Evaluation of Approximative Methods for Rainflow Damage of Broad-Banded Non-Gaussian Random Loads

2005 ◽  
Author(s):  
Magnus Karlsson
Keyword(s):  
Markov Chain ◽  
Lower Bound ◽  
Linear Combination ◽  
Fatigue Damage ◽  
Turning Points ◽  
Spectral Moments ◽  
Random Loads ◽  
Amplitude Spectra ◽  
Cycle Count ◽  
Non Gaussian

Two different methods for approximating the fatigue damage of broad banded non-Gaussian random loads using the rainflow cycle count method are evaluated using loads measured on a truck. Results for Gaussian loads are summarized, and transformations for non-Gaussian loads are discussed. One of the two methods is based on the spectral moments of the process, and the results are obtained as a linear combination of an upper and lower bound. The second method is based on the assumption that the sequence of turning points of the load can be considered a Markov chain, for which results can be obtained. Measurements performed on different markets are used to study the two methods. Results are presented in terms of expected damage and amplitude spectra. Problems and possible improvements of the models are discussed.

Fatigue damage assessment for a spectral model of non-Gaussian random loads

2009 ◽  
Vol 24 (4) ◽  
pp. 608-617 ◽  
Author(s):  
Sofia A˚berg ◽  
Krzysztof Podgórski ◽  
Igor Rychlik
Keyword(s):  
Fatigue Damage ◽  
Damage Assessment ◽  
Spectral Model ◽  
Random Loads ◽  
Non Gaussian

scholarly journals Parallel Markov chain Monte Carlo for non-Gaussian posterior distributions

Stat ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 304-319 ◽  
Author(s):  
Alexey Miroshnikov ◽  
Zheng Wei ◽  
Erin Marie Conlon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Posterior Distributions ◽  
Non Gaussian

scholarly journals Polynomial Mixing of the Edge-Flip Markov Chain for Unbiased Dyadic Tilings

2018 ◽  
Vol 28 (3) ◽  
pp. 365-387
Author(s):  
S. CANNON ◽  
D. A. LEVIN ◽  
A. STAUFFER
Keyword(s):  
Markov Chain ◽  
Relaxation Time ◽  
Lower Bound ◽  
Upper Bound ◽  
Open Problem ◽  
Mixing Time ◽  
Perpendicular Bisector ◽  
Unit Square

We give the first polynomial upper bound on the mixing time of the edge-flip Markov chain for unbiased dyadic tilings, resolving an open problem originally posed by Janson, Randall and Spencer in 2002 [14]. A dyadic tiling of size n is a tiling of the unit square by n non-overlapping dyadic rectangles, each of area 1/n, where a dyadic rectangle is any rectangle that can be written in the form [a2−s, (a + 1)2−s] × [b2−t, (b + 1)2−t] for a, b, s, t ∈ ℤ⩾ 0. The edge-flip Markov chain selects a random edge of the tiling and replaces it with its perpendicular bisector if doing so yields a valid dyadic tiling. Specifically, we show that the relaxation time of the edge-flip Markov chain for dyadic tilings is at most O(n4.09), which implies that the mixing time is at most O(n5.09). We complement this by showing that the relaxation time is at least Ω(n1.38), improving upon the previously best lower bound of Ω(n log n) coming from the diameter of the chain.

scholarly journals Fatigue Life Analysis of Aluminum Alloy Notched Specimens under Non-Gaussian Excitation based on Fatigue Damage Spectrum

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Kuanyu Chen ◽  
Guangwu Yang ◽  
Jianjun Zhang ◽  
Shoune Xiao ◽  
Yang Xu
Keyword(s):  
Aluminum Alloy ◽  
Fatigue Life ◽  
Fatigue Damage ◽  
Relative Error ◽  
Gaussian Distribution ◽  
Calculation Method ◽  
Shaking Table ◽  
Notched Specimens ◽  
Acceleration Method ◽  
Non Gaussian

In this study, a non-Gaussian excitation acceleration method is proposed, using aluminum alloy notched specimens as a research object and measured acceleration signal of a certain airborne bracket, during aircraft flight as input excitations, based on the fatigue damage spectrum (FDS) theory. The kurtosis and skewness of the input signal are calculated and the non-Gaussian characteristics and amplitude distribution are evaluated. Five task segments obey a non-Gaussian distribution, while one task segment obeys a Gaussian distribution. The fatigue damage spectrum calculation method of non-Gaussian excitation is derived. The appropriate FDS calculation method is selected for each task segment and the acceleration parameters are set to construct the acceleration power spectral density, which is equivalent to the pseudo-acceleration damage. A finite-element model is established, the notch stress concentration factor of the specimen is calculated, the large mass point method is used to simulate the shaking table excitation, and a random vibration analysis is carried out to calculate the accelerated fatigue life. The simulation results show that the relative error between the original cumulative damage and test original fatigue life is 15.7%. The shaking table test results show that the relative error of fatigue life before and after acceleration is less than 16.95%, and the relative error of test and simulation is 24.27%. The failure time of the specimen is accelerated from approximately 12 h to 1 h, the acceleration ratio reaches 12, and the average acceleration ideal factor is 1.125, which verifies the effectiveness of the acceleration method. It provides a reference for the compilation of the load spectrum and vibration endurance acceleration test of other airborne aircraft equipment.

Fatigue Under Combined High and Low Frequency Loads

2006 ◽  
Author(s):  
Wenbo Huang ◽  
Torgeir Moan
Keyword(s):  
Numerical Simulation ◽  
Fatigue Damage ◽  
Low Frequency ◽  
Flow Prediction ◽  
Non Gaussian ◽  
New Formula

Based on Gaussian load processes, a new formula suitable for evaluating the combined fatigue damage due to high and low frequency loads is derived. Then, by using of the Winterstein’s transformation, the developed formula is extended for the combination of non-Gaussian loads. The numerical simulation shows that the predicted damage by the derived formula is very simple to use and close to the rain-flow prediction.

MARKOV CHAIN METHOD FOR COMPUTING THE RELIABILITY OF HAMMOCK NETWORKS

2020 ◽  
pp. 1-18
Author(s):  
Marilena Jianu ◽  
Daniel Ciuiu ◽  
Leonard Dăuş ◽  
Mihail Jianu
Keyword(s):  
Markov Chain ◽  
Lower Bound ◽  
Relative Error ◽  
Fundamental Matrix ◽  
Approximation Methods ◽  
Arbitrary Length ◽  
Reliability Polynomial ◽  
Absorbing Markov Chain ◽  
Markov Chain Method ◽  
The Mean

In this paper, we develop a new method for evaluating the reliability polynomial of a hammock network. The method is based on a homogeneous absorbing Markov chain and provides the exact reliability for networks of width less than 5 and arbitrary length. Moreover, it produces a lower bound for the reliability polynomial for networks of width greater than or equal to 5. To investigate how sharp this lower bound is, we compare our method with other approximation methods and it proves to be the most accurate in terms of absolute as well as relative error. Using the fundamental matrix, we also calculate the average time to absorption, which provides the mean length of a network that is expected to work.

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