CN103246821B - A kind of many stress small sample accelerated life test plan design optimization method based on emulation - Google Patents

Abstract

A kind of many stress small sample accelerated life test plan design optimization method based on emulation, its step is as follows: (one) determines EXPERIMENTAL DESIGN alternative collection, optimization object function, acceleration variation model and simulation scale Ω_d, this alternative collection tentatively can construct according to acceleration based on engineering experience change plan design method, it is possible to directly traveling through under given EXPERIMENTAL DESIGN constraints and obtain, simulation scale is chosen according to practical situation；(2) for selected alternative, Monte Carlo method is utilized to generate the Ω under the program_dGroup l-G simulation test data, then carry out statistical analysis to it, obtain the optimization object function value under the program；(3) carry out the trap queuing of alternative finally according to the optimization object function value obtained, determine optimal test scheme.It compensate for being generally basede on the optimization method that priori resolves, when EXPERIMENTAL DESIGN dimension increases, the defect that Optimization Modeling is the most difficult, has expanded the method the emulating base application in this field further.

Description

A kind of many stress small sample accelerated life test plan design optimization method based on emulation

Technical field

The present invention proposes a kind of many stress small sample accelerated life test plan design optimization method based on emulation, particularly to a kind of accelerated life test plan design optimization method, belongs to accelerated test design field.

Background technology

Along with development and the raising of industrial level of modern science and technology, and the development of reliability engineering with, increasing product all has the feature of high reliability long life.The manufacturing cost of this series products is higher, which dictates that the total sample size accelerating can to put in change test is the least.And himself life level is higher, projected life is as long as the several years, how in shorter test period, test data according to a small amount of sample carries out high accuracy and evaluates its index of aging, on the one hand the information utilization to assessment method proposes high requirement, on the other hand also proposes huge challenge to EXPERIMENTAL DESIGN.It is known that accelerated degradation test does not require that large-tonnage product arrives failure state, can directly according to the Changing Pattern of particular product performance parameters, life of product be evaluated.

Accelerated degradation test (Accelerateddegradationtests, ADT) is by collecting product Performance Degradation Data under high stress level, and utilizes these data estimation product reliability and prediction product life-span under routine uses stress.Being introduced as of ADT solves the accelerated life test the fail data the most even problem of zero failure that face in the application and provides new way.How design experiment scheme, such as test sample amount, monitoring time interval, monitoring number of times etc., makes test assessment result the most accurate, tests Least-cost, be the major issue faced in accelerated degradation test engineer applied.

ADT optimizes design and mainly obtains optimal case by analytical optimization method based on priori at present.When the dimension of plan design variable increases, Optimization Modeling is extremely difficult.Additionally, the analytic solutions of optimal case are difficult to even not existed in many instances, and analysis ratiocination process is extremely complex.Therefore, the ADT scheme optimization general framework setting up Engineering Oriented application is the most difficult.

Summary of the invention

It is difficult to assess the problem that complicated accelerated test scheme is good and bad for analytic method, and the problem of high reliability long life product design small sample accelerated test scheme, the invention provides a kind of many stress small sample accelerated life test plan design optimization method based on emulation.

A kind of many stress small sample accelerated life test plan design optimization method based on emulation of the present invention, its objective is: make up and be generally basede on the optimization method that priori resolves, when EXPERIMENTAL DESIGN dimension increases, the defect that Optimization Modeling is the most difficult., under many stress Small Sample Size, accelerated test design will be optimized based on the method for emulation meanwhile, expand the method the emulating base application in this field further.

First this method determines EXPERIMENTAL DESIGN alternative collection, optimization object function, acceleration variation model and simulation scale Ω_d, then for certain alternative, utilize Monte Carlo (MonteCarlo) method to generate the Ω under the program_dGroup l-G simulation test data, then carry out statistical analysis to it, obtain the optimization object function value under the program, carry out the trap queuing of alternative finally according to the optimization object function value obtained, determine optimal test scheme.

A kind of many stress small sample accelerated life test plan design optimization method based on emulation of the present invention can set up required hypothesis, and (these conditions are the hypotheses that accelerated degradation test can be carried out, only these assume to set up, and test just can be carried out) as follows:

The change assuming 1 performance parameter is irreversible, should be i.e. dull；

Assume that 2 normal stress levels are consistent with the performance parameter variations mechanism under proof stress level.For from statistical nature, normal stress level is similar with the performance parameter variations rule under proof stress level, all can use same model form to describe；

Assuming that 3 proof stress levels are the highest, performance parameter variations is the fastest.

Based on above-mentioned it is assumed that the present invention proposes a kind of many stress small sample accelerated life test plan design optimization method based on emulation, as it is shown in figure 1, the method specifically comprises the following steps that

Step one: determine EXPERIMENTAL DESIGN alternative collection, optimization object function, acceleration variation model and simulation scale Ω_d, wherein alternative collection is tentatively to construct according to acceleration based on engineering experience change plan design method, also directly can travel through under given EXPERIMENTAL DESIGN constraints and obtain.Simulation scale is chosen according to practical situation.

Step 2: for selected alternative, utilizes MonteCarlo method to generate the Ω under the program_dGroup l-G simulation test data, then carry out statistical analysis to it, obtain the optimization object function value under the program.

Step 3: carry out the trap queuing of alternative finally according to the optimization object function value obtained, determine optimal test scheme.

Wherein, in " the alternative collection " described in step one, its building method is as follows:

The element that alternative collection comprises: proof stress level, sample number under each stress level, the test period at each temperature, the testing time etc. at a temperature of each.

Alternative collection tentatively constructs according to acceleration based on engineering experience change plan design method, also directly can travel through under given EXPERIMENTAL DESIGN constraints and obtain.

During structure alternative collection, need to be considered as following simplification measure:

(1) proof stress number of levels and the horizontal span of proof stress are directly specified, and proof stress level rounds after being spacedly distributed.If proof stress is temperature, test temperature is taken as the integral multiple of 5 DEG C, and test temperature interval is more than or less than 5 DEG C.Such as, proof stress number of levels is 3, and the highest and minimum test temperature is respectively 90 DEG C and 65 DEG C, then intermediate experiment temperature is 75 DEG C or 80 DEG C.

(2) distribution of the sample size equivalent under each proof stress level, distributes surplus for unequal situation by minimum stress level one by one.Such as, proof stress number of levels is 3, has 8 samples, then first 2 (8/3=2.67) of equivalent distribution under each stress level, each one sample of distribution under minimum and intermediate stress level, minimum, the middle and sample size under high stress level is respectively 3,3,2.

(3) test period under each proof stress level is less than 2 times of this level lower life-span.

(4) test period of each proof stress level is fixed, and tests the most at equal intervals；Test period is not shorter than the time under this stress level needed for single test all over products；Meanwhile, test period is taken as the integral multiple of predetermined minimum time length (the most directly regulation).

(5) testing time under each proof stress level is no less than 10 times, less than the time needed for the test period under this stress level/single test all over products.

Wherein, refer in " optimization object function " described in step one:

Accelerate change EXPERIMENTAL DESIGN optimization object function to be intended to set up a kind of function, weigh the estimated accuracy size of life of product (particularly Q-percentile life), to determine the trap queuing of testing program.Life estimation precision can be weighed with the asymptotic variance of life estimation, mean square error, simple error (such as relative error, absolute error), width of confidence interval expectation etc..

It is most commonly used that asymptotic variance, is based on large sample theory using asymptotic variance as the criterion weighing life estimation precision, may be used for solving Maximum-likelihood estimation (MLE) etc. and estimate complex distribution, be difficult to resolve estimated accuracy when providing estimate variance and weigh problem.According to large sample theory, the limiting distribution of estimator is normal distribution.

Asymptotic variance is mainly used in weighing unbiased or the estimated accuracy of Asymptotic upbiased estimation.Q-percentile life asymptotic variance computational methods of based on MLE are given below:

IfFor the MLE of θ, and(can try to achieve according to Fisher information battle array).So, Q-percentile life t_R=h (θ) is estimated as

${\hat{t}}_R=h\left(\widehat{\mathrm{\θ}}\right)---\left(1\right)$

Its asymptotic variance can be estimated to obtain by following formula

$\mathrm{AVar}\left(t_R\right)={\hat{H}}^{T}V\hat{H}---\left(2\right)$

Wherein $\hat{H}={\frac{\∂h\left(\mathrm{\θ}\right)}{\∂\mathrm{\θ}}|}_{\mathrm{\θ}=\widehat{\mathrm{\θ}}}.$

Wherein, it is derived by according to physical process in " the acceleration variation model " described in step one, also can obtain according to test data fitting.The former explicit physical meaning, but generally model form is complicated, and model parameter randomness is difficult to obtain, the more difficult enforcement of its fail-safe analysis；The latter directly uses statistical model to describe the Changing Pattern of performance parameter, without physics derivation, although partial parameters cannot provide clear and definite physical significance, but model form is relatively simple, model parameter randomness can directly obtain according to statistic analysis result, and the scope of application in engineering is wider.

In engineering reality, the acceleration variation model of information completely is generally difficult to obtain.When accelerating change EXPERIMENTAL DESIGN, that this prior information does not usually have or inapt.It is given below and the one that all kinds of Changing Pattern fitness are stronger is accelerated variation model:

If y_ijkFor i-th temperature T_iLower jth sample kth moment t_ijkAmount of degradation, i=1,2 ..., M, j=1,2 ..., n_i, k=1,2 ..., l_i, and

$y_{\mathrm{ijk}}=\mathrm{Aexp}(-\frac{B}{T_i})t_{\mathrm{ijk}}^{\mathrm{\α}}+{\mathrm{\ϵ}}_{\mathrm{ijk}},{\mathrm{\ϵ}}_{\mathrm{ijk}}~N(0,{\mathrm{\σ}}_{\mathrm{\ϵ}}^2)---\left(3\right)$

In formula, A is stochastic effect parameter；B=E/k_BIt is fixed effect parameter with α, the most identical to the whole samples at all temperature.

Assume that the defective threshold value of particular product performance parameters is D, then temperature T₀Under life-span t₀Can be calculated by following formula

$t_0={\left[\frac{D}{A}\exp \left(\frac{B}{T_0}\right)\right]}^{1/\mathrm{\α}}---\left(4\right)$

Wherein, " the optimization object function value under the program " described in step 2, its circular is as follows:

For alternative d_l, utilize MonteCarlo method to generate the Ω under the program_dGroup l-G simulation test data.For ω group l-G simulation test data, carry out statistical analysis, obtain optimization object function partial estimation value U of Life estimating corresponding to these group data and correspondence_lω。

All Ω_dAfter group l-G simulation test data analysis completes, by U_lωMeansigma methods optionally d_lOptimization object function value, i.e.

$U_l=\frac{1}{{\mathrm{\Ω}}_d}\underset{\mathrm{\ω}=1}{\overset{{\mathrm{\Ω}}_d}{\mathrm{\Σ}}}{U}_{\mathrm{l\ω}}---\left(5\right)$

Wherein, should be noted that problems with during " carrying out the trap queuing of alternative according to the optimization object function value obtained " described in step 3:

In engineering reality, by sensitivity analysis, the robustness of testing program estimated accuracy can be analyzed, if the robustness of optimal test scheme is poor, the most sane testing program should be chosen from more excellent alternative as optimal test scheme.

The deviation between Robustness Analysis Main Analysis prior information and its actual value of the testing program estimated accuracy influence degree to testing program estimated accuracy, can by there being zero deflection time optimization object function value between ratio weigh, i.e.

$\mathrm{RV}=\frac{U_{\mathrm{bias}}}{U_0}---\left(6\right)$

Wherein, U₀And U_biasBeing respectively prior information is true and optimization object function value time prior information there is certain deviation.Clearly for given prior information deviation, RV is closer to 1, and testing program is the most insensitive to the deviation of prior information, and its estimated accuracy is the most sane；Otherwise, RV is further away from 1, then testing program is the most sensitive to the deviation of prior information, and its estimated accuracy is the most unstable.

A kind of many stress small sample accelerated life test plan design optimization method based on emulation of the present invention, its advantage is:

First EXPERIMENTAL DESIGN alternative collection, optimization object function, acceleration variation model and simulation scale Ω are determined_d, then for certain alternative, utilize MonteCarlo method to generate the Ω under the program_dGroup l-G simulation test data, then carry out statistical analysis to it, obtain the optimization object function value under the program, carry out the trap queuing of alternative finally according to the optimization object function value obtained, determine optimal test scheme.

Make up and be generally basede on the optimization method that priori resolves, when EXPERIMENTAL DESIGN dimension increases, the defect that Optimization Modeling is the most difficult., under many stress Small Sample Size, accelerated test design will be optimized based on the method for emulation meanwhile, expand the method the emulating base application in this field further.

Accompanying drawing explanation

Fig. 1 is a kind of many stress small sample accelerated life test plan design optimization method flow chart based on emulation of the present invention；

Fig. 2 is certain accelerometer constant multiplier accelerated life test plan method for optimizing flow chart in detailed description of the invention;

Fig. 3 is distribution of the pseudo-life-span (Ω at certain accelerometer constant multiplier 60 DEG C and 90 DEG C_y=1000).

In figure, symbol description is as follows:

D alternative collection

d_iConcrete testing program

Ω_dSimulation scale

S_lAccelerated test stress level

Detailed description of the invention:

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Following example are to carry out implementing according to flow process as shown in Figure 1, and the present embodiment have chosen certain accelerometer constant multiplier and implements example as the method.Constant multiplier is as one of accelerometer critical performance parameters, and the long-life of this product is an important performance indexes of high-precision accelerometer.This method is that the acceleration change EXPERIMENTAL DESIGN optimization of certain accelerometer constant multiplier provides effective way.

A kind of many stress small sample accelerated life test plan design optimization method based on emulation of the present invention, as a example by certain accelerometer constant multiplier, it is as follows that it is embodied as step, as shown in Figure 2:

Step one: first determine EXPERIMENTAL DESIGN alternative collection, optimization object function, acceleration variation model and simulation scale Ω_d。

This example mainly utilizes above method, selects to be optimized to test period.According to EXPERIMENTAL DESIGN result, accelerometer constant multiplier accelerates change test and determines that respectively carrying out about 500h at 60 DEG C and 90 DEG C tests, taking testing scheme at equal intervals under each test temperature, test period is defined as the integral multiple of 4h, i.e. 4h, 8h, 12h, 16h ....Regulation testing time is no less than 30 times.Thus structure accelerometer constant multiplier accelerates the alternative collection of change test, is shown in Table 1.

Certain accelerometer constant multiplier of table 1 accelerates variation model checking test alternative collection

Optimization object function elects progressive variance as, and its concrete form is as the formula (2).The parameter set up accelerates variation model

Wherein μ_A=2.31×10⁵,σ_AAnd σ_BCan determine according to the dispersibility of magnet steel trial curve model parameter, it is assumed here that the coefficient of variation of parameter A and B is respectively 0.05 and 0.01, i.e. σ_A=0.05μ_A, σ_B=0.01μ_B；Random scatter characteristic (can be obtained by actual-structure measurement) according to this accelerometer constant multiplier test error, determines σ_ε=5ppm。

Step 2 calculates corresponding object function for different scheme collection.

This object function is relevant with parameter puppet life parameter estimation.So for solving object function, needing first to emulate according to different schemes and the acceleration variation model determined, thus the parameter in pseudo-life-span estimated.

Test temperature T is generated according to given acceleration variation model_iUnder Ω_yGroup change curve emulation data.For one group of emulation data therein, being obtained the pseudo-life estimation of correspondence by nonlinear fitting, model of fit sees below formula

${\left(\frac{\mathrm{\Δ}{K}_1}{K_1}\right)}^{\′}=\mathrm{Aexp}(-\frac{B}{8.314}\·\frac{1}{T})\ln t---\left(8\right)$

Pseudo-life estimation is

$\hat{t}=\exp \left[\frac{1}{\hat{A}}{\left|{\left(\frac{\mathrm{\Δ}{K}_1}{K_1}\right)}^{\′}\right|}_f\exp (\frac{\hat{B}}{8.314}\·\frac{1}{T})\right]---\left(9\right)$

WhereinWithIt is respectively the match value of A and B.

In test temperature T obtained_iUnder Ω_yOn the basis of individual pseudo-life estimation, determine distribution pattern and the distributed constant in pseudo-life-span.Fig. 3 gives the pseudo-life-span experience distribution of the corresponding 1000ppm obtained according to model, and wherein transverse axis is the logarithm puppet life-span, and red curve is the logarithm normal distribution probability density curve of matching.The most visible, the pseudo-life-span preferably can describe by logarithm normal distribution.Table 2 gives corresponding estimation of distribution parameters result.

Pseudo-life-span distributed constant (Ω at 260 DEG C and 90 DEG C of table_d=2000)

In view of the pseudo-life-span can use logarithm normal distribution approximate description, using the logarithm variance of Q-percentile life at a temperature of normal shelf as optimization object function.

For testing program d_l, first pseudo-life-span distribution determined by basis, generate one group of puppet life-span emulation data that the program is corresponding.According to formula, pseudo-life-span acceleration model is

$\ln t={\left|{\left(\frac{\mathrm{\Δ}{K}_1}{K_1}\right)}^{\′}\right|}_f{A}^{-1}\exp \left(\frac{B}{T}\right)=A^{\′}\exp \left(\frac{B}{T}\right)---\left(10\right)$

WhereinTo data (T_i, lnt_ij), use nonlinear fitting can obtain the estimation of parameter A ' and BWith, then normal shelf temperature T₀Under the logarithm Life estimating of reliability R be

In formula, s (T_i) it is test temperature T_iThe sample standard deviation of corresponding emulation of pseudo-life-span data.

Repeat said process Ω_dSecondary, obtain Ω_dIndividual logarithm Life estimating.By testing program d_lUnder object function be defined as

Wherein For kth (k=1,2 ..., Ω_d) organize the logarithm Life estimating emulating data.

Table 2 lists the target function value of each testing program in table 1, it should be noted that the target function value of each testing program numerical value during carrying out Multi simulation running, it may happen that change, if Multi simulation running result difference is relatively big, can be averaged by Multi simulation running.

Target function value (the Ω of each testing program of table 2_d=2000)

Step 3: the principle of preferred version is to carry out the trap queuing of alternative according to optimization object function value, is defined as optimal test scheme by the alternative that optimization object function value is minimum.So, according to the comparison of each scheme object function of table 2, scheme 4 should be used as optimal test scheme, its scheme is: respectively carry out the test of 5 samples of 496h at 60 DEG C and 90 DEG C, taking testing scheme at equal intervals under each test temperature, test period is 16h, and testing time is 31 times.Owing to the progressive variance difference between above scheme is little, it is possible to according to the constraint of actual each side, testing program is carried out suitable adjustment.

Based on above example is plan design result, carry out the preferred of testing program with observation interval for changing value.According to above step, it is also possible to stress level number, under each stress, sample number is carried out preferably as changing value, and method is similar to above example, and therefore not to repeat here.

Claims (5)

1. many stress small sample accelerated life test plan design optimization method based on emulation, this meter optimization method needs following assumed condition to set up:

Assume 1: the change of performance parameter is irreversible, should be i.e. dull；

Assume 2: normal stress level is consistent with the performance parameter variations mechanism under proof stress level；For from statistical nature, normal stress level is similar with the performance parameter variations rule under proof stress level, all can use same model form to describe；

Assume 3: proof stress level is the highest, and performance parameter variations is the fastest；

It is characterized in that: the method specifically comprises the following steps that

Step one: determine EXPERIMENTAL DESIGN alternative collection, optimization object function, acceleration variation model and simulation scale Ω_d, wherein alternative collection is tentatively to construct according to acceleration based on engineering experience change plan design method, or direct traversal under given EXPERIMENTAL DESIGN constraints obtains, and simulation scale is chosen according to practical situation；

Step 2: for selected alternative, utilizes MonteCarlo method to generate the Ω under the program_dGroup l-G simulation test data, then carry out statistical analysis to it, obtain the optimization object function value under the program；

Step 3: carry out the trap queuing of alternative finally according to the optimization object function value obtained, determine optimal test scheme；

Wherein, in " the alternative collection " described in step one, its building method is as follows:

The element that alternative collection comprises: proof stress level, sample number under each stress level, the test period at each temperature, the testing time at a temperature of each；

During structure alternative collection, use and simplify measure below:

(1) proof stress number of levels and the horizontal span of proof stress are directly specified, and proof stress level rounds after being spacedly distributed；If proof stress is temperature, test temperature is taken as the integral multiple of 5 DEG C,

(2) distribution of the sample size equivalent under each proof stress level, distributes surplus for unequal situation by minimum stress level one by one；

(3) test period under each proof stress level is less than 2 times of this level lower life-span；

(4) test period is not shorter than the time under this stress level needed for single test all over products, and meanwhile, test period is taken as the integral multiple of predetermined minimum time length；Taking testing scheme at equal intervals under each test temperature, test period is defined as the integral multiple of 4h, i.e. 4h, 8h, 12h, 16h；

In the test of each stress level, each test period is identical, tests the most at equal intervals

(5) testing time under each proof stress level is no less than 10 times, less than the test period under this stress level divided by the time needed for single test all over products.

A kind of many stress small sample accelerated life test plan design optimization method based on emulation the most according to claim 1, it is characterised in that: refer in " optimization object function " described in step one:

Accelerating change EXPERIMENTAL DESIGN optimization object function is to set up a kind of function, weighing the estimated accuracy size of life of product particularly Q-percentile life, to determine the trap queuing of testing program；Life estimation precision can be weighed with the expectation of the asymptotic variance of life estimation, mean square error, simple error or width of confidence interval；

Asymptotic variance is the estimated accuracy for weighing unbiased and Asymptotic upbiased estimation；Q-percentile life asymptotic variance computational methods of based on Maximum-likelihood estimation MLE are given below:

IfFor the MLE of θ, andSo, Q-percentile life t_R=h (θ) is estimated as

${\hat{t}}_R=h\left(\widehat{\mathrm{\θ}}\right)---\left(1\right)$

Its asymptotic variance is estimated to obtain by following formula

$AVar\left(t_R\right)={\hat{H}}^{T}V\hat{H}---\left(2\right)$

Wherein $\hat{H}=\frac{\∂h\left(\mathrm{\θ}\right)}{\∂\mathrm{\θ}}{|}_{\mathrm{\θ}=\widehat{\mathrm{\θ}}}.$

A kind of many stress small sample accelerated life test plan design optimization method based on emulation the most according to claim 1, it is characterized in that: be to be derived by according to physical process in " the acceleration variation model " described in step one, or obtain according to test data fitting；

A kind of accelerate variation model to all kinds of Changing Pattern matchings be given below:

If y_ijkFor i-th temperature T_iLower jth sample kth moment t_ijkAmount of degradation, i=1,2 ..., M, j=1,2 ..., n_i, k=1,2 ..., l_i, and

$y_{ijk}=A\exp (-\frac{B}{T_i})t_{ijk}^{\mathrm{\α}}+{\mathrm{\ϵ}}_{ijk},{\mathrm{\ϵ}}_{ijk}~N(0,{\mathrm{\σ}}_{\mathrm{\ϵ}}^2)---\left(3\right)$

In formula, A is stochastic effect parameter；B=E/k_BIt is fixed effect parameter with α, the most identical to the whole samples at all temperature；

Assume that the defective threshold value of particular product performance parameters is D, then temperature T₀Under life-span t₀Calculated by following formula

$t_0={\[\frac{D}{A}\exp \left(\frac{B}{T_0}\right)\]}^{1/\mathrm{\α}}.---\left(4\right)$

A kind of many stress small sample accelerated life test plan design optimization method based on emulation the most according to claim 1, it is characterised in that: " the optimization object function value under the program " described in step 2, its circular is as follows:

For alternative d_l, utilize MonteCarlo method to generate the Ω under the program_dGroup l-G simulation test data；For ω group l-G simulation test data, carry out statistical analysis, obtain optimization object function partial estimation value U of Life estimating corresponding to these group data and correspondence_lω；

All Ω_dAfter group l-G simulation test data analysis completes, by U_lωMeansigma methods optionally d_lOptimization object function value, i.e.

$U_l=\frac{1}{{\mathrm{\Ω}}_d}\underset{\mathrm{\ω}=1}{\overset{{\mathrm{\Ω}}_d}{\Σ}}{U}_{l\mathrm{\ω}}.---\left(5\right)$

A kind of many stress small sample accelerated life test plan design optimization method based on emulation the most according to claim 1, it is characterized in that: during " carrying out the trap queuing of alternative according to the optimization object function value obtained " described in step 3, carry out according to following rule:

The Robustness Analysis of testing program estimated accuracy is the influence degree analyzing the deviation between prior information and its actual value to testing program estimated accuracy, and during by there being zero deflection, the ratio between optimization object function value is weighed, i.e.

$RV=\frac{U_{bias}}{U_0}---\left(6\right)$

Wherein, U₀And U_biasBeing respectively prior information is true and optimization object function value time prior information there is certain deviation；For given prior information deviation, RV is closer to 1, and testing program is the most insensitive to the deviation of prior information, and its estimated accuracy is the most sane；Otherwise, RV is further away from 1, then testing program is the most sensitive to the deviation of prior information, and its estimated accuracy is the most unstable.