can be converted into a solution square multiplication set problem by utilizing the KKT condition for simplification:
Figure FDA0002687180360000033
where ξ is a normalization parameter, In＝[1，1，...，1]T,
Figure FDA0002687180360000034
a＝[a1，a2，...，an]T，y＝[y1，y2，...，yn]T
Figure FDA0002687180360000035
Wherein x is an input variable, ai、
Figure FDA0002687180360000036
Is a Lagrangian multiplier, ai、
Figure FDA0002687180360000037
Eta is the offset, and eta is the offset,
Figure FDA0002687180360000038
is a mapping function;
to avoid high-dimensional inner product operation, a kernel function k (x) is introducediX) substitution
Figure FDA0002687180360000039
Equation (6) is updated as:
Figure FDA0002687180360000041
selecting a Gaussian radial basis kernel function, wherein the expression is as follows:
k(xi，x)＝exp[-γ||xi-x||2],γ＞0 (8)
where γ is 1/σ 2, σ is a width parameter of the radial basis function, affects the range of influence of the sample selected as the support vector, | | xi-x | | is the euclidean distance between the sample point and any point in space.
7. The method for researching the reliability of the traction power supply system based on the small sample condition as claimed in claim 1, wherein in step 5, the method specifically comprises the following steps:
step 51: carrying out quantitative analysis on the fault tree by adopting a BDD algorithm;
step 52: the BDD algorithm can be used for analyzing and modeling the subsystem of the traction substation:
the minimum cut set for powering up (G, M) up and down on the left side is:
{(E1,E2),(E4,E6),(E1,E3,E6),(E2,E3,E4)}
the minimum cut set for powering up and down (H, N) to the right is:
{(E1,E2),(E5,E7),(E1,E3,E7),(E2,E3,E5)}；
step 53: the fault of the power supply subsystem of the traction substation is represented as follows:
FTS＝F GM +F HN (9)
wherein, the subscript _ indicates the abnormal event corresponding to the normal event, i.e. the fault state;
step 54: the minimum cut set corresponding to the fault model of the traction substation is as follows:
{(E1,E2),(E4,E6),(E5,E7),(E1,E3,E6),(E2,E3,E4),(E1,E3,E7),(E2,E3,E5)}；
step 55: the failure rate of the traction substation is as follows:
λTS＝λE1λE2+λE4λE6+λE5λE7+λE1λE3λE6+λE2λE3λE4+λE1λE3λE7+λE2λE3λE5 (10)。
8. the method for researching the reliability of the traction power supply system based on the small sample condition as claimed in claim 1, wherein in step 6, the method specifically comprises the following steps:
step 61: the contact net mainly comprises a contact line, a catenary, an insulator, a central anchor section joint and a compensator, so that the reliability of a contact net subsystem can be expressed as follows:
Rc(t)＝∏Ri(t)(i＝1,2,3,4,5) (11)
wherein R isc(t) contact network subsystem reliability, Ri(t) reliability of main parts of the contact network subsystem;
step 62: from step 55, the failure rate of the traction substation subsystem is obtained, and then from the weibull distribution, the reliability r (t) and the failure rate λ (t) of the equipment are:
R(t)＝exp[-(t/α)β] (12)
Figure FDA0002687180360000051
wherein alpha is the characteristic life of the Weibull distribution, and beta is a shape parameter;
and step 63: reliability R of traction substation subsystemT(t) can be derived from the following formula:
Figure FDA0002687180360000052
step 64: because the traction substation is in series connection with the contact network, the reliability R of the traction power supply systemTS(t) can be expressed as:
RTS(t)＝RT(t)·Rc(t) (15)
wherein R isT(t) reliability of traction substation subsystem, Rc(t) contact network subsystem reliability;
step 65: the non-intermittency of railway transportation requires that the power supply system has only 2 states: and (3) normal operation or complete failure, wherein the average failure time of the power supply system is the average service life MTTF:
Figure FDA0002687180360000053
CN202010979983.3A 2020-09-17 2020-09-17 Reliability research method of traction power supply system based on small sample condition Active CN112070413B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010979983.3A CN112070413B (en) 2020-09-17 2020-09-17 Reliability research method of traction power supply system based on small sample condition

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010979983.3A CN112070413B (en) 2020-09-17 2020-09-17 Reliability research method of traction power supply system based on small sample condition

Publications (2)

Publication Number Publication Date
CN112070413A true CN112070413A (en) 2020-12-11
CN112070413B CN112070413B (en) 2023-10-31

Family

ID=73682361

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010979983.3A Active CN112070413B (en) 2020-09-17 2020-09-17 Reliability research method of traction power supply system based on small sample condition

Country Status (1)

Country Link
CN (1) CN112070413B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113343433A (en) * 2021-05-19 2021-09-03 暨南大学 KKT condition and differential evolution algorithm-based first-order reliability analysis method
CN113885511A (en) * 2021-10-22 2022-01-04 温州大学乐清工业研究院 Track optimization method of breaker flexible assembly robot
CN115983005A (en) * 2022-12-30 2023-04-18 哈尔滨工业大学 Electric connector reliability prediction method based on failure physics and quality consistency
CN118245710A (en) * 2024-05-20 2024-06-25 天津华凯电气有限公司 Optimization method for state estimation of energy management and control system

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103971024A (en) * 2014-05-26 2014-08-06 华北电力大学（保定） Method for evaluating reliability of relaying protection systems under small sample failure data
WO2016029590A1 (en) * 2014-08-28 2016-03-03 北京交通大学 Fault prediction and condition-based maintenance method for urban rail train bogie
CN110647136A (en) * 2019-09-29 2020-01-03 华东交通大学 Composite fault detection and separation method for traction motor driving system
CN110930072A (en) * 2019-12-12 2020-03-27 湖南铁路科技职业技术学院 Reliability research method of traction power supply system
CN111127242A (en) * 2018-10-31 2020-05-08 国网河北省电力有限公司 Power system reliability dynamic real-time assessment method based on small sample data

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103971024A (en) * 2014-05-26 2014-08-06 华北电力大学（保定） Method for evaluating reliability of relaying protection systems under small sample failure data
WO2016029590A1 (en) * 2014-08-28 2016-03-03 北京交通大学 Fault prediction and condition-based maintenance method for urban rail train bogie
CN111127242A (en) * 2018-10-31 2020-05-08 国网河北省电力有限公司 Power system reliability dynamic real-time assessment method based on small sample data
CN110647136A (en) * 2019-09-29 2020-01-03 华东交通大学 Composite fault detection and separation method for traction motor driving system
CN110930072A (en) * 2019-12-12 2020-03-27 湖南铁路科技职业技术学院 Reliability research method of traction power supply system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
张文仁;: "高速铁路牵引供电系统谐波谐振抑制方案研究", 北京交通大学学报, no. 05, pages 110 - 117 *
赵峰;张庆平;王思华: "牵引供电系统可靠性预测及建模方法研究", 铁道科学与工程学报, vol. 12, no. 3, pages 678 - 684 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113343433A (en) * 2021-05-19 2021-09-03 暨南大学 KKT condition and differential evolution algorithm-based first-order reliability analysis method
CN113343433B (en) * 2021-05-19 2022-08-09 暨南大学 KKT condition and differential evolution algorithm-based first-order reliability analysis method
CN113885511A (en) * 2021-10-22 2022-01-04 温州大学乐清工业研究院 Track optimization method of breaker flexible assembly robot
CN113885511B (en) * 2021-10-22 2023-12-12 温州大学乐清工业研究院 Track optimization method of flexible assembly robot of circuit breaker
CN115983005A (en) * 2022-12-30 2023-04-18 哈尔滨工业大学 Electric connector reliability prediction method based on failure physics and quality consistency
CN118245710A (en) * 2024-05-20 2024-06-25 天津华凯电气有限公司 Optimization method for state estimation of energy management and control system

Also Published As

Publication number Publication date
CN112070413B (en) 2023-10-31

Similar Documents

Publication Publication Date Title
CN112070413B (en) Reliability research method of traction power supply system based on small sample condition
CN107609725B (en) Power transmission network risk assessment method considering transformer substation influence
CN103245881B (en) Power distribution network fault analyzing method and device based on tidal current distribution characteristics
CN104573906B (en) System and method for analyzing oscillation stability in power transmission system
CN105976257A (en) Power grid vulnerability evaluation method based on membership function fuzzy comprehensive evaluation method
CN109034461A (en) A kind of voltage dip Stochastic prediction method based on actual electric network monitoring information
CN113239132B (en) Online out-of-tolerance identification method for voltage transformer
CN112069727B (en) Intelligent transient stability evaluation system and method with high reliability for power system
CN102611102A (en) Power system partition modeling method based on actual measurement by aid of PMU (phasor measurement units)
Qiao et al. A novel bias compensation recursive least square‐multiple weighted dual extended Kalman filtering method for accurate state‐of‐charge and state‐of‐health co‐estimation of lithium‐ion batteries
CN110826228B (en) Regional power grid operation quality limit evaluation method
CN112288303A (en) Method and device for determining line loss rate
CN115688574A (en) Transient stability online evaluation method and system for power system
CN114997566A (en) Power grid blocking risk assessment method and system considering node connectivity loss
CN110412417B (en) Micro-grid data fault diagnosis method based on intelligent power monitoring instrument
CN108596450B (en) Power grid risk early warning method and system
CN107146166B (en) Distribution network planning auxiliary system
CN117767275A (en) Method and system for monitoring voltage support strength in real time, storage medium and electronic equipment
CN112001073B (en) Reliability analysis and research method for traction power supply system
CN105095659A (en) Method for province and region coordinative distributed state estimation based on cloud computing
CN116166847A (en) Power distribution network running state analysis method and system based on graph data
Kaiyuan et al. Reliability study for distribution network considering adverse weather
Kotsalos et al. On the development of a framework for the advanced monitoring of LV grids
Zhang et al. A good point set-based knowledgebase generation scheme for power system intelligent dynamic security assessment
Parlaktuna et al. Improved situational awareness for power distribution systems based on wlav estimator and direct load flow solution

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
TR01 Transfer of patent right
TR01 Transfer of patent right

Effective date of registration: 20240503

Address after: Room 313, 3rd Floor, Building 1, No. 1180 Xingxian Road, Jiading District, Shanghai, 2018

Patentee after: SHANGHAI JIUDAO INFORMATION TECHNOLOGY CO.,LTD.

Country or region after: China

Address before: 200235 Caobao Road, Xuhui District, Shanghai, No. 120-121

Patentee before: SHANGHAI INSTITUTE OF TECHNOLOGY

Country or region before: China