CN111814342B - Complex equipment reliability hybrid model and construction method thereof - Google Patents
Complex equipment reliability hybrid model and construction method thereof Download PDFInfo
- Publication number
- CN111814342B CN111814342B CN202010688009.1A CN202010688009A CN111814342B CN 111814342 B CN111814342 B CN 111814342B CN 202010688009 A CN202010688009 A CN 202010688009A CN 111814342 B CN111814342 B CN 111814342B
- Authority
- CN
- China
- Prior art keywords
- distribution
- data
- parameter
- psi
- algorithm
- 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.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Complex Calculations (AREA)
Abstract
The invention discloses a complex equipment reliability mixed model and a construction method thereof, wherein the method comprises the following steps: (S100) constructing a mixed distribution model by normal distribution, weibull distribution, exponential distribution and lognormal distribution, and setting an observed equipment life data set to obtain a mixed density function of observed data; (S200) estimating unknown parameters in the mixed density function by adopting an EM algorithm, and converting the estimation of the unknown parameters into an optimization problem by means of maximum likelihood estimation; (S300) optimizing the complex equipment reliability modeling module by adopting Bayesian random classification and a K-means algorithm to obtain a complex equipment reliability mixed model based on Bayesian random classification. According to the method, the distribution parameters are optimized through the EM algorithm, and the Bayesian random classification and the K-means algorithm are combined to optimize the reliability modeling module of the complex equipment, so that the accuracy of parameter estimation is greatly improved, and the iteration speed is improved.
Description
Technical Field
The invention relates to a complex equipment reliability hybrid model, in particular to a complex equipment reliability hybrid model and a construction method thereof.
Background
The faults or failures of the equipment are random and difficult to avoid, so the time of the faults or failures of the equipment also occurs randomly, the fault rules of different equipment or the same equipment under different conditions are presented in different distribution types, and the general application range of the common fault distribution types is shown in table 1.
TABLE 1 Fault distribution function types and their application ranges
As can be seen from table 1, the failure rates of the same type of devices obey a certain specific probability distribution function, and if a parameter value of the failure probability distribution function of the certain type of devices can be obtained, the failure rates can be accurately characterized. As shown in fig. 1 (a), it is a fault distribution whose fault probability obeys a normal function, and it can be seen that if an equipment fault obeys a single fault distribution function, the fault rate at each moment is relatively easy to obtain, but when the equipment fault distribution is as shown in fig. 1 (b) and (c), that is, the equipment fault is simultaneously affected by the combination of multiple fault distribution functions, the complexity of the equipment fault distribution is greatly increased, and because the equipment is in different conditions such as working environment, use intensity and processing technique, the difference of the fault distribution functions of the same type of equipment is relatively large, the fault characteristics of the equipment fault distribution functions are often fuzzy, so that it is very difficult to find a method for accurately describing the fault probability distribution function of the equipment fault.
For the reliability prediction problem in fig. 1 (b), (c), many scholars have proposed a series of models, such as black box theory based on fault interval time data modeling, and random process theory based on system state. However, both of the two reliability modeling theories have certain defects, only simple faults can be modeled according to the black box theory, and when system faults are caused by multiple failure modes, the accuracy rate is not high; the stochastic process theory requires that the service life distribution, the repair time distribution after the fault and other distributions of each part of the system are exponential distributions, and if the system does not meet the assumption, the stochastic process modeling method is very difficult.
Disclosure of Invention
The invention aims to provide a complex equipment reliability hybrid model and a construction method thereof, which solve the problem that the existing method can only carry out modeling on simple faults according to the black box theory, can optimize distribution parameters by an EM (effective electromagnetic radiation) algorithm aiming at various faults in hybrid distribution, and optimizes a complex equipment reliability modeling module by combining Bayesian random classification and a K-means algorithm, greatly improves the accuracy of parameter estimation, and improves the iteration speed.
In order to achieve the above object, the present invention provides a method for constructing a complex device reliability hybrid model, the method comprising:
(S100): constructing a mixed distribution model by normal distribution, weibull distribution, exponential distribution and lognormal distribution, and setting an observed equipment life data set y = (y) 1 ,y 2 ,…,y n ) T ，y j The sample value of j =1,2, \8230;, n, n is the total amount of the collected data, the observed device life data comes from a mixed distribution formed by combining a normal distribution, an exponential distribution, a Weibull distribution and a lognormal distribution, and the distribution amount of the normal distribution, the exponential distribution, the Weibull distribution and the lognormal distribution in the mixed distribution is weighted as { pi; (pi) } distribution) 1 ，π 2 ，π 3 ，π 4 }, the sum of which is 1, observation data y j The mixing density function of (a) is as shown in formula (1):
wherein, the first and the second end of the pipe are connected with each other,
in the formula, all unknown parameters are psi = (pi) 1 ,π 2 ,π 3 ,π 4 ,μ 1 ,σ 1 ,μ 2 ,σ 2 ,λ,θ,β)，π 1 、π 2 、π 3 、π 4 Weights, σ, representing the total distribution of normal, exponential, weibull and lognormal distributions, respectively 1 、μ 1 Is a normally distributed parameter, theta and beta are parameters of Weibull distribution, lambda is a parameter of exponential distribution, sigma 2 、μ 2 A parameter that is lognormal distributed; pi represents a circumferential ratio; f. of 1 (y j ) Is composed of
f 2 (y j ) Is f 2 (y j ；λ)，f 3 (y j ) Is f 3 (y j ；θ,β)，f 4 (y j ) Is composed of
(S200) estimating unknown parameters psi in the mixed density function by adopting an EM algorithm, converting the estimation of the unknown parameters psi into an optimization problem by means of maximum likelihood estimation, wherein the optimized objective function is a likelihood function L (psi) or an equivalent log likelihood function lnL (psi), and the definition domain of the optimized objective function is the whole parameter value space;
the likelihood function for the unknown parameter Ψ is:
the equivalent log-likelihood function lnL (Ψ) for the unknown parameter Ψ is:
(S300) optimizing the complex equipment reliability modeling module by adopting Bayesian random classification and K-means algorithm to obtain a complex equipment reliability mixed model based on Bayesian random classification, which comprises the following steps:
(S310) classifying the equipment life data set by using Kmeans cluster analysis, and performing maximum likelihood estimation on independent distribution parameters of each type of data to serve as prior distribution parameters of each independent distribution, wherein the distribution parameter corresponding to the ith type of life data is psi i Data amount g of each type of life data i The ratio of the data quantity G occupying the service life data is the weight w of each independent distribution i Is w i ＝g i /G；
(S320) calculating the density function value f of the j point in the i type independent distribution ij (y j ) Density function values f of four distributions ij (y j ) Respectively calculated by formulas (2) to (5), and normalized according to formula (14) to obtain p ij ，p ij The posterior probability of the j point belonging to the i type independent distribution is represented as follows:
(S330) assigning the jth point to the posterior probability interval of the ith type independent distribution
Wherein p is j0 =0, each point generating a random probability r according to a uniform distribution j According to r j Judging the classification of the j point according to whether the i-th independent distribution posterior probability interval belongs to the i-th independent distribution posterior probability interval or not, and updating the corresponding parameters of each independent distribution according to the current sample classification;
(S340) calculating the maximum likelihood function value of the sample classification after Kmeans clustering according to the formula (15), and selecting the sample with the maximum likelihood function value as the current optimal classification:
wherein N represents the number of independent distributions;
(S350) repeating (S320) - (S340) until the maximum likelihood function converges or the number of iterations ends.
The method of constructing a hybrid model of complex plant reliability as claimed in claim 1, wherein in step (S200), under EM framework, each y is j One component, considered to come from a finite mixture model, is defined by z = (z) 1 ,z 2 ,…,z n ) T An indicator vector representing the non-observable component, wherein
In formula (8), i =1,2,3,4, j =1,2, \ 8230;, n;
observing a data vector y = (y) 1 ,y 2 ,…,y n ) T And missing data vector z = (z) 1 ,z 2 ,…,z n ) T Combined together, the complete data vector x = (y) is obtained T ,z T ) T Then, in the mixed distribution model, the log-likelihood function lnL is obtained based on the complete data of the parameter Ψ c (ψ) is:
preferably, in step (S200), the parameter estimation method based on the EM algorithm includes:
e, step E: computing conditional probability expectation Q (psi; psi) of a joint distribution k ) In the k +1 th iteration of the EM algorithm, there are:
at a given y and current Ψ k Conditional expectation of log-likelihood function of complete data
Comprises the following steps:
wherein, tau i (y j ；Ψ k ) Is the jth observable data y j A posterior probability of an ith component belonging to the finite mixture model; superscript k represents the kth iteration;
then the log-likelihood function lnL derived from the complete data based on the parameter Ψ is combined c (psi) conditional expectation of log-likelihood function of complete data
From formulas (9) and (11), it is possible to obtain:
wherein, pi i Weights for the respective distributions;
and M: updating the estimated value Ψ of Ψ k+1 Such that the entire parameter space of Ψ is Q (Ψ; Ψ) k ) The function takes the maximum value, and the parameter iteration formula is as follows:
determination of parameter Ψ k+1 If yes, stopping iteration, if not, repeating step E and step M until final convergence, and outputting psi k+1 。
It is another object of the present invention to provide a complex plant reliability hybrid model constructed by the method.
The complex equipment reliability hybrid model and the construction method thereof solve the problem that the existing model can only be established for simple faults according to the black box theory, and have the following advantages:
according to the model constructed by the method, the EM algorithm is adopted to optimize the distribution parameters, and although the EM algorithm has the advantages of easiness in implementation, high reliability, easiness in understanding and the like, the whole data set needs to be traversed during iteration, the iteration speed of the algorithm is low when the data volume is excessive, and the EM algorithm has global search capability unlike a genetic algorithm, so that the problems that whether the EM algorithm can obtain a global optimal solution or not and whether the selected initial parameters are appropriate or not excessively depend on the selected initial parameters exist. The invention combines a Bayesian random classification method to randomly distribute the data sets to each independent distribution so as to make up for the defects.
The model constructed by the method overcomes the defect that a mixed model constructed by the traditional EM algorithm is easy to be locally optimal, parameters of each independent distribution are adaptively adjusted according to data characteristics, the weights of each independent distribution can be used for accepting or rejecting whether each independent distribution is reserved, the performance of the model is far higher than that of the mixed model constructed by the traditional EM algorithm when the parameters are fitted, the model is iterated for 7 times, the precision of parameter estimation is up to 99.97%, however, the iteration frequency of the mixed model constructed by the traditional EM algorithm is about 35 times, and the precision is only 82.17%.
Drawings
Fig. 1 is a three-dimensional diagram of a distribution function of a fault of a conventional device.
FIG. 2 is a flow chart of the method of the present invention.
Fig. 3 is a conventional EM algorithm computation framework diagram.
FIG. 4 shows normal distribution parameters
And (5) a variation graph.
FIG. 5 shows a normal distribution parameter μ 1 And (5) a variation graph.
Fig. 6 is a graph of the variation of the exponential distribution parameter λ.
Fig. 7 is a diagram showing a change in the weibull distribution parameter β.
Fig. 8 is a diagram showing a variation of the weibull distribution parameter θ.
FIG. 9 is a diagram of a lognormal distribution parameter μ 2 And (5) a variation graph.
FIG. 10 is a diagram of lognormal distribution parameters
And (5) a variation graph.
FIG. 11 shows distribution weights π 1 、π 2 、π 3 、π 4 A change map of (c).
FIG. 12 is a Bayesian stochastic classification reliability hybrid model error graph.
FIG. 13 is a diagram of a hybrid model error of a conventional EM algorithm.
FIG. 14 is a graph of a Bayesian stochastic classification reliability mixture model cumulative distribution function.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Example 1
A construction method of a complex equipment reliability mixed model is disclosed, the flow of the construction method is shown in figure 2, the complex equipment reliability mixed model based on Bayesian random classification is constructed according to a black box theory, the Bayesian random classification is utilized to optimize the defect that the traditional EM algorithm is easy to be trapped in local optimization, the fault targeted by the mixed model is the result of the comprehensive effect of various fault distributions (table 1), the sudden failure has randomness, and the degradation failure has predictability.
The EM algorithm is an optimization algorithm capable of performing Maximum Likelihood Estimation (MLE) through iteration, and is generally used for performing parameter Estimation on a probabilistic model containing hidden variables (latent) or missing data (incomplete-data), and the basic process of the EM algorithm is as follows: firstly, estimating the value of a model parameter according to the given observation data; then, the value of the missing data is estimated according to the parameter value estimated in the previous step, the parameter value is estimated again according to the estimated missing data and the previously observed data, iteration is repeated until the last convergence is reached, and the iteration is finished, as shown in fig. 3, a frame diagram is calculated for the EM algorithm.
The specific steps of the traditional EM algorithm are as follows:
(S1) inputting: observed data x = (x) 1 ,x 2 ,…,x n ) T Joint distribution p (x, z; theta), conditional distribution p (z | x; theta), maximum number of iterations J, where z = (z =) 1 ,z 2 ,…,z n ) T For implicit data which is not observed, theta is a sample model parameter, and T represents transposition;
(S2) initializing an initial value theta of a model parameter theta at random 0 I.e. the shape and position of the initialization curve (1);
(S3) starting EM algorithm iteration:
(S31) E step: computing a conditional probability expectation L (θ, θ) of the joint distribution j ) I.e. the increment of curve (1) to curve (2):
Q i (z i )＝P(z i |x i ,θ j ) (1’)
wherein Q i (z i ) For implicit data z i Distribution of (2).
(S32) M step: maximization of L (theta ) j ) To obtain theta j+1 Namely, calculating a parameter theta when the curve (2) intersects the curve (4):
(S33) if θ j+1 After convergence, the algorithm ends, otherwiseAnd returning to the step (S31) to perform E-step iteration operation, namely changing another parameter of the curve (3) when the curve (3) intersects with the curve (4) and continuing the iteration operation.
(S4) outputting the model parameter theta.
The method for constructing the complex equipment reliability hybrid model specifically comprises the following steps:
(S100): constructing a mixed distribution model by normal distribution, weibull distribution, exponential distribution and lognormal distribution, and setting an observed equipment life data set y = (y) 1 ,y 2 ,…,y n ) T ，y j The sample value representing the j-th collected point, j =1,2, \ 8230 \ 8230;, n, n is the total number of the collected data, the observed data is from a mixed distribution formed by combining a normal distribution, an exponential distribution, a Weibull distribution and a lognormal distribution, and the weights of the distribution quantities of the normal distribution, the exponential distribution, the Weibull distribution and the lognormal distribution in the mixed distribution are recorded as { pi |) 1 ，π 2 ，π 3 ，π 4 (iii) the sum thereof is 1; then observe the data y j Is shown in formula (1):
wherein the content of the first and second substances,
in the formula, all unknown parameters are psi = (Pi) 1 ,π 2 ,π 3 ,π 4 ,μ 1 ,σ 1 ,μ 2 ,σ 2 ,λ,θ,β)，π 1 、π 2 、π 3 、π 4 Weights, σ, representing the total distribution of normal, exponential, weibull and lognormal distributions, respectively 1 、μ 1 Is a normally distributed parameter, theta and beta are parameters of Weibull distribution, lambda is a parameter of exponential distribution, sigma 2 、μ 2 A parameter that is lognormal distributed; pi represents the weight of each distribution in the total distribution; f. of 1 (y j ) Is composed of
f 2 (y j ) Is f 2 (y j ；λ)，f 3 (y j ) Is f 3 (y j ；θ,β)，f 4 (y j ) Is composed of
For mixed distributions, it is difficult to resolve each sample value y from the data itself alone j From which distribution, the observation does not contain all the information of the data in this sense, and is "incomplete data". The estimates of the finite mixture model of the four distributions eventually end up as estimates of the parameter vector Ψ.
(S200) estimating an unknown parameter Ψ in the mixed density function by adopting an EM algorithm, and converting the estimation of the unknown parameter Ψ into an optimization problem by means of Maximum Likelihood Estimation (MLE), wherein an optimized objective function is a likelihood function L (Ψ) or an equivalent log likelihood function lnL (Ψ), and a definition domain is a whole parameter value space, and the method comprises the following specific steps:
the likelihood function for the unknown parameter Ψ is:
under EM framework, each y j One component, considered to be from the finite mixture model, is represented by z = (z) 1 ,z 2 ,…,z n ) T An indicator vector representing the unobservable component, wherein
Wherein i =1,2,3,4,j =1,2, \8230;, n.
Observing a data vector y = (y) 1 ,y 2 ,…,y n ) T And missing data vector z = (z) 1 ,z 2 ,…,z n ) T Combined together, the complete data vector x = (y) is obtained T ,z T ) T . Then, in the mixed distribution model, the log-likelihood function lnL is obtained based on the complete data of the parameter Ψ c (ψ) is:
the parameter estimation steps based on the EM algorithm are as follows:
e, step E: calculating the conditional probability expectation Q (psi; psi) of the joint distribution using the E step in the conventional EM algorithm calculation k ) In the k +1 iteration of the EM algorithm, there are:
at a given y and current Ψ k Conditional expectation of log-likelihood function of complete data
Comprises the following steps:
wherein, tau i (y j ；Ψ k ) Is the jth observable data y j A posterior probability of an ith component belonging to the finite mixture model; the superscript k represents the kth iteration.
Then the log-likelihood function lnL derived from the complete data based on the parameter Ψ is combined c Conditional expectation of log likelihood functions for (psi) and integrity data
From formulas (9) and (11), it is possible to obtain:
wherein, pi i The weights of the respective distributions.
And M: updating the estimated value psi of psi by using M steps in the traditional EM algorithm calculation k+1 Such that the entire parameter space of Ψ is Q (Ψ; Ψ) k ) The function takes the maximum value, and the parameter iteration formula is as follows:
determination of parameter Ψ k+1 If yes, stopping iteration, if not, repeating step E and step M until final convergence, and outputting psi k+1 。
(S300) modeling of complex equipment reliability hybrid model based on Bayesian stochastic classification
And optimizing the reliability modeling module of the complex equipment by adopting Bayesian random classification and a K-means algorithm to obtain a complex equipment reliability mixed model based on Bayesian random classification.
Although the EM algorithm has the advantages of easiness in implementation, high reliability, easiness in understanding and the like, the whole data set needs to be traversed when the EM algorithm is iterated, when the data volume is excessive, the iteration speed of the EM algorithm is low, and the EM algorithm does not have the global search capability like a genetic algorithm, whether the EM algorithm can obtain a global optimal solution or not depends excessively on whether the selected initial parameters are proper or not. The traditional EM algorithm adopts a random selection or experience selection method to initialize parameters to be estimated, so that the iterative algorithm is easy to fall into local optimum. The mixed model is generally obtained by superimposing a plurality of independent distributions, a certain intersection exists between the independent distributions, and if absolute classification initialization parameters are adopted, the intersection is inconsistent with the theoretical condition.
Aiming at the problems existing in the optimization of the EM initial parameters, a Bayesian random classification method is adopted to randomly distribute the data sets to each independent distribution so as to make up the defects. The method comprises the following specific steps:
(S310) classifying the equipment life data set by using Kmeans cluster analysis, and performing maximum likelihood estimation on independent distribution parameters of each type of data to serve as prior distribution parameters of each independent distribution, wherein the distribution parameter corresponding to the ith type of life data is psi i Data amount g of each type of life data i The ratio of the data volume G occupying the service life data is the weight w of each independent distribution i Is w i ＝g i /G。
(S320) calculating the density function value f of the j point in the i type independent distribution ij (y j ) Density function values f of four distributions ij (y j ) Respectively calculated by formulas (2) to (5), and normalized according to formula (14) to obtain p ij ，p ij The posterior probability of the j point belonging to the i type independent distribution is represented as follows:
(S330) assigning the jth point to the posterior probability interval of the ith type independent distribution
Wherein p is j0 =0, eachGenerating random probability r by uniform distribution of point-by-point illumination j According to r j Whether the classification belongs to the posterior probability interval of the ith independent distribution or not is judged, and the corresponding parameter of each independent distribution is updated according to the classification of the current sample.
(S340) calculating the maximum likelihood function value of the sample classification after Kmeans clustering according to the formula (15), and selecting the sample with the maximum likelihood function value as the current optimal classification:
where N represents the number of independent distributions.
(S350) repeating (S320) to (S340) until the maximum likelihood function converges or the number of iterations ends.
Specific application of the model of example 1
In order to verify the accuracy of the model constructed by the invention, the mixed distribution of the reliability of the complex equipment is constructed by normal distribution, exponential distribution, weibull distribution and logarithmic normal distribution, the data of the mixed distribution is generated by randomly selecting mixed distribution parameters, the specific parameter setting is shown as the mixed distribution 1 in table 2, the capacity of the generated reliability data is 10000, the cluster number of the Bayesian random classification reliability mixed model is 4, the maximum iteration time is set to be 1000 times, the absolute value of the difference value between the random mixed distribution of the generated data and the complex equipment reliability mixed model based on the Bayesian random classification is defined as an error, and the setting error is less than 1 multiplied by 10 -3 For the convergence condition, a reliability mixed model constructed by the traditional EM algorithm is selected for the comparison test, the set parameters of the reliability mixed model are the same as those of a complex equipment reliability mixed model based on Bayesian random classification, and the effectiveness of the model provided by the invention is verified by comparing the iteration errors of the two algorithms.
TABLE 2 respective mixing distribution parameters
As can be seen from fig. 4 to 11 and fig. 14, the bayesian stochastic classification reliability hybrid model constructed by the present invention can overcome the defect that the hybrid model constructed by the conventional EM algorithm is prone to be locally optimal, adaptively adjust parameters of each independent distribution according to data characteristics, and accept or reject whether each independent distribution is retained by using the weight of each independent distribution. As can be seen from fig. 12 to 13, when the bayesian stochastic classification reliability hybrid model is used for parameter fitting, the performance of the bayesian stochastic classification reliability hybrid model is much higher than that of the hybrid model constructed by the conventional EM algorithm, the iteration is performed for 7 times, and the accuracy of parameter estimation is as high as 99.97%, whereas the iteration is performed for 35 times to start convergence, and the accuracy is only 82.17%.
While the present invention has been described in detail with reference to the preferred embodiments thereof, it should be understood that the above description is not to be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (4)
1. A method for constructing a complex equipment reliability hybrid model is characterized by comprising the following steps:
(S100): constructing a mixed distribution model by normal distribution, weibull distribution, exponential distribution and lognormal distribution, and setting an observed equipment life data set y = (y) 1 ,y 2 ,…,y n ) T ，y j The sample value of j =1,2, \ 8230 \ 8230;, n, n is the total number of the collected data, the observed device lifetime data is from a mixed distribution formed by combining a normal distribution, an exponential distribution, a Weibull distribution and a lognormal distribution, and the distribution quantity of the normal distribution, the exponential distribution, the Weibull distribution and the lognormal distribution in the mixed distribution is weighted as { pi ^ distribution 1 ，π 2 ，π 3 ，π 4 1, the sum of which is 1, observed data y j Is expressed by formula (1):
wherein the content of the first and second substances,
in the formula, all unknown parameters are psi = (Pi) 1 ,π 2 ,π 3 ,π 4 ,μ 1 ,σ 1 ,μ 2 ,σ 2 ,λ,θ,β)，π 1 、π 2 、π 3 、π 4 Weights, σ, representing the total distribution of normal, exponential, weibull and lognormal distributions, respectively 1 、μ 1 Is a normally distributed parameter, theta and beta are parameters of Weibull distribution, lambda is a parameter of exponential distribution, sigma 2 、μ 2 A parameter that is lognormal distributed; pi represents the circumference ratio; f. of 1 (y j ) Is composed of
f 2 (y j ) Is f 2 (y j ；λ)，f 3 (y j ) Is f 3 (y j ；θ,β)，f 4 (y j ) Is composed of
(S200) estimating unknown parameters psi in the mixed density function by adopting an EM algorithm, converting the estimation of the unknown parameters psi into an optimization problem by means of maximum likelihood estimation, wherein the optimized objective function is a likelihood function L (psi) or an equivalent log likelihood function lnL (psi), and the definition domain is the whole parameter value space;
the likelihood function for the unknown parameter Ψ is:
the equivalent log-likelihood function lnL (Ψ) for the unknown parameter Ψ is:
(S300) optimizing the reliability modeling module of the complex equipment by adopting Bayesian random classification and K-means algorithm to obtain a reliability mixed model of the complex equipment based on Bayesian random classification, which comprises the following steps:
(S310) classifying the equipment life data set by using Kmeans cluster analysis, carrying out maximum likelihood estimation on independent distribution parameters of each type of data as prior distribution parameters of each independent distribution, wherein the distribution parameter corresponding to the ith type of life data is psi i Data amount of each type of lifetime data g i The ratio of the data volume G occupying the service life data is the weight w of each independent distribution i Is w i ＝g i /G；
(S320) calculating the density function value f of the j point in the i type independent distribution ij (y j ) Density function values f of four distributions ij (y j ) Respectively calculated by formulas (2) - (5), and normalized according to formula (14) to obtain p ij ，p ij The posterior probability of the j point belonging to the i type independent distribution is represented as follows:
(S330) assigning the jth point to the posterior probability interval of the ith type independent distribution
Wherein p is j0 =0, each point generating a random probability r according to a uniform distribution j According to r j Judging the classification of the j point according to the posterior probability interval of whether the j point belongs to the i-th independent distribution, and updating the corresponding parameter of each independent distribution according to the current sample classification;
(S340) calculating the maximum likelihood function value of the sample classification after Kmeans clustering according to the formula (15), and selecting the sample classification with the maximum likelihood function value as the current optimal classification:
wherein N represents the number of independent distributions;
(S350) repeating (S320) to (S340) until the maximum likelihood function converges or the number of iterations ends.
2. The method of constructing a hybrid model of complex plant reliability as claimed in claim 1, characterized in that in step (S200), under EM framework, each y is j One component, considered to be from the finite mixture model, is represented by z = (z) 1 ,z 2 ,…,z n ) T An indicator vector representing the non-observable component, wherein
In formula (8), i =1,2,3,4, j =1,2, \ 8230;, n;
observing a data vector y = (y) 1 ,y 2 ,…,y n ) T And missing data vector z = (z) 1 ,z 2 ,…,z n ) T Are combined together to obtainComplete data vector x = (y) T ,z T ) T Then, in the mixed distribution model, the log-likelihood function lnL is obtained based on the complete data of the parameter Ψ c (ψ) is:
3. the method for constructing a hybrid model of complex plant reliability according to claim 2, wherein in the step (S200), the parameter estimation method based on the EM algorithm comprises:
e, step E: computing conditional probability expectation Q (psi; psi) of a joint distribution k ) In the k +1 th iteration of the EM algorithm, there are:
at a given y and current Ψ k Conditional expectation of log-likelihood function of complete data
Comprises the following steps:
wherein, tau i (y j ；Ψ k ) Is the jth observable data y j A posterior probability of the ith component belonging to the finite mixture model; superscript k represents the kth iteration;
then the log-likelihood function lnL derived from the complete data based on the parameter Ψ is combined c Conditional expectation of log likelihood functions for (psi) and integrity data
From formulas (9) and (11), it is possible to obtain:
wherein, pi i Weights for the respective distributions;
and M: updating the estimated value Ψ of Ψ k+1 Such that the entire parameter space of Ψ is Q (Ψ; Ψ) k ) The function takes the maximum value, and the parameter iteration formula is as follows:
determination of parameter Ψ k+1 If the convergence is not achieved, continuing to repeat the steps E and M until the convergence is achieved finally, and outputting psi k+1 。
4. A complex device reliability hybrid model constructed by the method of any one of claims 1-3.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010688009.1A CN111814342B (en) | 2020-07-16 | 2020-07-16 | Complex equipment reliability hybrid model and construction method thereof |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010688009.1A CN111814342B (en) | 2020-07-16 | 2020-07-16 | Complex equipment reliability hybrid model and construction method thereof |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111814342A CN111814342A (en) | 2020-10-23 |
| CN111814342B true CN111814342B (en) | 2022-10-11 |
Family
ID=72865693
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010688009.1A Active CN111814342B (en) | 2020-07-16 | 2020-07-16 | Complex equipment reliability hybrid model and construction method thereof |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111814342B (en) |
Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112529037A (en) * | 2020-11-06 | 2021-03-19 | 重庆恢恢信息技术有限公司 | Construction site construction optimization method based on big data analysis |
| CN113420425A (en) * | 2021-06-03 | 2021-09-21 | 杭州电子科技大学 | ARMA model parameter estimation method and system based on low-quality data |
| CN114972341B (en) * | 2022-07-28 | 2022-12-16 | 华南理工大学 | WSI image classification method, system and medium based on Bayesian assisted learning |
| CN115329895A (en) * | 2022-09-06 | 2022-11-11 | 南昌大学 | Multi-source heterogeneous data noise reduction analysis processing method |
| CN117371876B (en) * | 2023-12-07 | 2024-04-02 | 深圳品阔信息技术有限公司 | Index data analysis method and system based on keywords |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106683122A (en) * | 2016-12-16 | 2017-05-17 | 华南理工大学 | Particle filtering method based on Gaussian mixture model and variational Bayes |
| CN111369002A (en) * | 2020-02-20 | 2020-07-03 | 杭州电子科技大学 | Gibbs parameter sampling method applied to random point mode finite hybrid model |
-
2020
- 2020-07-16 CN CN202010688009.1A patent/CN111814342B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106683122A (en) * | 2016-12-16 | 2017-05-17 | 华南理工大学 | Particle filtering method based on Gaussian mixture model and variational Bayes |
| CN111369002A (en) * | 2020-02-20 | 2020-07-03 | 杭州电子科技大学 | Gibbs parameter sampling method applied to random point mode finite hybrid model |
Non-Patent Citations (1)
| Title |
|---|
| 正态分布和瑞利分布混合情形下的参数估计及分类问题;王小英等;《数学建模及其应用》;20160915(第03期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111814342A (en) | 2020-10-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111814342B (en) | Complex equipment reliability hybrid model and construction method thereof | |
| Malinsky et al. | Causal structure learning from multivariate time series in settings with unmeasured confounding | |
| CN106874581B (en) | Building air conditioner energy consumption prediction method based on BP neural network model | |
| CN111860982A (en) | Wind power plant short-term wind power prediction method based on VMD-FCM-GRU | |
| CN110910004A (en) | Reservoir dispatching rule extraction method and system with multiple uncertainties | |
| CN111523778A (en) | Power grid operation safety assessment method based on particle swarm algorithm and gradient lifting tree | |
| Oliinyk et al. | The decision tree construction based on a stochastic search for the neuro-fuzzy network synthesis | |
| CN105825045B (en) | Phased mission systems can repair spare parts demand Forecasting Methodology | |
| CN113962145A (en) | Parameter uncertainty quantitative modeling method under interval data sample condition | |
| CN112686971A (en) | Method and system for undirected graph orientation of building system relation topology | |
| CN113484813A (en) | Intelligent ammeter fault rate estimation method and system under multi-environment stress | |
| CN107204616B (en) | Power system random state estimation method based on self-adaptive sparse pseudo-spectral method | |
| CN115345222A (en) | Fault classification method based on TimeGAN model | |
| CN109540089B (en) | Bridge deck elevation fitting method based on Bayes-Kriging model | |
| CN114330549A (en) | Chemical process fault diagnosis method based on depth map network | |
| Li et al. | Distribution grid topology and parameter estimation using deep-shallow neural network with physical consistency | |
| CN112287605B (en) | Power flow checking method based on graph convolution network acceleration | |
| CN113222263A (en) | Photovoltaic power generation power prediction method based on long-term and short-term memory neural network | |
| CN117330963A (en) | Energy storage power station fault detection method, system and equipment | |
| CN110543108B (en) | Heating system measurement data correction method and system based on mechanism model prediction | |
| CN116303786B (en) | Block chain financial big data management system based on multidimensional data fusion algorithm | |
| CN115408949B (en) | Load model parameter identification method System, apparatus and medium | |
| CN115184055B (en) | Test set determination method and system for hierarchical testability optimization | |
| Gebhardt et al. | Predicting parts demand in the automotive industry—an application of probabilistic graphical models | |
| CN115409317A (en) | Transformer area line loss detection method and device based on feature selection and machine learning |
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 |