CN104463331A - Accelerated degradation experiment modeling method based on fuzzy theory - Google Patents
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Abstract
The invention discloses an accelerated degradation experiment modeling method based on a fuzzy theory. The accelerated degradation experiment modeling method comprises the specific steps of 1 utilizing the fuzzy theory to enable degradation data to be reasonably fuzzified so as to obtain fuzzy degradation data, 2 utilizing fuzzy degradation regression to establish an accelerated degradation test fuzzy linear degradation model and 3 performing model parameter evaluation and reliability degree prediction. According to the established fuzzy linear degradation model, a fuzzy evaluation value of a model parameter is given, and a fuzzy life prediction interval and a fuzzy reliability interval of a product are further given. Compared with a point estimated value given by means of a traditional statistical analysis method, the result obtained by means of the accelerated degradation experiment modeling method is reasonable and has reference value.
Description
Technical Field
The invention discloses an accelerated degradation test modeling method based on a fuzzy theory, belongs to the technical field of accelerated degradation tests, and is used for solving the technical problems in the fields of reliability and system engineering.
Background
With the development of science and technology and the higher and higher requirements on product reliability, for products with the characteristics of long service Life and high reliability, an ALT-assisted Life Testing (ALT-assisted Life Testing) which needs to utilize failure data observed in a test cannot meet the requirements. This presents significant difficulties in assessing the longevity and reliability of the product, as long-lived and high reliability products sometimes have difficulty observing failure in ALT or not at all. The accelerated degradation test (ADT-accelerated degradation Testing) was developed in this context. The accelerated degradation test is a test technology and a method for extrapolating or evaluating the life characteristics of a product at a normal stress level by searching the relation (an accelerated model) between the service life and the stress of the product on the basis of unchanging failure mechanism and utilizing performance degradation data of the product at a high (accelerated) stress level. The accelerated test is the main means for evaluating the service life of a long-service-life and high-reliability product. Compared with an accelerated life test, actual failure does not need to be observed in ADT, and key performance parameter values of the product contain a large amount of product life and reliability information, so that certain cost can be saved. Therefore, the accelerated degradation test has wider application prospect.
ADT was mainly studied for performance degradation failure. For ADT, the same stress application as for ALT is used. In ADT, the speed of degradation of a performance parameter is generally related to the magnitude of applied stress, and the rate of change of such a degradation parameter is described by an acceleration model. In ADT, the selection of the acceleration model is consistent with the idea and method of establishing the acceleration model in ALT, and can be mutually universal.
Statistical analysis of accelerated degradation testing is based primarily on the selection of a degradation model. The degradation models are mainly divided into three categories: 1) a Data-drive based performance degradation model; 2) a Model-based (Model-based) performance degradation Model; 3) hybrid (Hybrid) model based on data and model. Statistical methods of type 1 generally incorporate SVM (reference [1 ]: Shuzhen Li; Xiaoyang Li; Tongmin Jiang; "Life and Reliability for evaluating the CSA DT using Supported vector Machines [ C ]," Reliability and Main availability Symposium (RAMS), "2010 proceeding spp.1-6,25-28Jan.2010), neural networks (reference [2 ]: Shuzhen Li; Xiayang Li; Tongmin Jiang;" Aprediction method of Life and Reliability for using the grid RBF neural networks [ C ], "Experimental Engineering Management,2009. Experimental and Transmission Management, III, J.E.;" arrival data, III, J.E.; "arrival data, 23. C.," arrival Management, III. E.S., "arrival data, 23. C.," arrival data, III. C.S.S.23. C., "arrival Management, III. C.E.E.S.S., pp.1313-1317,20-24July 2009), etc. The statistical methods of type 2 are mainly based on the maintenance process (reference [4 ]: Gorjan N, Ma L, Mittity M, et al. A review on degradation models in Reliability resources [ M ]// Engineering Asset Lifecycle management. Springer London,2010:369 384.), the gamma process (reference [5 ]: Tseng S T, Balkrishnan N, Tsai C. operational step-stress estimation test plant for gamma degradation processes [ J ]. Reliability, IEEE Transactions on 2009,58(4): 611) and the like. Type 3 is a statistical Method that combines the two (reference [6 ]: Wang L Z, Wang X H, JiangT M, et al. A Lifetime Prediction Method Based on Multi-performance Parameters [ J ]. Journal of applied Sciences,2013,13 (20)).
Since the ADT gathers performance degradation data of the product under accelerated stress conditions, what is ultimately needed is the product's life at normal stress levels. Thus, the statistical analysis of data problem in ADT is essentially a predictive problem. And its prediction includes two aspects: extrapolation of high stress to low stress in the stress dimension and prediction of failure life without crossing the critical value to crossing the critical value for performance in the time dimension. The extrapolation in the stress dimension may be performed by a regression method using a previously obtained acceleration model, or by a gray prediction method. The extrapolation in the time dimension can adopt the life prediction methods such as the random process analysis, the neural network, the time sequence and the like.
The key to the ADT study was: and a scientific and reasonable mathematical model is searched for fitting the product performance degradation trend, and the design of a test scheme and the data evaluation research are carried out on the ADT under the assumption of different fitting models. Most scholars choose to drift brownian motion, except for a new way to find a new degradation process fitting model. Since the first arrival of the drift brownian motion follows inverse gaussian distribution, many researchers have conducted various studies on the inverse gaussian distribution.
The fuzzy theory is mainly studied as follows:
in 1965, professor l.a.zadeh, the american treatise on the concept of fuzzy sets was first proposed, thereby opening up a branch of fuzzy mathematics. Fuzzy mathematics is the mathematics of dealing with the problem of being and being, it remedies the deficiency of "not so that" binary logic for deterministic mathematics. Since the creation of "fuzzy mathematics", fuzzy mathematics has been widely used in many fields such as automatic control, artificial intelligence, system analysis, etc., and has achieved remarkable results.
Viertl mainly considers the evaluation of system reliability based on Bayesian theory under the condition that life data is fuzzy (reference [7 ]: Viertl R.On reliability evaluation based on fuzzy life data [ J ]. Journal of statistical planning and reference, 2009,139(5): 1750-. The Huanghong clock analyzes the reliability of a competition failure system according to Fuzzy degradation data, and provides a Fuzzy degradation reliability model of the competition failure of the system (reference [8 ]: Huang H Z, Zuo MJ, Sun Z Q. Bayesian reliability analysis for Fuzzy life time data [ J ]. Fuzzy Sets and Systems,2006,157(12): 1674-. Jamkhaneh gives more details about the lifetime distribution model of the fuzzy parameters: two distributions, an exponential Distribution and a Weibull Distribution, and the reliability of the system was evaluated (reference [9] Jamkhaneh E B. analysis System reliability Using Fuzzy Weibull Life Distribution [ J ]. International Journal of Applied,2014,4(1): 93-102). Lin gives membership functions for certain repairable system features and describes system failure and repair time with fuzzy index distributions (ref [10 ]: Lin C H, Ke J C, Huang H I. reliability-based measures for a system with an undivided parameter environment [ J ]. International Journal of Systems Science,2012,43(6): 1146-1156.).
Li Xiaoyang (Beijing university of aerospace. accelerated degradation test prediction method based on fuzzy theory: China, CN200910093518.3[ P ].2010-3-10.) considers the ambiguity existing in the failure threshold value in the accelerated degradation test, and thus provides an accelerated degradation test prediction model based on drift Brownian motion. In addition to this, there has been no study of the fuzzy theory in accelerated degradation tests so far.
Disclosure of Invention
The invention aims to solve the problem that degradation data in the existing accelerated degradation test has subjectivity and fuzziness, and provides an accelerated degradation test modeling method based on a fuzzy theory.
The accelerated degradation test modeling method based on the fuzzy theory comprises the following specific steps:
the method comprises the following steps that firstly, degradation data are reasonably fuzzified by using a fuzzy theory to obtain fuzzy degradation data;
establishing a linear fuzzy degradation model of an accelerated degradation test by using fuzzy degradation regression;
and step three, model parameter evaluation and service life and reliability fuzzy prediction.
The invention has the advantages that:
(1) the subjectivity and the fuzziness of degradation data in the accelerated degradation test are analyzed for the first time, the fuzzy theory is introduced into the statistical analysis of the accelerated degradation test for the first time, and a linear degradation regression model based on the fuzzy theory is established;
(2) according to the method, the fuzzy evaluation value of the model parameter is given according to the established fuzzy linear degradation model, and the fuzzy life prediction interval and the fuzzy reliability interval of the product are further given.
Drawings
FIG. 1 is a fuzzy reliability graph;
FIG. 2 is a product life prediction profile for a fixed failure threshold;
FIG. 3 is a fuzzy first-pass envelope plot of a product;
fig. 4 is a flow chart of a method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention relates to an accelerated degradation test modeling method based on fuzzy theory, as shown in figure 4, comprising the following steps:
the method comprises the following steps of reasonably fuzzifying constant stress accelerated degradation data by using a fuzzy theory to obtain fuzzy degradation data.
In the statistical analysis of the accelerated degradation test, a random process is generally used to describe the performance degradation process of the product. Since brownian motion is a random process with continuous temporal parameters and continuous spatial parameters. Many other processes can often be viewed as a functional or promotional in some sense. At present, brownian motion and its popularization have been widely appeared in many pure scientific fields, such as physics, economy, communication theory, biology, management science, and mathematical statistics. Meanwhile, because the brownian motion is closely related to differential equations (such as heat conduction equations and the like), the brownian motion becomes an important channel for probability and analysis. Thus, drifting brownian motion is a random process commonly used to describe the process of performance degradation in statistical analysis of accelerated degradation experiments. For this reason, the present invention assumes the following:
the performance degradation process of the product is assumed to be monotonous, namely, the degradation of the performance is irreversible;
assuming 2 that the product's degradation failure mechanism does not change at each stress level;
suppose 3 that the residual life of the product depends only on the accumulated failure fraction at the time and the stress level at the time, and not on the accumulation mode;
assume that there is no failure in test 4 due to degradation, i.e., the performance degradation of the product does not cross the failure threshold;
the performance degradation of the product of hypothesis 5 can be represented by the drifting brownian motion shown below.
Y(t)＝σB(t)+d(s)·t+y0 (1)
Wherein, Y (t) -random process of product performance degradation. t is a time scale. For example, for a linear degradation process, t is the actual time τ; for the nonlinear degradation process, t can represent the functional form of different actual time τ such as the actual time ln (τ), and the distribution density function is denoted as f (y, t);
y0drift starting point of Brownian motion, product performance at initial time t0Initial value of (2)
B (t) -standard Brownian motion, B (t) N (0, t)
d(s) -drift coefficient, which may also be referred to as the degradation rate. It is a deterministic function only related to stress s and therefore an acceleration model;
σ — diffusion coefficient. The influence of random factors such as inconsistency and instability in the production process of products, measurement capability and measurement error of performance measurement equipment and external noise in the test process on the performance of the products is described. In general, these random factors do not change with time and changes in stress conditions, and thus the diffusion coefficient also does not change with stress and time, and is constant.
A total of n products are divided into k groups, and constant stress accelerated degradation tests are performed at k stress levels, each stress level having nlSamples, collecting m at each stress levellAnd (4) data. Performance degradation data was collected at each stress level.
Fitting the degradation process by the formula (1), selecting different time function forms according to the change trend of failure data, and using a regression equation:
E(Y(t))＝d(S)·t+y0 (2)
a linear or non-linear fit is performed. And then regressing to obtain the degradation rate d (S) at each stress levell). The rate of performance degradation is a deterministic function related only to stress:
whereinIs a function of stress. Obtaining d (S) at each stress levell) And then withForm a plurality of pairsThe regression method was used to extrapolate the degradation rate at normal stress levels.
Estimating the diffusion coefficient of the drifting Brown motion by adopting a maximum likelihood method:
the obtained degradation rate at each stress level is taken into formula (3), and an estimated value of the diffusion coefficient is obtained. Then the product life and reliability are predicted by combining the formula (1) and the formula (4)
And on the premise of giving failure threshold value, a product first-pass time distribution formula
The invention takes a Constant Stress Accelerated Degradation Test (CSADT) as an example, introduces a method for establishing and evaluating a fuzzy life and reliability evaluation model of the accelerated degradation test and a fuzzy theory-based accelerated degradation test prediction method provided by the invention.
(1) Determining a life distribution and an acceleration model of the product.
The life distribution of the product is assumed to follow an exponential distribution. Common acceleration models include Arrhenius (Arrhenius) model, inverse power rate model, allin (Eyring) model, etc., and all of them can represent a log-linear form:wherein,is a certain known function of stress s, for example, for the Arrhenius (Arrhenius) model,s ═ T, T is the absolute temperature; for the inverse power-rate model,s may represent voltage, current, power, etc.; d(s) is the rate of performance degradation; a. b is a constant. And determining an acceleration model of the product according to the characteristics of the product, the sensitive stress, the performance parameter degradation condition and the like.
(2) Processing test data using fuzzy theory
The current statistical analysis method for accelerated degradation tests mainly solves the problem of random uncertainty, such as the influence of product difference, errors and the like on test results. The influence of random uncertainty can be well weakened by the existing model such as particle filtering and combination of Bayesian theory. There is also cognitive uncertainty in accelerated degradation testing. Accuracy of single applied sensitive stress in the test if correlation between working stresses of the product is unknown; the generality of the acceleration model, etc. Due to the defects of cognition and the condition restriction of equipment, expenditure and the like, the accelerated degradation test can only select sensitive stress for testing. In view of test data, accelerated degradation test design is based on a plurality of fully-compliant assumed conditions, but a test environment cannot simulate a real and complex working environment, and only sensitive stress is selected for accelerated stress. Common membership functions can be classified into smaller, larger and intermediate types. Therefore, the invention adopts the symmetrical triangular membership function belonging to the intermediate type to describe data. The specific definition form is:
wherein: k is the number of stress levels, r is the number of failures at each stress level, consistent with the test set in the invention;as a fuzzy numberThe central value of (1), i.e. the actual recording time;is composed ofMagnitude of deviation from the central value (which may also be referred to as blur magnitude), and
the membership function is:
in the present invention, the definitionThe membership function of the current accelerated degradation test data relative to the accelerated degradation test data in the integrated state under the same condition; the central value is set to the actually monitored degradation value, and the blur amplitude is defined as a central value of 0.1 times.
After fuzzy processing, the accurate failure data t of the accelerated degradation test is obtainedijFuzzification into fuzzy failure data with symmetric triangular membership functions
Step two, establishing a linear fuzzy degradation model by combining a fuzzy least square regression method;
(1) fuzzy linear least square regression model
Consider the following fuzzy linear regression model:
wherein x isi(i ═ 1,2,. p) for clarity,for fuzzy numbers, both are considered symmetric triangular fuzzy numbers in the present invention, i.e.(k＝1,2,...,n),Remember m ═ m1,m2,...mn}，g＝{g1,g2,...gn}，a＝{a0,a1,...an}，r＝{r0,r1,...rn}，
Then the regression resultsRespectively as follows:
(2) establishing a linear fuzzy regression model;
from equation (2), it can be seen that the degraded data is blurred, and the time is accurate, so that an accurate input-blur coefficient-blur is formedThe output fuzzy regression model, i.e. the degradation data and the performance degradation rate at stress level l are considered to be fuzzy and recorded asMonitoring time t for product performance at each timelijLet the product performance degradation monitoring value be recorded asAveraging the performance degradation data of the samples used at each stress level to obtainI.e. the average degradation data of the product performance at each stress level, and form data pairsK, wherein l is 1.. k; j ═ 1.. ml. The specific form is shown in table 1.
TABLE 1 regression test data
By adopting the fuzzy least square regression method, the time matrix under each stress level is as follows:
obtaining the stress levels l according to equation (8)Andform a plurality of pairsAccording to an acceleration modelA fuzzy regression model of exact input-fuzzy output-fuzzy coefficients is also constructed. But do notThe method is not a symmetric triangular fuzzy number, and the membership function is not easy to give. And converting the fuzzy number into an interval number by using the concept of horizontal truncation. Given an alpha-level cut set, a fuzzy degradation rate is obtainedAlpha-truncated interval of (2)Interval toolHas monotonicity, so that the natural logarithm value is removed from the interval boundary to obtainAlpha-truncated interval of (2)The invention adopts a traversing calculation method to calculate parameters and determine parameter membership functions.
Step three, model parameter evaluation and service life and reliability fuzzy prediction
(1) Parameter calculation for traversal algorithm
Parameter(s)The form of the fuzzy function is no longer a symmetric triangular fuzzy number, so that the membership function is not easy to give. However, it is not limited toThe value of (A) is correlated with the value of the fuzzy degradation rate, so that the parameter is determined directly in a traversal modeThe fuzzy interval value of (1). Known rate of fuzzy degradationWhen the fuzzy degradation rate under each stress level is taken as a value in the respective fuzzy interval, a group of real degradation rates can be obtained. For example: when in useEach group of [ d ]1(S1)，d1(S2)，...,d1(Sk)]Then a degradation rate d at normal temperature is obtained1(S0). If the value interval is small enough and the degradation rate group number is large enough, the interval of the obtained normal temperature degradation rate true value is closer to the actual value. Practice ofIn the calculation, k stress levels are total, if the fuzzy degradation rate interval under each stress level takes p values, p ^ k groups of degradation rates under high stress exist, p ^ k degradation rates under normal temperature can be obtained through regression, and then a normal temperature degradation rate interval is obtained.
Similarly, according to the formula (3), each group of degradation rate values can obtain an estimated value of the diffusion coefficient, so that p ^ k corresponding sigma values are obtained. According to equation (4), a set of reliability curves can be obtained by using each set of degradation rates and corresponding diffusion coefficients, and the number of the reliability curves is p ^ k.
Example (b):
and (3) analyzing a failure mechanism of a certain transistor to obtain temperature which is sensitive stress of the transistor, and selecting an Arrhenizi model as an acceleration model to carry out an accelerated degradation test on the transistor. It is known that when the temperature is higher than 270 ℃, a remarkable inflection point appears in the degradation curve, which indicates that a new high-temperature failure mechanism is introduced. The test temperature is therefore within 270 ℃. For this purpose, the temperature stress in the test was set to 200 ℃, 220 ℃, 240 ℃ and 260 ℃, respectively. One sample at each stress level. Sampling interval is 0.1 hour, and 500 data are collected under each stress; parameters in the Arrheniz model were set as: a-8.3 x 105Ea is 0.5eV, and σ is 0.5; the initial value is 0 and the performance threshold is 500; the actual working temperature of the product is 55 ℃. Test data were obtained by matlab simulation.
Step one, reasonably fuzzifying accelerated degradation data by using a fuzzy theory to obtain fuzzy degradation data
(1) The accelerated degradation test is basically assumed.
The performance degradation process of the product is assumed to be monotonous, namely, the degradation of the performance is irreversible;
assuming 2 that the product's degradation failure mechanism does not change at each stress level;
suppose 3 that the residual life of the product depends only on the accumulated failure fraction at the time and the stress level at the time, and not on the accumulation mode;
assume that there is no failure in test 4 due to degradation, i.e., the performance degradation of the product does not cross the failure threshold;
the performance degradation of the product of hypothesis 5 can be represented by the drifting brownian motion shown below.
Y(t)＝σB(t)+d(s)·t+y0 (10)
Wherein, Y (t) -random process of product performance degradation. t is a time scale. For example, for a linear degradation process, t is the actual time τ; for the nonlinear degradation process, t can represent the functional form of different actual time τ such as the actual time ln (τ), and the distribution density function is denoted as f (y, t);
y0drift starting point of Brownian motion, product performance at initial time t0Initial value of (2)
B (t) -standard Brownian motion, B (t) N (0, t)
d(s) -drift coefficient, which may also be referred to as the degradation rate. It is a deterministic function only related to stress s and therefore an acceleration model;
σ — diffusion coefficient.
A total of n products are divided into k groups, and constant stress accelerated degradation tests are performed at k stress levels, each stress level having nlSamples, collecting m at each stress levellAnd (4) data. Performance degradation data was collected at each stress level.
Fitting the degradation process by equation (10), selecting different time function forms according to the change trend of the failure data, and using a regression equation:
E(Y(t))＝d(S)·t+y0 (11)
a linear or non-linear fit is performed. Then regressing to obtain each stressDegradation rate at level d (S)l). The rate of performance degradation is a deterministic function related only to stress:
whereinIs a function of stress. Obtaining d (S) at each stress levell) And then withForm a plurality of pairsThe regression method was used to extrapolate the degradation rate at normal stress levels.
Estimating the diffusion coefficient of the drifting Brown motion by adopting a maximum likelihood method:
the obtained degradation rate at each stress level is taken into formula (13), and an estimated value of the diffusion coefficient is obtained. Then, the product life and reliability are predicted by combining the formula (11) and the formula (14)
(1) Determining an acceleration model of a product
Model: the temperature is taken as an acceleration stress, and an acceleration model is selected as an Arrhenius (Arrhenius) model:
when temperature is used as stress, SkI.e. corresponding to the kelvin temperature applied to the product.
(2) Obfuscating degraded data
The central value of the fuzzy degradation data is set as an actual monitoring value, and the fuzzy amplitude is set to be 0.1 time of the actual monitoring value under the stress level.
Establishing a linear fuzzy degradation model of an accelerated degradation test by using fuzzy degradation regression;
(1) fuzzy linear least square regression model
According to the following fuzzy linear regression model:
wherein x isi(i ═ 1,2,. p) for clarity,for the fuzzy number, both are considered as symmetric triangular fuzzy numbers in the present invention, i.e.(k＝1,2,...,n),Recording:
then in the accelerated degradation test, the corresponding parameter matrix becomes:
(2) establishing a linear fuzzy regression model;
according to the fuzzy least square regression theory, regression is carried out on the fuzzy degradation data under each stress level to obtain the fuzzy degradation rate under each stress levelWhereinAlso fuzzy numbers with symmetric trigonometric membership functions, i.e.
Rate of fuzzy degradationForm a plurality of pairsAccording to an acceleration modelA fuzzy regression model of exact input-fuzzy output-fuzzy coefficients is also constructed. But do notThe method is not a symmetric triangular fuzzy number, and the membership function is not easy to give.
The fuzzy degradation rate under each stress level can be obtained through over-simulation calculationComprises the following steps:
step three, model parameter evaluation and service life and reliability fuzzy prediction
And converting the fuzzy number into an interval number by using the concept of horizontal truncation. Given an alpha-level cut set, a fuzzy degradation rate is obtainedAlpha-truncated interval of (2)The interval has monotonicity, so that the natural logarithm value is removed from the interval boundary to obtainAlpha-truncated interval of (2)According to the simulation calculation result, fuzzy logarithm intervals under 4 stress levels are respectively as follows:
each interval takes 11 values (including boundary values), according to the concept of permutation and combination, there are 11^4 ^ 14641 sets of degradation rate value combination, 14641 normal temperature degradation rates are obtained through a regression method, then the interval of the normal temperature degradation rate is [0.0139,0.0172], and corresponding 14641 diffusion coefficient evaluation values are obtained, and the interval [0.5088,0.5130] is obtained through sorting.
According to the reliability formula:
the life prediction formula of the product is as follows:
on the premise of giving a failure threshold value, a product first-pass time distribution formula is as follows:
the fuzzy reliability interval graph (figure 1) of the product, the life prediction value distribution graph (figure 2) of the product fixed failure threshold value and the fuzzy first-pass distribution envelope graph (figure 3) of the product can be obtained.
Claims (1)
1. The accelerated degradation test modeling method based on the fuzzy theory comprises the following steps:
the method comprises the following steps that firstly, a fuzzy theory is utilized, constant stress accelerated degradation data are reasonably fuzzified, and fuzzy degradation data are obtained;
suppose that:
the performance degradation process of the product is assumed to be monotonous, namely, the degradation of the performance is irreversible;
assuming 2 that the product's degradation failure mechanism does not change at each stress level;
suppose 3 that the residual life of the product depends only on the accumulated failure fraction at the time and the stress level at the time, and not on the accumulation mode;
assume that there is no failure in test 4 due to degradation, i.e., the performance degradation of the product does not cross the failure threshold;
suppose 5 the performance degradation of the product can be represented by a drifting brownian motion as shown below;
Y(t)＝σB(t)+d(s)·t+y0 (1)
wherein, Y (t) -a random process of product performance degradation; t represents a time scale;
y0drift starting point of Brownian motion, product performance at initial time t0An initial value of (1);
b (t) -standard Brownian motion, B (t) N (0, t);
d(s) -drift coefficient;
σ — diffusion coefficient;
a total of n products are divided into k groups, and constant stress accelerated degradation tests are performed at k stress levels, each stress level having nlSamples, collecting m at each stress levellA piece of data; collecting performance degradation data at each stress level;
fitting the degradation process by the formula (1), selecting different time function forms according to the change trend of failure data, and using a regression equation:
E(Y(t))＝d(S)·t+y0 (2)
performing linear or nonlinear fitting; and then regressing to obtain the degradation rate d (S) at each stress levell) (ii) a The rate of performance degradation is a deterministic function related only to stress:
wherein:is a function of stress; obtaining d (S) at each stress levell) And then withForm a plurality of pairsExtrapolating by using a regression method to obtain the degradation rate under the normal stress level;
estimating the diffusion coefficient of the drifting Brown motion by adopting a maximum likelihood method:
bringing the obtained degradation rate under each stress level into formula (3) to obtain an estimated value of the diffusion coefficient; then the product life and reliability are predicted by combining the formula (1) and the formula (4)
And on the premise of giving failure threshold value, a product first-pass time distribution formula
Specifically, when the constant stress accelerated degradation test is performed, the following steps are specifically performed:
(1) determining a life distribution and an acceleration model of a product;
setting the service life distribution of the product to obey exponential distribution, and determining an acceleration model of the product according to the self characteristics of the product, the sensitive stress and the performance parameter degradation condition;
(2) processing test data by using a fuzzy theory;
the data are described by adopting a symmetric triangular membership function belonging to an intermediate type, and the specific definition form is as follows:
wherein: k is the number of stress levels, r is the number of failures at each stress level;as a fuzzy numberThe central value of (1), i.e. the actual recording time;is composed ofMagnitude of deviation from central value, and
the membership function is:
definition ofThe membership function of the current accelerated degradation test data relative to the accelerated degradation test data in the integrated state under the same condition; the central value is set as the actually monitored degradation value, and the fuzzy amplitude is defined as the central value which is 0.1 time;
after fuzzy processing, the accurate failure data t of the accelerated degradation test is obtainedijFuzzification into fuzzy failure data with symmetric triangular membership functions
Step two, establishing a linear fuzzy degradation model by combining a fuzzy least square regression method;
(1) fuzzy linear least square regression model
Fuzzy linear regression model:
wherein x isi(i ═ 1,2,. p) for clarity,for the fuzzy number, both are considered as symmetric triangular fuzzy numbers in the present invention, i.e.Remember m ═ m1,m2,...mn}，g＝{g1,g2,...gn}，a＝{a0,a1,...an}，r＝{r0,r1,...rn}，
Regression resultsRespectively as follows:
(2) establishing a linear fuzzy regression model;
the degradation data and the rate of performance degradation at stress level l are ambiguous and are recorded asMonitoring time t for product performance at each timelijLet the product performance degradation monitoring value be recorded asAveraging the performance degradation data of the samples used at each stress level to obtainI.e. the average degradation data of the product performance at each stress level, and form data pairsK, wherein l is 1.. k; j ═ 1.. ml(ii) a The specific form is shown in table 1;
TABLE 1 regression test data
By adopting the fuzzy least square regression method, the time matrix under each stress level is as follows:
obtaining the stress levels l according to equation (8)Andform a plurality of pairsAccording to an acceleration modelA fuzzy regression model of accurate input-fuzzy output-fuzzy coefficient is also formed; converting the fuzzy number into an interval number by using the concept of horizontal truncation; given an alpha-level cut set, a fuzzy degradation rate is obtainedAlpha-truncated interval of (2)The interval has monotonicity, and natural logarithm values are removed from the interval boundary to obtainAlpha-truncated interval of (2)The invention adopts a traversing calculation method to calculate parameters and determine parameter membership functions;
step three, model parameter evaluation and service life and reliability fuzzy prediction
(1) Parameter calculation for traversal algorithm
Determining parameters in a traversal mannerThe value of the fuzzy interval of (1); known rate of fuzzy degradationWhen the fuzzy degradation rate under each stress level is taken as a value in each fuzzy interval, a group of real degradation rates are obtained;
setting a total of k stress levels, if the fuzzy degradation rate interval under each stress level takes p values, then having p ^ k groups of degradation rates under high stress, regressing to obtain p ^ k degradation rates under normal temperature, and further obtaining a normal temperature degradation rate interval;
similarly, according to the formula (3), each group of degradation rate values obtains an estimated value of a diffusion coefficient, and p ^ k corresponding sigma values are obtained; and (4) obtaining a group of reliability curves according to the formula (4) by utilizing each group of degradation rates and corresponding diffusion coefficients, wherein the number of the reliability curves is p ^ k.
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107194478A (en) * | 2017-06-21 | 2017-09-22 | 中国人民解放军国防科学技术大学 | Merge the unit method for predicting residual useful life of lifetime data and Performance Degradation Data |
| CN107220500A (en) * | 2017-05-27 | 2017-09-29 | 上海无线电设备研究所 | Performance degradation experiment Bayesian reliability appraisal procedure based on inverse Gaussian process |
| CN108446475A (en) * | 2018-03-14 | 2018-08-24 | 哈尔滨理工大学 | Based on the electromagnetic relay reliability estimation method for accelerating to degenerate |
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101666662A (en) * | 2009-09-25 | 2010-03-10 | 北京航空航天大学 | Accelerated degradation test prediction method based on fuzzy theory |
| CN102042848A (en) * | 2010-11-23 | 2011-05-04 | 北京航空航天大学 | Prediction method of multi-functional parameter accelerated degradation testing product life based on multivariate hybrid time sequence analysis |
| CN104077445A (en) * | 2014-07-01 | 2014-10-01 | 北京航空航天大学 | Statistical analysis method of accelerated life tests based on fuzzy theory |
| WO2014177041A1 (en) * | 2013-09-18 | 2014-11-06 | 中兴通讯股份有限公司 | Decoding method and device for transmission format combination |
-
2014
- 2014-12-29 CN CN201410838307.9A patent/CN104463331B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101666662A (en) * | 2009-09-25 | 2010-03-10 | 北京航空航天大学 | Accelerated degradation test prediction method based on fuzzy theory |
| CN102042848A (en) * | 2010-11-23 | 2011-05-04 | 北京航空航天大学 | Prediction method of multi-functional parameter accelerated degradation testing product life based on multivariate hybrid time sequence analysis |
| WO2014177041A1 (en) * | 2013-09-18 | 2014-11-06 | 中兴通讯股份有限公司 | Decoding method and device for transmission format combination |
| CN104077445A (en) * | 2014-07-01 | 2014-10-01 | 北京航空航天大学 | Statistical analysis method of accelerated life tests based on fuzzy theory |
Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107220500B (en) * | 2017-05-27 | 2020-07-31 | 上海无线电设备研究所 | Bayesian reliability evaluation method for performance degradation test based on inverse Gaussian process |
| CN107220500A (en) * | 2017-05-27 | 2017-09-29 | 上海无线电设备研究所 | Performance degradation experiment Bayesian reliability appraisal procedure based on inverse Gaussian process |
| CN107194478A (en) * | 2017-06-21 | 2017-09-22 | 中国人民解放军国防科学技术大学 | Merge the unit method for predicting residual useful life of lifetime data and Performance Degradation Data |
| CN107194478B (en) * | 2017-06-21 | 2020-10-27 | 中国人民解放军国防科学技术大学 | Single machine residual life prediction method fusing life data and performance degradation data |
| CN108446475A (en) * | 2018-03-14 | 2018-08-24 | 哈尔滨理工大学 | Based on the electromagnetic relay reliability estimation method for accelerating to degenerate |
| CN109557397A (en) * | 2018-12-03 | 2019-04-02 | 北京遥感设备研究所 | A kind of accelerated storage test method suitable for vacuum device |
| CN109766518A (en) * | 2018-12-13 | 2019-05-17 | 北京航空航天大学 | Consider the uncertain acceleration degeneration modeling and analysis method of individual of sample difference |
| CN109856483A (en) * | 2019-01-30 | 2019-06-07 | 中国电子产品可靠性与环境试验研究所（（工业和信息化部电子第五研究所）（中国赛宝实验室）） | The Primary Component reliability estimation method and device of MMC power module |
| CN109856483B (en) * | 2019-01-30 | 2022-01-11 | 中国电子产品可靠性与环境试验研究所（（工业和信息化部电子第五研究所）（中国赛宝实验室）） | Reliability evaluation method and device for key device of MMC power module |
| CN111832226A (en) * | 2020-07-13 | 2020-10-27 | 中国南方电网有限责任公司超高压输电公司柳州局 | IGBT residual life estimation method based on auxiliary particle filtering |
| CN111832226B (en) * | 2020-07-13 | 2024-04-26 | 中国南方电网有限责任公司超高压输电公司柳州局 | IGBT residual life estimation method based on auxiliary particle filtering |
| CN112069732A (en) * | 2020-09-03 | 2020-12-11 | 中国人民解放军陆军工程大学 | Comprehensive evaluation method for artillery reliability identification test |
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