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

摘要

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.

主权项

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 p0(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 Ep0(θ)[M(θ)]=α, wherein α is a mean of the response measures from one or more target components; andthe posterior distribution is expressed asp⁡(θ)∝exp⁡[λ⁢⁢M⁡(θ)]⁢exp⁢{-12⁢∑i=1n⁢⁢[ai-Mi⁡(θ)σɛ]2}, where ai represents new crack length measurements associated with the one or more target components, σε is a standard deviation of Gaussian likelihood, and n is a total number of new crack length measurements; andwherein the Lagrange multiplier λ is obtained by solving, via the processor,∂ln⁢∫λ⁢⁢M⁡(θ)⁢ⅆθ∂λ=a_;and
predicting, via the processor, fatigue crack growth in the material based on the posterior distribution.