CN102682208A - Turbine disk probability failure physical life predicting method based on Bayes information update - Google Patents

Abstract

The invention relates to a turbine disk probability failure physical life predicting method based on Bayes information update, which comprises the following steps that 1, failure physical information of a turbine disk is determined in a reliability analyzing method based on physics of failure according to the structural characteristics of the aircraft engine turbine disk; 2, the failure physical information of the aircraft engine turbine disk obtained in step 1 and the existing failure information obtained by maintenance data statistics are analyzed in an FTA (failure tree analysis) /FMECA (failure mode, effects & criticality analysis) method to obtain the main failure mode and the failure position of the turbine disk, and uncertain factors and inaccurate data of the turbine disk facing whole life cycle are collected and cleared up; and 3, a failure physical life predicting model of the aircraft engine turbine disk is established according to the main failure mode and the failure position of the turbine disk obtained in step 2. The method disclosed by the invention has the beneficial effects that the design cycle of the aircraft engine turbine disk can be obviously shortened, the development cost is reduced, and the life reliability of the aircraft engine turbine disk can be obviously improved.

Description

Turbine disk probability fault physical life Forecasting Methodology based on the Bayes information updating

Technical field

The invention belongs to the reliability design and the life prediction field of engineering goods, specifically is a kind of reliability design and life prediction new method towards the aeromotor wheel disc.

Background technology

Aeromotor is the aircraft power device, for it provides flight thrust, is described as " heart " of aircraft.Aeromotor is accurate, complicated high-tech product, and a large amount of parts are worked under the ten minutes rugged environment, are bearing high temperature, high pressure and high-revolving working load.Development along with aircraft industry; Aero-engine performance is required to improve constantly; Thrust-weight ratio constantly increases; Make that temperature all improves constantly with rotating speed before the aero-turbine, cause each parts of aeromotor particularly the turbine rotor parts under the cycling hot load of complicacy more and mechanical load, work, its fatigue at high temperature Problem of Failure is more and more outstanding.Therefore, want to design efficient turbine, must have more accurately, the life prediction model and the analysis method for reliability of more perfect this class formation of reflection.This reliability of service life and health evaluating to aeromotor high temperature labyrinth has proposed stern challenge.

As the gas turbine of one of gas turbine three big vitals, the quality of its performance has fundamental influence to the overall performance of gas-turbine unit, and wherein the turbine disk is the typical permanance of aeromotor and one of fracture key component.Shown in Figure 1 is certain type aero-turbine structural representation, and the major function of the turbine disk is that mounting blades is with through-put power.The turbine disk is in high temperature, at a high speed down work, in a single day owner's load part is bearing the reciprocation of load such as centrifugal force, thermal stress and vibration stress during work, under this harsh and unforgiving environments, destructive malfunction takes place and will cause extremely serious consequence.Therefore; The residual life of correct assessment and prediction aero-engine turbine disk; Bring into play the effect of aeromotor to greatest extent and avoid unexpected accident and disaster, be of great practical significance for China's sustainable economic development and conservation-minded society's construction.

The main failure mode of the turbine disk is: low-cycle fatigue, break, the interaction between creep etc. and these patterns.The turbine disk avoids the ability of these faults to depend on its design, material character and working environment.The material that Component Design adopted is certain, and working environment can change, thereby the uncertain factor that parts were faced in cycle life-cycle in each stage has decisive influence to its life-span.The mutual relationship of all of these factors taken together has influence on the consumption of component life.The other factors that influences life consumption also has: manufacturing and fault in material, assembling and maintenance error, foreign object damage, transfinite.The life-span of aero-engine turbine disk and reliability are one of principal elements of restriction machine life and reliability level.

The working environment of high temperature, high pressure makes that the fatigure failure mechanism of aero-engine turbine disk is complicated unusually; Be mainly reflected on the characteristics such as complex load, multiple environmental factor and multiple failure mode, the life prediction of turbine disk research mainly concentrates on the determinacy life prediction of simplifying under load and the single failure mode at present.Along with improving gradually and working environment harsher of turbine disc structure performance parameter; The contradiction that it is found that traditional fatigue life prediction method and engineering practice manifests further, and this is because traditional determinacy fatigue life prediction method can not be described the uncertainty of outwardness in the engineering preferably.For economy and the security that guarantees structure, people have successively been developed safe life design, permanance and damage tolerance design.Yet; Mechanical component by conventional fatigue strength design also can damage sometimes; Trace it to its cause; Important problem is in conventional fatigue strength design, regards the performance index of load, material, the data such as physical dimension of part as determined value, but these factors random character of all having significantly, can not ignore in fact.When using determinacy fatigue life prediction model to carry out life prediction, often be difficult to complex optimum and balance are carried out in aspects such as target weight, serviceable life and other design criteria, also can't provide quantitative reliability index.To the uncertainty that has in the structure fatigue life analysis, be incorporated in the structural fatigue analysis reliability imperative.

The load form that the turbine disk bears is various, thereby sets up accurately physical model and describe its life-span rule and have big difficulty.At present do not find as yet it is carried out based on the fatigue lifetime of probability fault physics and the research of fail-safe analysis aspect.Existing determinacy fatigue life prediction method develops towards the uncertain fatigue life prediction direction based on probability statistics, and tradition is based on the theoretical statistical method of large sample progressive learning and be not suitable for the rare characteristics of aero-engine turbine disk test sample.Therefore; For having the significantly aeromotor of characteristics such as " highly reliable ", " small sample "; Failure mechanism, inefficacy cause and uncertainty analysis in conjunction with the turbine disk; The method that needs a kind of probability fatigue life prediction based on Bayes information updating, Physical Methods of Reliability Failure of research is to carry out reliability design to it.

Summary of the invention

Deficiency when the object of the invention is used for the aero-engine turbine disk Intensity Design to traditional fatigue life prediction method has proposed the aeromotor wheel disc probability fault physical life Forecasting Methodology based on the Bayes information updating.

Technical scheme of the present invention is: the aeromotor wheel disc probability fault physical life Forecasting Methodology based on the Bayes information updating comprises the steps:

Step 1:, use the fault physical message of confirming the turbine disk based on the analysis method for reliability of fault physics according to aeromotor wheeling disk structure characteristic;

Step 2: the fault physical message of the aeromotor wheel disc that utilization FTA/FMECA method obtains step 1 and obtain the main failure mode and the abort situation thereof of wheel disc by the existing failure message analysis that the mantenance data statistics obtains, collect also the arrangement wheel disc towards the uncertain factor and the imprecise data in cycle life-cycle;

Step 3: the fault physical life forecast model that main failure mode of wheel disc that obtains according to step 2 and abort situation are set up the aeromotor wheel disc.

Step 4: the uncertainty in the wheel disc expectancy life prediction that the utilization Probability Statistics Theory is confirmed and quantization step 2 obtains.

Step 5: the fault physical life forecast model that obtains according to step 3; Utilization Bayes information updating and fault physical technique; Model parameter in the life prediction model that step 4 is obtained is imported with distribution form with test control parameter; And, set up the mixing probability fault physical life Forecasting Methodology of wheel disc with the output of the form of Life Distribution;

Step 6: the higher-dimension integral and calculating of Bayes reasoning in the utilization Markov chain Monte-Carlo emulation settlement steps to deal 5, the probability fault physics bimetry and the range of indeterminacy thereof of calculating aeromotor wheel disc.

The invention has the beneficial effects as follows: in conventional fatigue strength design; Tradition determinacy fatigue life prediction method can not be described the uncertainty of outwardness in the engineering preferably; And regard the performance index of load, material, the data such as physical dimension of part as determined value, but these factors random character of all having significantly, can not ignore in fact.When using determinacy fatigue life prediction model to carry out life prediction, often be difficult to complex optimum and balance are carried out in aspects such as target weight, serviceable life and other design criterias, also can't provide quantitative reliability index.Because the aeromotor wheel disc has characteristics such as " small sample ", " highly reliable " significantly; Failure message and relevant mantenance data are seldom; Therefore traditional based on the theoretical statistical method of large sample progressive learning and be not suitable for the rare characteristics of aeromotor test sample; And traditional determinacy life-span prediction method has bigger limitation in the life prediction of wheel disc, is not suitable for the engine wheel disc is carried out expectancy life prediction and fail-safe analysis towards cycle life-cycle.And, can carry out localization of fault and Analysis of Failure Mechanism to structure based on the life-span prediction method of probability fault physics; Through setting up fault physical life model, before the physical test of aeromotor wheel disc, just find out structure latent defect and fault cause; Thereby estimate structure residual Q-percentile life, and, reduce unnecessary test number (TN) and cost, avoided " small sample " of aeromotor wheel disc and cause the few problem of failure message through taking all factors into consideration existing knowledge and the information in cycle structure life-cycle.The utilization Probability Statistics Theory is classified to the uncertainty in cycle structure life-cycle and is quantized; Through repetition test and MCMC virtual emulation; Probabilistic dispersiveness and randomness are to the rule that influences of its life-span and reliability in announcement cycle structure life-cycle; Final different target or the bimetry of the influence of uncertain factor in various degree that obtains to take all factors into consideration in the fault physical modeling distributes and range of indeterminacy, thereby reaches the purpose of improving structural design.The present invention can shorten the aeromotor wheel disc design cycle significantly; Reduce the expense of aeromotor wheel disc exploitation; Owing to can improve the precision and the informedness of test findings, thereby improve design or carry out innovative design, therefore can improve the reliability of service life of aeromotor wheel disc significantly.

Description of drawings

The aero-engine turbine disk structural representation that Fig. 1 one embodiment of the invention is directed against.

Bayes reasoning frame diagram in Fig. 2 embodiments of the invention in the step 5.

Fig. 3 main flow chart of the present invention.

In Fig. 4 embodiments of the invention in the step 6 bimetry based on No. 6 sample of VBM model distribute and actual measurement life-span comparison diagram.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment the present invention is described further.

Combine embodiment, accompanying drawing that the present invention is done further describes at present: a kind of turbine disk probability fault physical life Forecasting Methodology based on the Bayes information updating, and as shown in Figure 3, comprise the steps:

Step 1:, use the fault physical message of confirming the turbine disk based on the analysis method for reliability of fault physics according to aeromotor wheeling disk structure characteristic;

In this step; According to aeromotor wheeling disk structure characteristic; As shown in Figure 1, the aeromotor wheel disc is carried out the reliability failure physical analysis, analyze and the loading spectrum data processing through stress analysis, heat; Confirm the fault physical message of aeromotor wheel disc, comprise abort situation, failure mechanism, fault mode and impact analysis thereof.

Step 2: utilization FTA/FMECA method (fault tree analysis; Fault Tree Analysis; Be called for short FTA)/(failure mode influence and seriousness analysis; Failure Mode; Effects and Criticality Analysis is called for short FMECA) the fault physical message of aeromotor wheel disc that step 1 is obtained and obtain the main failure mode and the abort situation thereof of wheel disc by the existing failure message analysis that the mantenance data statistics obtains, collect also the arrangement wheel disc towards the uncertain factor and the imprecise data in cycle life-cycle;

In this step; The easy damaged position that mainly obtains wheel disc is the low cycle fatigue failure at wheel disc pinhole position and the fatigue-creep failure of wheel rim with main failure mode, and obtains uncertain factor and the imprecise data of wheel disc from cycle life-cycle in each stages such as design, manufacturing, test, use and maintenances.Consider mainly that when the aeromotor wheel disc being carried out the expectancy life prediction physics aspect following two is uncertain: 1. loading environment is (like test loading stress, strain and loading cycle T ₀); 2. material properties is (like elastic modulus E and fatigue limit σ _Lim); The statistical uncertainty of three aspects below considering: the 1. uncertain and output measuring error of crack detection; 2. import the dispersiveness of control variable; 3. associated materials property parameters distribution (like cyclic strain hardenability value n '); The model uncertainty of two aspects below considering: 1. model parameter; 2. model output error.

Various fail datas such as the fault data through the resulting wheel disc of direct statistics, maintenance record, detections regularly and performance degradation data are the failure messages in the design of aeromotor wheel disc, test or the actual moving process, so can be used as known technology and do not describe its statistic processes in detail.In addition, the FTA/FMECA in this step analyzes and is the prior art in the fail-safe analysis, therefore this step is not elaborated, but those of ordinary skill in the art can implement this step based on above-mentioned prompting.

Step 3: the fault physical life forecast model that main failure mode of wheel disc that obtains according to step 2 and abort situation are set up the aeromotor wheel disc;

In the present embodiment; The physical model of aeromotor wheel disc is as shown in Figure 1, is set out by wheel disc material properties and loading environment that step 2 obtains, and Physical Methods of Reliability Failure is applied in the fatigue life prediction; Based on the fault physical analysis in the step 2; (Viscosity-Based Model VBM), promptly has formula (1) to set up the fault physical life forecast model-correction viscosity model of physical construction

N _f=C (Δ ε _In(E _p-Δ W _FLT ₀) ^φ) ^αFormula (1)

In the formula, N _fBe the wheel disc actual measurement life-span;

Δ ε _InBe the inelastic strain scope, available plastic strain ranges Δ ε under the pure fatigue condition _pReplace;

Δ W _FLPlastic strain ability density during for the following stress of fatigue limit, the formula of embodying does

σ _LimFatigue limit for wheel disc;

E is the elastic modulus of wheel disk material;

T ₀Be the primary stress circulation complete period;

C, φ and α are model parameter, can be obtained by the test figure utilization least square fitting of wheel disc;

E _pBe sticky parameter, the formula of embodying is formula (2):

$E_p=\left\{\begin{array}{cc}{T}_{\mathrm{Du}}{\mathrm{\σ}}_{\mathrm{Max}}+(T_{\mathrm{Dl}}+T){\mathrm{\σ}}_{\mathrm{Min}}+\frac{T}{2}\mathrm{\Δ\; \σ},& {\mathrm{\σ}}_{\mathrm{Min}}>0\\ T_{\mathrm{Du}}{\mathrm{\σ}}_{\mathrm{Max}}+\frac{T}{2}\·\frac{{\mathrm{\σ}}_{\mathrm{Max}}^2}{\mathrm{\Δ\; \σ}},& {\mathrm{\σ}}_{\mathrm{Min}}\≤0\end{array}\right.$ Formula (2)

In the formula, T _DuBe the stretching retention time in the primary stress circulation;

T _DlBe the compression retention time in the primary stress circulation;

T promptly has T=T for not comprising the cycle of hold time ₀-T _Du-T _Dl

σ _MaxBe maximum stress;

σ _MinBe minimum stress;

Δ σ is the range of stress, and Δ σ=σ is promptly arranged _Max-σ _Min

Step 4: according to the failure message in the step 2, the utilization Probability Statistics Theory is confirmed and is quantized the uncertainty in the prediction of wheel disc expectancy life.

In the present embodiment, the uncertain factor that step 2 is obtained is defined as stochastic variable, like the common Normal Distribution of material properties; Load distribution is often obtained by the measured data match; Shown in table 1 and table 2, the distribution pattern of these stochastic variables can be with distribution inspection or has been had experience to confirm, and distribution parameter can be used maximum likelihood estimate; Because these methods those of ordinary skill in the art can obtain according to existing information, therefore be not described in detail its detailed process.

The input of table 1 test controlled variable is uncertain

The stochastic distribution of table 2 wheel disc material properties

Step 5: the fault physical life forecast model that obtains according to step 3; Utilization Bayes information updating (Bayesian Information Updating) and fault physics (Physics of Failure) technology; Concrete Bayes reasoning framework is as shown in Figure 2; Model parameter in the life prediction model that step 4 is obtained is imported with distribution form with test control parameter, and with the form output of Life Distribution, sets up the mixing probability fault physical life Forecasting Methodology of wheel disc;

In the present embodiment, adopt the Bayes theory and carry out information updating, to reduce the influence that subjective uncertainty is worked out relevant decision-making as far as possible based on existing new and old, subjective and objective knowledge.Its detailed process is:

Step 51: according to the fault physical life prediction VBM model that step 3 obtains, the lognormality likelihood function of setting up the characterization model parameter uncertainty is:

$L\left(D\right|\{C,\mathrm{\α},\mathrm{\φ},s\})=\underset{i=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}s{N}_f}\mathrm{Exp}(-\frac{1}{2}{\left[\frac{\mathrm{Ln}\left(N_f\right)-\mathrm{Ln}\left(C\right)+\mathrm{\α}\mathrm{Ln}\left({\mathrm{\Δ\; \ϵ}}_{\mathrm{In}}\right)+\mathrm{\α\; \φ}\mathrm{Ln}(E_p-\mathrm{\Δ}{W}_{\mathrm{FL}}{T}_0)}{s}\right]}^2)$ Formula (3)

In the formula, L () is a likelihood function;

S is the natural logarithm standard deviation of life value;

D is the existing life information or the data of wheel disc.

Step 52: under the specified load situation; The test controlled variable that obtains according to the Bayes reasoning framework among Fig. 2 and step 4 and the uncertainty of material properties obtain model parameter and the isoparametric posteriority distribution of material properties with the formula in the step 51 (3) substitution Bayes formula (4)

$\mathrm{\π}\left(\mathrm{\ξ}\right|D)=\frac{{\mathrm{\π}}_0\left(\mathrm{\ξ}\right)L\left(D\right|\mathrm{\ξ})}{{\∫}_{\mathrm{\ξ}}{\mathrm{\π}}_0\left(\mathrm{\ξ}\right)L\left(D\right|\mathrm{\ξ})\mathrm{D\ξ}}$ Formula (4)

In the formula, ξ={ φ, s} are model parameter vector for C, α; π ₀(ξ) be the prior probability distribution function of model parameter vector ξ; π (ξ | D) be the posterior probability distribution function.

The model parameter and the isoparametric posteriority of material properties that obtain based on formula (4) distribute and formula (1), and the bimetry expectation value that integration obtains wheel disc is:

${\tilde{N}}_f=\underset{C,\mathrm{\α},\mathrm{\φ},s}{\∫}\mathrm{\π}\left(\right\{C,\mathrm{\α},\mathrm{\φ},s\left\}\right|D)\left(C{\left({\mathrm{\Δ\; \ϵ}}_{\mathrm{In}}\right)}^{\mathrm{\α}}{(E_p-\mathrm{\Δ}{W}_{\mathrm{FL}}\·T_0)}^{\mathrm{\α\; \φ}}\right)\mathrm{DCd\α\; D\φ\; Ds}$ Formula (5)

Step 6: utilization Markov chain Monte-Carlo (Markov Chain Monte Carlo; MCMC) the higher-dimension integral and calculating of Bayes reasoning in the emulation settlement steps to deal 52, the probability fault physics bimetry and the range of indeterminacy thereof of calculating aeromotor wheel disc.

In this step, (Markov chain Monte Carlo, MCMC) emulation solves the higher-dimension integral and calculating of the Bayes reasoning in the formula (5) to the utilization Markov chain Monte-Carlo.MCMC emulation is a kind ofly to sample repeatedly based on given distribution, and when target distribution can not direct sampling to the target posteriority sampling that distributes correct progressively to approach the method for its actual value.In Analysis of structural reliability, often use the MCMC simulation analysis and solve the structural reliability computational problem under the stochastic variable, this algorithm can realize in Matlab software that also available at present WinBUGS software calculates.In view of MCMC emulation is the common method in this area, therefore be not described in detail.

The concrete thinking of present embodiment is: utilization MCMC emulation technology, and to model parameter (C, φ and α), input variable (Δ ε _p, σ _MaxAnd T ₀) and material properties (E, σ _LimAnd n ') sample, calculate, thereby the posteriority that obtains these parameters distributes according to formula (4).Distribute based on this posteriority then, the probability fault physics bimetry that calculates wheel disc according to formula (5) distributes.For characterizing the error profile of VBM model, with the model prediction life-span N of wheel disc to the wheel disc bimetry _FpWith test life N _FtAll be regarded as its actual physical life-span N _RealIndependent expression.In order to contrast the difference of actual physical between the life-span of they and wheel disc, the ratio with actual physical life-span and model prediction life-span, test life is the stochastic variable of obeys logarithm normal distribution here, and definition test error F _{T, i}With model prediction error F _{P, i}Be respectively:

$\frac{N_{\mathrm{Real},i}}{N_{\mathrm{Ft},i}}=F_{t,i};F_t~\mathrm{LN}(b_t,s_t)$ Formula (6)

In the formula, i is the numbering of wheel disc test; LN is a lognormal distribution; b _tAnd s _tBe respectively average and the standard deviation of test life with respect to the multiplication error profile in actual physical life-span;

$\frac{N_{\mathrm{Real},i}}{N_{\mathrm{Fp},i}}=F_{p,i};F_p~\mathrm{LN}(b_p,s_p)$ Formula (7)

In the formula, b _pAnd s _pBe respectively average and the standard deviation of model prediction life-span with respect to the multiplication error profile in actual physical life-span.

N wheel disc sample carried out torture test, obtain test N fatigue lifetime of wheel disc _Ft={ N _{Ft, 1}, N _{Ft, 2}..., N _{Ft, n}, the VBM model that applying step 3 obtains carries out life prediction, obtains the model predication value N of wheel disc _Fp={ N _{Fp, 1}, N _{Fp, 2}..., N _{Fp, n}, in conjunction with initial prior distribution π ₀(b _p, s _p) and following likelihood function:

$L(N_{\mathrm{Ft},i},N_{\mathrm{Fp},i},b_t,s_t|b_p,s_p)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}\left(\frac{N_{\mathrm{Ft},i}}{N_{\mathrm{Fp},i}}\right)\sqrt{s_p^2+s_t^2}}\mathrm{Exp}(-\frac{1}{2}\×\frac{{[\mathrm{Ln}\left(\frac{N_{\mathrm{Ft},i}}{N_{\mathrm{Fp},i}}\right)-(b_p-b_t)]}^2}{s_p^2+s_t^2})$ Formula

（8）

According to the formula in the step 52 (4), the posteriority that obtains the model uncertainty parameter distributes:

$\mathrm{\π}(b_p,s_p|N_{\mathrm{Ft},i},N_{\mathrm{Fp},i},b_t,s_t)=\frac{{\mathrm{\π}}_0(b_p,s_p)L(N_{\mathrm{Ft},i},N_{\mathrm{Fp},i},b_t,s_t|b_p,s_p)}{\underset{s_p}{\∫}\underset{b_p}{\∫}{\mathrm{\π}}_0(b_p,s_p)L(N_{\mathrm{Ft},i},N_{\mathrm{Fp},i},b_t,s_t|b_p,s_p){\mathrm{Db}}_p{\mathrm{Ds}}_p}$ Formula (9)

In the formula, π ₀(b _p, s _p) be the priori joint distribution of model uncertainty parameter; π (b _p, s _p| N _{Ft, i}, N _{Fp, i}, b _t, s _t) be the posteriority joint distribution of model uncertainty parameter.

According to the wheel disc bimetry error profile of formula (9) calculating VBM model, as shown in table 3, fractile 2.5% and 97.5% pairing F _pValue is respectively the bound based on the expectancy life prediction range of indeterminacy of VBM model, is VBM (7.20%, 8.28%).Existing probability fault physics bimetry distribution N with No. 6 wheel disc sample _FpWith actual measurement life-span N _FtComparison diagram (Fig. 4) is an example, and comparing result is as shown in table 4, and result's demonstration predicts the outcome based on probability fault physical life of the present invention and its actual measurement life-span coincide well, and provides range of indeterminacy for reference.

The statistical abstract of table 3VBM model

The actual measurement life-span of No. 6 sample of table 4 and bimetry distribute and contrast

Those of ordinary skill in the art will appreciate that embodiment described here is in order to help reader understanding's principle of the present invention, should to be understood that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not break away from essence of the present invention according to these teachings disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (1)

1. based on the aeromotor wheel disc probability fault physical life Forecasting Methodology of Bayes information updating, comprise the steps:

Step 1:, use the fault physical message of confirming the turbine disk based on the analysis method for reliability of fault physics according to aeromotor wheeling disk structure characteristic;

Step 2: the fault physical message of the aeromotor wheel disc that utilization FTA/FMECA method obtains step 1 and obtain the main failure mode and the abort situation thereof of wheel disc by the existing failure message analysis that the mantenance data statistics obtains, collect also the arrangement wheel disc towards the uncertain factor and the imprecise data in cycle life-cycle;

Step 3: the fault physical life forecast model that main failure mode of wheel disc that obtains according to step 2 and abort situation are set up the aeromotor wheel disc;

Step 4: the uncertainty in the wheel disc expectancy life prediction that the utilization Probability Statistics Theory is confirmed and quantization step 2 obtains;

Step 5: the fault physical life forecast model that obtains according to step 3; Utilization Bayes information updating and fault physical technique; Model parameter in the life prediction model that step 4 is obtained is imported with distribution form with test control parameter; And, set up the mixing probability fault physical life Forecasting Methodology of wheel disc with the output of the form of Life Distribution;

Step 6: the higher-dimension integral and calculating of Bayes reasoning in the utilization Markov chain Monte-Carlo emulation settlement steps to deal 5, the probability fault physics bimetry and the range of indeterminacy thereof of calculating aeromotor wheel disc.

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