Construction of entropy-based prior and posterior probability distributions with partial information for fatigue damage prognostics

Patent metadata

Field	Value
Publication number	US-9639637-B2
Application number	US-201314015084-A
Country	US
Kind code	B2
Filing date	Aug 30, 2013
Priority date	Oct 8, 2012
Publication date	May 2, 2017
Grant date	May 2, 2017

Abstract

A method for predicting fatigue crack growth in materials includes providing a prior distribution obtained using response measures from one or more target components using a fatigue crack growth model as a constraint function, receiving new crack length measurements, providing a posterior distribution obtained using the new crack length measurements, and sampling the posterior distribution to obtain crack length measurement predictions.

First claim

What is claimed is:

1. A computer-implemented method for predicting fatigue crack growth in materials, comprising:
providing, via a processor, a prior distribution obtained using response measures from one or more target components using a fatigue crack growth model as a constraint function;
receiving, via the processor, new crack length measurements;
generating, via the processor, a posterior distribution based on the new crack length measurements;
sampling, via the processor, the posterior distribution for generating crack length measurement predictions,
wherein the prior distribution is expressed as p 0 (θ)∝exp{λM(θ)}, wherein M is the fatigue crack growth model, θ is a fatigue crack growth model parameter, M(θ) is the output of the fatigue crack growth model, and λ is a Lagrange multiplier, and the constraint function is expressed as E p 0 (θ) [M(θ)]= α , wherein α is a mean of the response measures from one or more target components; and
the posterior distribution is expressed as

p
⁡

(
θ
)

∝

exp
⁡

[

λ
⁢

⁢

M
⁡

(
θ
)

]

⁢
exp
⁢

{

-

1
2

⁢

∑

i
=
1

n

⁢

⁢

[

a
i

-

M
i

⁡

(
θ
)

σ
ɛ

]

2

}

,

where a i represents new crack length measurements associated with the one or more target components, σ ε is a standard deviation of Gaussian likelihood, and n is a total number of new crack length measurements; and
wherein the Lagrange multiplier λ is obtained by solving, via the processor,

∂
ln

⁢

∫

λ
⁢

⁢

M
⁡

(
θ
)

⁢

ⅆ
θ

∂
λ

=

a
_

;

and
predicting, via the processor, fatigue crack growth in the material based on the posterior distribution.

2. The computer-implemented method of claim 1 , wherein the posterior distribution is sampled using a Markov-chain Monte-Carlo simulation.

3. The computer-implemented method of claim 1 , wherein σ ε =√{square root over (σ ε 1 2 +σ ε 2 2 )}, wherein σ ε 1 is a standard deviation associated a statistical uncertainty of the fatigue crack growth model M, and σ ε 2 is a standard deviation associated with a measurement uncertainty.

4. The computer-implemented method of claim 1 , further comprising updating the posterior distribution as new crack length measurements are received.

5. The computer-implemented method of claim 1 , wherein the fatigue crack growth model is Paris' model, expressed as

ⅆ
a

ⅆ
N

=

c
⁡

(

Δ
⁢

⁢
K

)

m

,

wherein a is a crack size, N is a number of applied cyclic loads,

Δ
⁢

⁢
K

=

π
⁢

⁢
a

⁢
Δ

Assignees

• Guan Xuefei
• Zhang Jingdan
• Zhou Shaohua Kevin
• Siemens Ag

Inventors

• Guan Xuefei
• Zhang Jingdan
• Zhou Shaohua Kevin

Classifications

• G06F30/20 Primary

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• G06F2111/08

  Probabilistic or stochastic CAD · CPC title

• G06F2119/04

  Ageing analysis or optimisation against ageing · CPC title

• G06F2217/76

  Physics · mapped topic

• G06F17/5009 Primary

  Physics · mapped topic