Probabilistic structural reliability of PWR pressure vessels

Lucia, A.C.

doi:10.1016/0029-5493(85)90093-7

Cited by 11 publications

(11 citation statements)

References 14 publications

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“…This model is suitable for all advanced algorithms, such as EKF and ALF, and is created by the state-space representation of the general equation (4) and therefore is compatible with all semiempirical laws of type (1) [25]. In detail, the state and measurement equations are:…”

Section: The Nonlinear State-space Modelmentioning

confidence: 99%

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Adaptive Estimation of FCG Using Nonlinear State-Space Models

Moussas

Katsikas

Lainiotis

2005

Stochastic Analysis and Applications

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In this paper, an efficient adaptive nonlinear algorithm for estimation and identification, the so-called adaptive Lainiotis filter (ALF), is applied to the problem of fatigue crack growth (FCG) estimation, identification, and prediction of the final crack (failure). A suitable nonlinear state-space FCG model is introduced for both ALF and extended Kalman filter (EKF). Both algorithms are tested in order to compare their efficiency. Through extensive analysis and simulation, it is demonstrated that the ALF has superior performance both in FCG estimation, as well as in predicting the remaining lifetime to failure. Furthermore, it is shown that the ALF is faster and easier to implement in a parallel/distributed processing mode, and much more robust than the classic EKF.

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Section: The Nonlinear State-space Modelmentioning

confidence: 99%

“…[2,3]; complex and high risk plants (e.g., chemical factories, nuclear reactors, etc.) [4]; and, in general, any rare, expensive, or, dangerous structure that is impossible to test a priori in statistically large samples.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Estimation of FCG Using Nonlinear State-Space Models

Moussas

Katsikas

Lainiotis

2005

Stochastic Analysis and Applications

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“…Its main advantage over equation (4) lies in the fact that the presence of 5 ( t ) on its right-hand side renders A ( t ) a Markov process. On the other hand, a drawback of this modeling is that the white noise process t ( t ) theoretically allows for the growth rate dA/dt to take on negative values [I], 121.…”

Section: Clearly Equation (8) Is An Approximate Equation Governing Tmentioning

confidence: 99%

“…Thus, of particular importance in fatigue investigations is the determination of two distributions: that of the crack size, and that of the time required by the crack to reach a specified length. Several analytical methods, aiming at fitting available experimental data, have been developed towards this end, and one can find a fairly complete presentation of them in Refs [3] and [4]. These methods are of the phenomenological type and as yet there does not exist a workable model on the microscale level.…”

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confidence: 99%

Markov Approximation to Fatigue Crack Size Distribution

Solomos¹,

Lucia²

1990

Fatigue Fract Eng Mat Struct

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The distribution of the crack size during the fatigue crack propagation phenomenon is investigated. A Markovian modeling of the crack is introduced through the fatigue crack growth law, and the associated Fokker-Planck equation is written while special care is devoted to specifying its boundary conditions. This equation is solved by the method of separation of variables and the sought distribution function is obtained in the form of a convergent infinite series. An illustrative example, demonstrating the applicability of the approach, shows satisfactory agreement between theoretical results and experimental data. NOMENCLATURE A = crack size b = crack growth law parameter a,, a, = initial, limit crack size Cov = covariance D ( . ) = p.d.f. correction factor E [ .] = mathematical expectation f ( . ) = crack transition time p.d.f. G(a) = probability current K, = integration constants Q ( . ) =crack growth rate law D, = random variable defining pulse amplitude Q* = crack growth law parameter R,, = autocorrelation of Y ( t ) S,, = spectral density function of Y ( t ) T(t) = functions of time qA(. 1 .) = transition probability density function of A t = time v = dummy integration variable w ( .) = unit height rectangular pulse X ( t ) = random process, pulse train model Y ( t ) = random process, the fluctuation part of X ( t ) Z ( z ) = functions of z z = transformed space variable for a ( t ) B = dispersion parameter of X ( t ) y = parameter related to Q( .) A = duration of pulse w( .) 6 = Dirac delta function, small increment 1 = eigenvalues p = mean of process X ( t ) pv = parameter of distribution of z v = arrival rate of the rectangular pulses w ( .) uv = parameter of distribution of z 5 = time lag w = circular frequency [ ( t ) = white noise process 457 458

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“…The difference between the critical size and the smallest detectable size becomes the level ofsafety (Lucia 1985, Dufresne et al 1988). It might be necessary to guarantee, with confidence, that cracks smaller than the critical size are absent also.…”

Section: Introductionmentioning

confidence: 99%