Efficient Methods for Time-Dependent Fatigue Reliability Analysis

Liu, Yongming; Mahadevan, Sankaran

doi:10.2514/1.34331

Cited by 36 publications

(27 citation statements)

References 29 publications

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“…In particular, the inverse first-order reliability method (inverse-FORM) can be used to calculate probability bounds on RUL (in fact, the entire probability distribution of RUL at discrete probability levels), which are useful for decisionmaking. Though such analytical methods have been used for time-dependent reliability calculation, 12,13 their application to state space models poses several new challenges. The primary contribution of this paper is to extend the inverse FORM approach to include state space models and compute the uncertainty in the RUL prediction.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

Sankararaman

Goebel

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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This paper investigates the use of the inverse first-order reliability method (inverse-FORM) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in inverse-FORM, this paper extends the methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The inverse-FORM method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed methodology is illustrated using a numerical example.

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Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

Sankararaman

Goebel

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…Log‐Normal or Weibull random variables. More recently, Liu and Mahadevan postulated a model that includes actual correlation of fatigue lives across different stress amplitudes, based on the physical evidence that under variable amplitude loading, it is the behaviour of a given specimen at different stress amplitudes to generate the randomness of the distribution. Therefore, it is reasonable to assume that fatigue properties at different stress amplitudes may be correlated.…”

Section: Introductionmentioning

confidence: 99%

On the application of the stochastic approach in predicting fatigue reliability using Miner's damage rule

Paolino

Cavatorta

2013

Fatigue Fract Eng Mat Struct

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The present paper investigates the application of the stochastic approach when the commonly adopted Miner's linear damage rule is implemented, both in its traditional and modified forms to include the presence of a random stress threshold (random fatigue limit), below which the rate of damage accumulation is reduced. Main steps are provided to obtain the simulated distribution of the accumulated damage under variable amplitude loading. When the stochastic approach is applied in the presence of a random fatigue limit, an additional correlation structure, which takes into account the fatigue limit value, must be introduced in the analysis. If the number of cycles to failure under constant amplitude loading is Weibull (Log‐Normal) distributed, then the corresponding accumulated damage is Fréchet (Log‐Normal) distributed. The effects of the correlation structure on reliability prediction under variable amplitude loading are also investigated. To this aim, several experimental datasets are taken from the literature, covering various metallic materials and variable amplitude block sequences. The results show that the choice of the damage accumulation model is a key factor to value the improvement in the accuracy of reliability predictions introduced by the stochastic approach. Comparison of the predicted number of cycles to failure with experimental data shows that larger errors are non‐conservative, regardless of the adopted correlation structure. When the analysis is limited to reliability levels above 80%, for these large non‐conservative errors, it is the quantile approach to be closer to actual experimental data, thus limiting the overestimation of component's life. For the experimental datasets considered in the paper, adoption of a stochastic approach would improve the accuracy of Miner's predictions in 10% of cases.

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“…This approach is very useful for engineering design against fatigue since the service life is usually given in design problems. Both First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS) have been used for this purpose [1] . Another approach is the probabilistic life prediction, i.e.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic fatigue life prediction using Subset Simulation

Li¹,

Xiang²,

Liu³

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite

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A general simulation-based methodology is proposed for efficient and accurate probabilistic fatigue life prediction. The proposed methodology is based on an Equivalent Initial Flaw Size (EIFS) crack growth model and Subset Simulation. The original Subset Simulation algorithm is modified to be suitable for probabilistic figure life prediction, which is an inverse reliability problem. The simulation results are compared with direct Monte Carlo simulation and experimental data for model verification and validation. Nomenclature A, B, C, D = material parameter a = crack lengeh a i = equivalent intial flaw size a c = critical crack length at fauilure b, b i = threshold Δ K = stress intensity factor Δ K th = threshold stress intensity factor Δ σ f = fatigue limit Δ σ = stress range F T , F i = failure event G = a function of a random vector m = the number of simulation level N = fatigue life (number of cycles) N p , N 1-p = confidence bound of fatigue life p, p 0 = probability R = stress ratio Y = geometry correction factor σ 0 = the cyclic ultimate strength

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Efficient Methods for Time-Dependent Fatigue Reliability Analysis

Cited by 36 publications

References 29 publications

Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

On the application of the stochastic approach in predicting fatigue reliability using Miner's damage rule

Probabilistic fatigue life prediction using Subset Simulation

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