CN105426580A - Improved artificial fish swarm algorithm based complex reliability model parameter estimation method - Google Patents
Improved artificial fish swarm algorithm based complex reliability model parameter estimation method Download PDFInfo
- Publication number
- CN105426580A CN105426580A CN201510736220.5A CN201510736220A CN105426580A CN 105426580 A CN105426580 A CN 105426580A CN 201510736220 A CN201510736220 A CN 201510736220A CN 105426580 A CN105426580 A CN 105426580A
- Authority
- CN
- China
- Prior art keywords
- reliability model
- artificial fish
- parameter estimation
- function
- swarm 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.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Landscapes
- Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Microelectronics & Electronic Packaging (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Complex Calculations (AREA)
Abstract
The invention discloses an improved artificial fish swarm algorithm based complex reliability model parameter estimation method. The method comprises: obtaining reliability model information and invalid sample data, and initializing the invalid sample data; according to the reliability model information and the initialized invalid sample data, obtaining a target likelihood function; performing reliability model parameter estimation according to the target likelihood function by utilizing an improved artificial fish swarm algorithm; and checking a reliability model by Kolmogorov-Smirnov checking. According to the method, an analytic expression of maximum likelihood estimation does not need to be calculated, so that the method can be applied to the complex reliability model and is higher in applicability; and prior information of the reliability model and an initial value of an estimation parameter are not required and the convergence stability is higher.
Description
Technical field
The invention belongs to reliability model parameter estimation techniques field, particularly relating to a kind of complicated reliability model method for parameter estimation based on improving artificial fish-swarm algorithm.
Background technology
Artificial fish-swarm algorithm is a kind of intelligent optimization algorithm bionical to shoal of fish motor behavior.This algorithm has advantage: 1) algorithm possesses the ability of global optimizing, can jump out Local Extremum fast; 2) algorithm only needs comparison object functional value, not high to the Property requirements of objective function; 3) less demanding to initial value of algorithm, initial value can produce at random or be set as fixed value; 4) less demanding to setting parameter of algorithm, has larger permissible range.
Maximum-likelihood estimation is method for parameter estimation conventional and important in statistics, is used for the parameter of distribution function of an estimation sample set.
If the probability distribution of overall X is D, its probability density function (continuous distribution) is f
d, its unknown distribution parameter is θ=(θ
1, θ
2..., θ
m), θ ∈ Θ.X=(x
1, x
2..., x
n) be simple random sampling from overall X.Definition likelihood function:
If
be the estimator of θ, and meet
then claim
for θ=(θ
1, θ
2..., θ
m) Maximum-likelihood estimation.
In the application of reliability model parameter estimation, especially when processing part probabilistic information, Maximum-likelihood estimation has obvious advantage.
The Maximum-likelihood estimation method for solving of parameter:
When likelihood function is the continuous function of θ, and when existing about the partial derivative of each component of θ, the conventional differential method asks Maximum-likelihood estimation.By extreme value necessary condition and know that Maximum-likelihood estimation should meet:
be called likelihood equation.Conveniently, often take the logarithm to likelihood equation, likelihood equation can be written as:
Being similar to the simple distribution such as exponential distribution by solving likelihood equation, directly can obtaining the analytical expression of parameter estimation.But most complex model according to above method can only list parameter estimation the system of equations that meets, be difficult to the analytical expression directly obtaining separating.Normal employing Newton method, the numerical solution [1,2] of the equation method of value solving calculating parameters such as conjugate gradient method, but the convergence of these methods and initial value chosen much relations, be difficult to when lacking priori choose suitable initial value.
To in the parameter estimation application of complicated reliability model, there is many defects, be inconvenient to use: one) analytic expression of the Maximum-likelihood estimation of the parameter of the model of most complicated reliability is difficult to solve in above maximum likelihood parameter estimation method; Two) the ordinary numeric value solution of likelihood equation is difficult to choose suitable initial value, and can not ensure Algorithm Convergence.
Summary of the invention
Goal of the invention of the present invention is: utilize maximum likelihood parameter estimation method to carry out the problem existing for parameter estimation to complicated reliability model to solve in prior art, the present invention proposes a kind of complicated reliability model method for parameter estimation based on improving artificial fish-swarm algorithm.
Technical scheme of the present invention is: a kind of complicated reliability model method for parameter estimation based on improving artificial fish-swarm algorithm, comprises the following steps:
A, acquisition reliability model information and inefficacy sample data, and initialization process is carried out to inefficacy sample data;
B, according to the reliability model information in steps A and the inefficacy sample data after initialization process, obtain target likelihood function;
C, utilization improve artificial fish-swarm algorithm and carry out reliability model parameter estimation according to the target likelihood function in step B;
D, utilize Kolmogorov-Smirnov check reliability model is tested.
Further, described step B obtains target likelihood function according to the reliability model information in steps A and the inefficacy sample data after initialization process, be specially: according to function expression arbitrary in Cumulative Distribution Function F (t), probability density function f (t) and inefficacy efficiency function h (t) in reliability model information, obtained Cumulative Distribution Function F (t) and probability density function f (t) of reliability model by symbolic operation formulae discovery, then obtain target likelihood function according to the inefficacy sample data after initialization process.Further, described symbolic operation formula specifically comprises:
Further, described target likelihood function expression formula is specially:
Wherein, i is observation sequence number, t is observation time, and r is Failure count, and n is experiment number, and T is experimental period.
Further, described step C utilizes the target likelihood function improved in artificial fish-swarm algorithm solution procedure B, specifically comprises step by step following:
C1, using the target likelihood function in step B as objective function, setup parameter span, carries out Artificial Fish initialization;
C2, action selection is carried out to Artificial Fish, respectively the behavior of knocking into the back, foraging behavior and behavior of bunching are moved at random, the behavior state that jumps upgrades;
C3, judge whether objective function restrains, if objective function converges, then obtain solving result, operation terminates; If objective function is not restrained, then moving step length is upgraded, return step C2.
Further, the model information that reliability model information can obtain multiple acquisition reliability model is obtained in shown steps A.
Further, shown step D also comprises and utilizes AIC information criterion to carry out preferably multiple reliability model.
The present invention has following beneficial effect:
(1) the present invention is without the need to calculating the analytical expression of Maximum-likelihood estimation, and can be applied to complicated reliability model, applicability is better;
(2) prior imformation of the present invention without the need to reliability model and the initial value of estimated parameter, and it is better to restrain stability;
(3) the present invention is by carrying out initialization process to inefficacy sample data, and directly can obtain the objective function of artificial fish-swarm algorithm according to reliability model information, solution procedure is easy, and estimated result accuracy is high.
Accompanying drawing explanation
Fig. 1 is the complicated reliability model method for parameter estimation schematic flow sheet based on improving artificial fish-swarm algorithm of the present invention.
Fig. 2 is the convergence process schematic diagram based on improving artificial fish-swarm algorithm of the present invention.
Fig. 3 is that EMWE distribution function of the present invention and empirical distribution function contrast schematic diagram.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.
As shown in Figure 1, be the complicated reliability model method for parameter estimation schematic flow sheet based on improving artificial fish-swarm algorithm of the present invention.Based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, comprise the following steps:
A, acquisition reliability model information and inefficacy sample data, and initialization process is carried out to inefficacy sample data;
B, according to the reliability model information in steps A and the inefficacy sample data after initialization process, obtain target likelihood function;
C, utilization improve artificial fish-swarm algorithm and carry out reliability model parameter estimation according to the target likelihood function in step B;
D, utilize Kolmogorov-Smirnov check reliability model is tested.
In step, the present invention can select a reliability model, also can select multiple reliability model; Namely need to obtain one or more reliability model information and inefficacy sample data, reliability model information comprises Cumulative Distribution Function F (t), probability density function f (t) and inefficacy efficiency function h (t) etc. here.In the present invention, initialization process is carried out to inefficacy sample data and refer to that inefficacy sample data being arranged is canonical form.Such as, failtests is carried out to one group of 30 sample, in 300 hours, observe that 22 samples lost efficacy.As shown in table 1, for arranging the inefficacy sample data for canonical form; Wherein, 1st row " Time " are record inefficacy time of origin or observation end time, it is out-of-service time or observation truncated time that 2nd row " Censored " identified for the 1st row corresponding time, and the 3rd row " Frequency " represent that the corresponding time lost efficacy or the number of truncation sample.
Table 1. arranges the inefficacy sample data for canonical form
In stepb, the present invention is according to function expression arbitrary in Cumulative Distribution Function F (t), probability density function f (t) and inefficacy efficiency function h (t) in reliability model information, obtained Cumulative Distribution Function F (t) and probability density function f (t) of reliability model by symbolic operation formulae discovery, then obtain target likelihood function according to the inefficacy sample data after initialization process.Here symbolic operation formula specifically comprises:
In fail-test to a same batch products n sample, at observation time from 0 in T, observe r (0≤r≤n) secondary inefficacy altogether, its time of origin is respectively t
1, t
2..., t
r, separately have (n-r) individual sample not lose efficacy in 0 to T time.Then its target likelihood function is:
Wherein, i is observation sequence number, t is observation time, and r is Failure count, and n is experiment number, and T is experimental period.
According to Cumulative Distribution Function F (t) and probability density function f (t) of reliability model, and namely the inefficacy sample data of steps A Plays form can obtain target likelihood function.
Such as, for EMWE (ExponentiatedModifiedWeibullExtensionDistribution) reliability model, it includes 4 parameters (α, β, λ, γ), and its Cumulative Distribution Function is:
F(x；α,β,λ,γ)＝[1-exp(λα(1-exp(x/α)
β))
γ，α,β,λ,γ＞0,x≥0.
Probability density function is:
f(x；α,β,λ,γ)＝λβγ(x/α)
β-1exp((x/α)
β+λα(1-exp(x/α)
β))[1-exp(λα(1-exp(x/α)
β))]
γ-1，α,β,λ,γ＞0,x≥0。
For sample x=(x
1, x
2... x
n), its target likelihood function is:
In step C, utilize improvement artificial fish-swarm algorithm to carry out reliability model parameter estimation according to target likelihood function, specifically comprise step by step following:
C1, using the target likelihood function in step B as objective function, setup parameter span, carries out Artificial Fish initialization;
C2, action selection is carried out to Artificial Fish, respectively the behavior of knocking into the back, foraging behavior and behavior of bunching are moved at random, the behavior state that jumps upgrades;
C3, judge whether objective function restrains, if objective function converges, then obtain parameter estimation result, operation terminates; If objective function is not restrained, then moving step length is upgraded, return step C2.
As shown in Figure 2, be the convergence process schematic diagram based on improving artificial fish-swarm algorithm of the present invention.The present invention adopts improvement artificial fish-swarm algorithm, using the target likelihood function in step B as objective function, more easy to be easy-to-use; Meanwhile, setting parameter can use default parameters, also can be set by user oneself, making the present invention without the need to specifying estimated parameter initial value, needing the span of setup parameter, adaptability and convergence stability better.Table 2 is depicted as parameter estimation result of the present invention.
Table 2. parameter estimation result
Contrasted by the parameter estimation result separating likelihood equation method with the Newton-Raphson of prior art, the target likelihood function value that the inventive method obtains is larger, the residual sum of squares (RSS) of parameter estimation result is less, can show that the complicated reliability model method for parameter estimation convergence based on improving artificial fish-swarm algorithm of the present invention is better.
In step D, the present invention utilizes Kolmogorov-Smirnov inspection to test to reliability model.When the present invention carries out parameter estimation to multiple reliability model, the present invention also utilizes AIC information criterion to carry out preferably multiple reliability model.To a collection of fail data sample, the present invention is directed to multiple alternative reliability model and carry out data fitting, carry out parameter estimation respectively, choose optimal fitting model according to AIC information criterion (Akaikeinformationcriterion).
As shown in Figure 3, for EMWE distribution function of the present invention and empirical distribution function contrast schematic diagram.The EMWE distribution function that estimates of parameters of the present invention is corresponding and empirical distribution function fitting degree better.
Those of ordinary skill in the art will appreciate that, embodiment described here is to help reader understanding's principle of the present invention, should be understood to that protection scope of the present invention is not limited to so special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combination of not departing from essence of the present invention according to these technology enlightenment disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.
Claims (7)
1., based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, it is characterized in that, comprise the following steps:
A, acquisition reliability model information and inefficacy sample data, and initialization process is carried out to inefficacy sample data;
B, according to the reliability model information in steps A and the inefficacy sample data after initialization process, obtain target likelihood function;
C, utilization improve artificial fish-swarm algorithm and carry out reliability model parameter estimation according to the target likelihood function in step B;
D, utilize Kolmogorov-Smirnov check reliability model is tested.
2. as claimed in claim 1 based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, it is characterized in that, described step B obtains target likelihood function according to the reliability model information in steps A and the inefficacy sample data after initialization process, be specially: according to Cumulative Distribution Function F (t) in reliability model information, arbitrary function expression in probability density function f (t) and inefficacy efficiency function h (t), Cumulative Distribution Function F (t) and probability density function f (t) of reliability model is obtained by symbolic operation formulae discovery, target likelihood function is obtained again according to the inefficacy sample data after initialization process.
3., as claimed in claim 2 based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, it is characterized in that, described symbolic operation formula specifically comprises:
4., as claimed in claim 3 based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, it is characterized in that, described target likelihood function expression formula is specially:
Wherein, i is observation sequence number, t is observation time, and r is Failure count, and n is experiment number, and T is experimental period.
5. as claimed in claim 1 based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, it is characterized in that, described step C utilizes improvement artificial fish-swarm algorithm to carry out reliability model parameter estimation according to target likelihood function, specifically comprises step by step following:
C1, using the target likelihood function in step B as objective function, setup parameter span, carries out Artificial Fish initialization;
C2, action selection is carried out to Artificial Fish, respectively the behavior of knocking into the back, foraging behavior and behavior of bunching are moved at random, the behavior state that jumps upgrades;
C3, judge whether objective function restrains, if objective function converges, then obtain parameter estimation result, operation terminates; If objective function is not restrained, then moving step length is upgraded, return step C2.
6., as claimed in claim 1 based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, it is characterized in that, in shown steps A, obtain the model information that reliability model information can obtain multiple acquisition reliability model.
7. as claimed in claim 6 based on the complicated reliability model method for parameter estimation improving artificial fish-swarm algorithm, it is characterized in that, shown step D also comprises and utilizes AIC information criterion to carry out preferably multiple reliability model.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510736220.5A CN105426580A (en) | 2015-11-03 | 2015-11-03 | Improved artificial fish swarm algorithm based complex reliability model parameter estimation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510736220.5A CN105426580A (en) | 2015-11-03 | 2015-11-03 | Improved artificial fish swarm algorithm based complex reliability model parameter estimation method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN105426580A true CN105426580A (en) | 2016-03-23 |
Family
ID=55504789
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510736220.5A Pending CN105426580A (en) | 2015-11-03 | 2015-11-03 | Improved artificial fish swarm algorithm based complex reliability model parameter estimation method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105426580A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112257215A (en) * | 2019-07-02 | 2021-01-22 | 中车株洲电力机车研究所有限公司 | Maximum likelihood estimation solving method and system for product life distribution parameters |
-
2015
- 2015-11-03 CN CN201510736220.5A patent/CN105426580A/en active Pending
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112257215A (en) * | 2019-07-02 | 2021-01-22 | 中车株洲电力机车研究所有限公司 | Maximum likelihood estimation solving method and system for product life distribution parameters |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| WO2013103414A3 (en) | Method, system, and computer-readable medium for determining performance characteristics of an object undergoing one or more arbitrary aging conditions | |
| Holčík et al. | Transformations for Parametric Modeling of Censored Data in Survival Analysis | |
| CN103954567A (en) | Soil salinity determining method based on continuum removal method | |
| JP2017534850A5 (en) | ||
| CN105426580A (en) | Improved artificial fish swarm algorithm based complex reliability model parameter estimation method | |
| JP2012161379A5 (en) | ||
| CN108957120A (en) | A kind of weak signal extraction and system | |
| CN107884752A (en) | It is a kind of based on the external illuminators-based radar of compressed sensing to object detection method | |
| CN110536356B (en) | Public-private network interference investigation method and device | |
| CN105701004A (en) | Application test method and apparatus | |
| EP2763035A3 (en) | Method of evaluating one or more commands to be executed and related apparatus | |
| Jin-ping et al. | Fusion model of multi monitoring points on dam based on Bayes theory | |
| CN109670243B (en) | Service life prediction method based on Leeberg space model | |
| Weber et al. | P273. Validation of a smartphone-based patient monitoring system measuring calprotectin as the therapy follow-up marker | |
| CN106845050A (en) | Rolling bearing reliability assessment scheme | |
| Su et al. | Investigation on fishing activity and catch composition of coastal gillnet fisheries in waters off northwestern Taiwan | |
| Singh et al. | Advanced techniques for detection of filariasis–a review | |
| WO2007142964A3 (en) | Methods, systems, and computer program products for performing range-based directory number (dn) screening | |
| Ruggiero et al. | Dynamics of natural regeneration after disturbance in a remnant of Mixed Ombrophilous Forest in southern Brazil | |
| WO2014071237A3 (en) | Modifying time data values based on segment rules | |
| JP2014007995A5 (en) | ||
| CN203385583U (en) | Total moisture coal sample sampler | |
| Hessl et al. | How unusual was the 21st century drought in Mongolia?: placing recent extremes in an 1100-year context | |
| Kurnia et al. | TCMacro: A Simple and Robust ImageJ-Based Method for Automated Measurement of Tail Coiling Activity in Zebrafish. Biomolecules 2021, 11, 1133 | |
| CN103197051A (en) | Optimized platelet aggregation function detection analysis method suitable for automated instrument |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20160323 |
|
| WD01 | Invention patent application deemed withdrawn after publication |