Analytical Models for the Probability Distributions of Fatigue Parameters and Crack Size of Offshore Structures Based on Bayesian Updating

2002 ◽  
Author(s):  
Ernesto Heredia-Zavoni ◽  
Roberto Montes-Iturrizaga
Keyword(s):  
Crack Detection ◽  
Probability Distributions ◽  
Crack Depth ◽  
Error Variance ◽  
Crack Size ◽  
Offshore Structures ◽  
Probability Of Detection ◽  
Posterior Distributions ◽  
Fatigue Model ◽  
Normally Distributed

In this paper a bayesian framework is used for updating the probability distributions of the parameters of a fatigue model and of crack size in tubular joints using information from inspection reports of fixed offshore structures. For crack detection, the uncertainties are taken into account by means of probability-of-detection (POD) curves. According to the bayesian procedure, if during an inspection no crack is detected, the updated (posterior) distributions depend on the prior ones at time of such inspection and on the POD. On the other hand, if during an inspection a crack is detected and measured, the corresponding predicted crack depth at that time is estimated given values of parameters of a selected fatigue model and of the initial crack depth. Then, a sample value of the model and sizing error associated with the inspection performed, defined as the logarithmic difference between the measured and the predicted crack size, is calculated. Such error is considered to be a normally distributed random variable with known mean and uncertain variance. The distribution of the error variance is taken as a conjugate one for samples of normally distributed variables with known mean and uncertain variance. Based on these assumptions, an analytical expression is obtained for the updated (posterior) distributions of the parameters of the fatigue model and of crack size. It is shown that the updated distributions depend on POD and on the prior and updated parameters of the error variance distribution. Finally, the bayesian method proposed here is illustrated taking as a fatigue model the Paris-Erdogan relation, which estimates crack growth based on linear elastic fracture mechanics. Joint failure is considered to occur when the crack depth reaches the thickness of the element where the crack propagates. The evolution of reliability with time is assessed.

A Bayesian Model for the Probability Distribution of Fatigue Damage in Tubular Joints

2004 ◽  
Vol 126 (3) ◽  
pp. 243-249 ◽  
Author(s):  
Ernesto Heredia-Zavoni ◽  
Roberto Montes-Iturrizaga
Keyword(s):  
Fracture Mechanics ◽  
Probability Distributions ◽  
Error Variance ◽  
Crack Size ◽  
Offshore Structures ◽  
Density Functions ◽  
Time Varying ◽  
Tubular Joints ◽  
Mechanics Model ◽  
Distribution Of Stress

A Bayesian framework is used for updating the probability distributions of the parameters of a fracture mechanics model and of crack size in tubular joints using information from inspection reports of fixed offshore structures. An error model, defined as the logarithmic difference between measured crack size during inspection and crack size predicted by the fracture mechanics model, is assumed to have a normal distribution with known mean and uncertain variance. The distribution of the error variance is modeled by a conjugate distribution for samples of normal variables with known mean and uncertain variance. Based on these assumptions, an analytical model is obtained using a Bayesian approach for the updated distributions of the parameters of the fracture mechanics model and of crack size based. The capabilities of the model are illustrated by means of examples using the Paris-Erdogan formulation for crack growth. The examples illustrate the effects of inspection times, measured crack size, and the distribution of stress ranges on the updated density functions of crack size, time varying reliability and expected cost of failure.

A Review of Crack Detection In-Line Inspection Case Studies

2010 ◽  
Author(s):  
Neil Bates ◽  
David Lee ◽  
Clifford Maier
Keyword(s):  
Crack Growth ◽  
Case Studies ◽  
Crack Detection ◽  
Growth Parameters ◽  
Probability Distributions ◽  
Low Frequency ◽  
Probability Of Failure ◽  
Probability Of Detection ◽  
Inspection Data

This paper describes case studies involving crack detection in-line inspections and fitness for service assessments that were performed based on the inspection data. The assessments were used to evaluate the immediate integrity of the pipeline based on the reported features and the long-term integrity of the pipeline based on excavation data and probabilistic SCC and fatigue crack growth simulations. Two different case studies are analyzed, which illustrate how the data from an ultrasonic crack tool inspection was used to assess threats such as low frequency electrical resistance weld seam defects and stress corrosion cracking. Specific issues, such as probability of detection/identification and the length/depth accuracy of the tool, were evaluated to determine the suitability of the tool to accurately classify and size different types of defects. The long term assessment is based on the Monte Carlo method [1], where the material properties, pipeline details, crack growth parameters, and feature dimensions are randomly selected from certain specified probability distributions to determine the probability of failure versus time for the pipeline segment. The distributions of unreported crack-related features from the excavation program are used to distribute unreported features along the pipeline. Simulated crack growth by fatigue, SCC, or a combination of the two is performed until failure by either leak or rupture is predicted. The probability of failure calculation is performed through a number of crack growth simulations for each of the reported and unreported features and tallying their respective remaining lives. The results of the probabilistic analysis were used to determine the most effective and economical means of remediation by identifying areas or crack mechanisms that contribute most to the probability of failure.

Impact of Prognosis on Asset Life Extension and Readiness

2003 ◽  
Author(s):  
Yevgeny Macheret ◽  
Leo Christodoulou
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Crack Detection ◽  
Crack Size ◽  
Probability Of Detection ◽  
Life Extension ◽  
Growth Data ◽  
Damage State ◽  
The Impact

Fatigue response of structural components is determined by environmental conditions, material microstructure, and loading history. Variation of these factors results in significant scatter in fatigue-crack growth rates and component life. In this paper, the impact of prognosis capability on asset life extension and readiness is evaluated. Fatigue-crack growth data on aluminum samples under controlled spectrum loading are used to describe the statistics of the crack-size distribution. Several sensors with different probability of detection (POD) characteristics are considered for detecting cracks of critical size, and the effect of the POD on the component life extension is evaluated. Although the crack-detection capability leads to the asset life extension, it is not sufficient to maintain required mission readiness. On the other hand, the prognosis capability, which is based on the knowledge of the component’s current damage state, damage evolution laws, and upcoming mission loading, allows required mission readiness to be maintained.

Evaluation of GPM IMERG Rainfall Estimates in Singapore and Assessing Spatial Sampling Errors in Ground Reference

2020 ◽  
Vol 21 (12) ◽  
pp. 2963-2977
Author(s):  
Pradeep V. Mandapaka ◽  
Edmond Y. M. Lo
Keyword(s):  
Spatial Configuration ◽  
Probability Distributions ◽  
Error Variance ◽  
Probability Of Detection ◽  
Spatial Sampling ◽  
Sampling Errors ◽  
Diurnal Cycles ◽  
Spatial Configurations ◽  
Improved Performance ◽  
Using Data

AbstractWe evaluated the Integrated Multisatellite Retrievals for GPM (IMERG) V06B Early and Final Run products using data from a dense gauge network in Singapore as ground reference (GR). The evaluation is carried out at monthly, daily, and hourly scales, and conditioned on different seasons and rainfall intensities. Further, different spatial configurations and densities of the gauge networks (3–17 gauges per IMERG cell) used here allowed us to examine spatial sampling errors (SSE) in the GR. The results revealed a probability of detection of 0.95 (0.65), critical success index of 0.69 (0.35), and a correlation of 0.60 (0.41) for the daily (hourly) scale. Results also indicate an overestimation of rainy days (hours) by IMERG compared to GR, leading to a false alarm ratio of 0.29 (0.57) at daily (hourly) scales. Analysis of probability distributions and conditional error metrics showed overestimation of lighter (0.2–4 mm day−1) and moderate (4–8 mm day−1) rainfall by IMERG, but better performance for heavier rainfall (≥32 mm day−1). The seasonal analysis showed improved performance of IMERG during November–February compared to June–September months. The hourly analysis further revealed large discrepancies in diurnal cycles during June–September. The SSE are studied in a Monte Carlo framework consisting of several synthetic networks with varying spatial configurations and densities. The effect of SSE on IMERG evaluation results is characterized following the error variance separation approach. For the gauge networks studied here, the contribution of SSE variance to IMERG daily error variance ranges from 4% to 24% depending on gauge spatial configuration, and is as large as 36% during intermonsoon months when rainfall is highly convective in nature.

scholarly journals Dynamic Response of a Cracked Rotor With Some Comments on Crack Detection

1994 ◽  
Author(s):  
G. Meng ◽  
Eric J. Hahn
Keyword(s):  
Dynamic Response ◽  
Crack Detection ◽  
Harmonic Component ◽  
Major Axis ◽  
Vertical Axis ◽  
Crack Size ◽  
Cracked Rotor ◽  
Response Component ◽  
Crack Location ◽  
Backward Whirl

By considering time dependent terms as external excitation forces, the approximate dynamic response of a cracked horizontal rotor is analysed theoretically and numerically. The solution is good for small cracks and small vibrations in the stable operating range. For each steady state harmonic component the forward and backward whirl amplitudes, the shape and orientation of the elliptic orbit and the amplitude and phase of the response signals arc analysed, taking into account the effect of crack size, crack location, rotor speed and unbalance. It is found that the crack causes backward whirl, the amplitude of which increases with the crack. For a cracked rotor, the response orbit for each harmonic component is an ellipse, the shape and orientation of which depends on the crack size. The influence of the crack on the synchronous response of the system can be regarded as an additional unbalance whereupon, depending on the speed and the crack location, the response amplitude differs from that of the uncracked rotor. The nonsynchronous response provides evidence of crack in the sub-critical range, but is too small to be detected in the supercritical range. Possibilities for crack detection over the full speed range include the additional average (the constant) response component, the backward whirl of the response, the ellipticity of the orbit, the angle between the major axis and the vertical axis and the phase angle difference between vertical and horizontal vibration signals.

scholarly journals Monitoring a sudden crack of beam-like bridge during earthquake excitation

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Viet Khoa
Keyword(s):  
Fourier Transform ◽  
Crack Detection ◽  
Crack Depth ◽  
Sudden Change ◽  
Wavelet Spectrum ◽  
Cracked Beam ◽  
Earthquake Excitation ◽  
Time Frequency ◽  
Short Time ◽  
Time Information

This paper presents a wavelet spectrum technique for monitoring a sudden crack of a beam-like bridge structure during earthquake excitation. When there is a sudden crack caused by earthquake excitation the stiffness of the structure is changed leading to a sudden change in natural frequencies during vibration. It is difficult to monitor this sudden change in the frequency using conventional approaches such as Fourier transform because in Fourier transform the time information is lost so that it is impossible to analyse short time events. To overcome this disadvantage, wavelet spectrum, a time-frequency analysis, is used for monitoring a sudden change in frequency duringearthquake excitation for crack detection. In this study, a model of 3D crack is applied. The derivation of the stiffness matrix of a 3D cracked beam element with rectangular section adopted from fracture mechanics is presented. Numerical results showed that the sudden occurrence of the crack during earthquake excitation can be detected by the sudden change in frequency using wavelet power spectrum. When the crack depth increases, the instantaneous frequency (IF) of the structure is decreased.

Dynamic Behaviour and Crack Detection of a Multi Cracked Rotating Shaft using Adaptive Neuro-Fuzzy-Inference System

2016 ◽  
Vol 6 (4) ◽  
pp. 1-10 ◽  
Author(s):  
Rajeev Ranjan
Keyword(s):  
Finite Element ◽  
Fuzzy Inference System ◽  
Crack Detection ◽  
Fuzzy Inference ◽  
Crack Depth ◽  
Multiple Cracks ◽  
Rotating Shaft ◽  
Element Analysis ◽  
Inference System ◽  
Neuro Fuzzy

The presence of crack changes the physical characteristics of a structure which in turn alter its dynamic response characteristics. So it is important to understand dynamics of cracked structures. Crack depth and location are the main parameters influencing the vibration characteristics of the rotating shaft. In the present study, a technique based on the measurement of change of natural frequencies has been employed to detect the multiple cracks in rotating shaft. The model of shaft was generated using Finite Element Method. In Finite Element Analysis, the natural frequency of the shaft was calculated by modal analysis using the software ANSYS. The Numerical data were obtained from FEA, then used to train through Adaptive Neuro-Fuzzy-Inference System. Then simulations were carried out to test the performance and accuracy of the trained networks. The simulation results show that the proposed ANFIS estimate the locations and depth of cracks precisely.

Electrical Resistance Method for Fatigue Crack Detection of Steel Deck

2013 ◽  
Vol 361-363 ◽  
pp. 1397-1401 ◽  
Author(s):  
Zhou Zhi Yuan Yuan ◽  
Bo Hai Ji ◽  
Zhong Qiu Fu ◽  
Rong Liu ◽  
Miao Cheng
Keyword(s):  
Fatigue Crack ◽  
Electrical Resistance ◽  
Crack Detection ◽  
Crack Depth ◽  
Influential Factors ◽  
Element Analysis ◽  
Resistance Method ◽  
Electrode Space ◽  
Fatigue Crack Detection ◽  
Steel Deck

The present study employs an electrical resistance method for fatigue crack detection in steel deck. The detection influential factors are analyzed via the finite element analysis under different electrode space and deck width. As a result, the electrode space influenced on detecting precision, and the smaller the better. The resistance measurement method is presented, and the formula of fracture damage ratio and the equivalent crack depth are established. It is proved by fatigue crack detection experiment of U-rib specimen, which shows that using electrical resistance method to detect fatigue crack is feasible.

Dynamic Response of a Cracked Rotor With Some Comments on Crack Detection

1997 ◽  
Vol 119 (2) ◽  
pp. 447-455 ◽  
Author(s):  
G. Meng ◽  
E. J. Hahn
Keyword(s):  
Dynamic Response ◽  
Crack Detection ◽  
Harmonic Component ◽  
Major Axis ◽  
Vertical Axis ◽  
Crack Size ◽  
Cracked Rotor ◽  
Response Component ◽  
Crack Location ◽  
Backward Whirl

By considering time-dependent terms as external excitation forces, the approximate dynamic response of a cracked horizontal rotor is analyzed theoretically and numerically. The solution is good for small cracks and small vibrations in the stable operating range. For each steady-state harmonic component, the forward and backward whirl amplitudes, the shape and orientation of the elliptic orbit, and the amplitude and phase of the response signals are analyzed, taking into account the effect of crack size, crack location, rotor speed, and unbalance. It is found that the crack causes backward whirl, the amplitude of which increases with the crack. For a cracked rotor, the response orbit for each harmonic component is an ellipse, the shape and orientation of which depend on the crack size. The influence of the crack on the synchronous response of the system can be regarded as an additional unbalance whereupon, depending on the speed and the crack location, the response amplitude differs from that of the uncracked rotor. The nonsynchronous response provides evidence of crack in the subcritical range, but is too small to be detected in the supercritical range. Possibilities for crack detection over the full-speed range include the additional average (the constant) response component, the backward whirl of the response, the ellipticity of the orbit, the angle between the major axis and the vertical axis, and the phase angle difference between vertical and horizontal vibration signals.

scholarly journals An Improved Algorithm for Low-Level Turbulence Forecasting

2018 ◽  
Vol 57 (6) ◽  
pp. 1249-1263 ◽  
Author(s):  
Domingo Muñoz-Esparza ◽  
Robert Sharman
Keyword(s):  
Probability Distributions ◽  
Atmospheric Stability ◽  
Energy Dissipation Rate ◽  
Probability Of Detection ◽  
Percentage Error ◽  
Unmanned Aerial Systems ◽  
Low Level ◽  
Forecasting System ◽  
The One ◽  
Aerial Systems

AbstractA low-level turbulence (LLT) forecasting algorithm is proposed and implemented within the Graphical Turbulence Guidance (GTG) turbulence forecasting system. The LLT algorithm provides predictions of energy dissipation rate (EDR; turbulence dissipation to the one-third power), which is the standard turbulence metric used by the aviation community. The algorithm is based upon the use of distinct log-Weibull and lognormal probability distributions in a statistical remapping technique to represent accurately the behavior of turbulence in the atmospheric boundary layer for daytime and nighttime conditions, respectively, thus accounting for atmospheric stability. A 1-yr-long GTG LLT calibration was performed using the High-Resolution Rapid Refresh operational model, and optimum GTG ensembles of turbulence indices for clear-air and mountain-wave turbulence that minimize the mean absolute percentage error (MAPE) were determined. Evaluation of the proposed algorithm with in situ EDR data from the Boulder Atmospheric Observatory tower covering a range of altitudes up to 300 m above the surface demonstrates a reduction in the error by a factor of approximately 2.0 (MAPE = 55%) relative to the current operational GTG system (version 3). In addition, the probability of detection of typical small and large EDR values at low levels is increased by approximately 15%–20%. The improved LLT algorithm is expected to benefit several nonconventional turbulence-prediction sectors such as unmanned aerial systems and wind energy.

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