Probability Distribution Of Damage Research Articles

Ultrasonic guided wave-based probabilistic diagnostic imaging method with Single-Path-Scattering sparse reconstruction for Multi-Damage detection in composite structures

Plate-like carbon fiber composite structures are essential for equipment such as spacecraft and rail vehicles. These structures are exposed to long-term cyclic loads and harsh environmental conditions, leading to damage of unknown location and quantity. Ultrasonic guided wave (UGW) detection technology shows promise for evaluating the structural performance of composite structures due to its advantages of high precision, high speed, and real-time capabilities. However, multi-damage scattering sources interfere with and superimpose the received signals when multiple damages coincide. This interference can lead to artifacts in probability imaging methods that rely on features such as amplitude and time of flight (TOF). This paper proposes a single-path-scattering sparse reconstruction-based probabilistic diagnostic imaging (SSR-PDI) method. Firstly, a Lamb dictionary with time shift is constructed. Each actuator-receiver path is treated as a target signal, enabling the approximate separation and extraction of multiple scattering waves from different damages. It mitigates the “curse of dimensionality” associated with the sparse reconstruction (SR) method. Secondly, a new ring-shaped damage probability distribution is proposed based on the sparse representation matrix’s time mapping and amplitude weighting. The experimental results demonstrate that the SSR-PDI method effectively mitigates issues related to multi-damage detection, specifically false negatives/positives and localization errors arising from the superposition of scattering sources.

The Storage Tank Explosion Damage and the Effectiveness of Control Measures in the Chemical Industrial Parks of Smart Cities

Safety is one of the goals of a smart city. To study storage tank explosion damage in a city’s chemical industrial parks, determine the position of control measures according to the situation, and realize the analysis of the measured utility, we proposed the area damage probability importance distribution. In this way, the prediction and prevention of risk in chemical industrial parks can be achieved intelligently. The concept of area damage probability importance distribution was given, and the utility analysis method of the control measures for storage tank explosion accidents was put forward. It is concluded that the area damage probability importance distribution represents the change degree of damage probability: that is, the damage degree of storage tank explosion in a chemical industrial park. The control measures for a storage tank explosion can be set up in varying positions, as the explosion damage is mainly caused by shock waves; the blast walls are selected as the measure set, and the calculation method for the area damage probability is modified. By comparing the calculated area damage probability distribution before and after, evaluation of the control measures’ effectiveness can be achieved. Finally, the flow chart of the algorithm is given. The example analysis shows that the calculation process and analysis results meet the design requirements of the algorithm. The effectiveness of the method, the distribution characteristics, and the significance and function of the importance distribution of damage probability are discussed. This provides an effective method for smart cities to predict and prevent the impact of an explosion at chemical industrial parks.

Probabilistic modeling of double linear damage accumulation and its application in fatigue reliability analysis

AbstractIn this paper, a probabilistic double linear damage accumulation model is proposed to characterize the uncertainty of damage accumulation using the statistics of material fatigue life. The probabilistic modeling framework is performed under normal distribution assumption of fatigue life. By applying a one‐to‐one probability density function transformation method, the probability distribution of critical damage and cumulative damage can be extracted and derived. The proposed probabilistic damage accumulation model is then used for fatigue reliability analysis by building the reliability formulas with respect to the cumulative damage and the critical damage under both constant and variable amplitude loadings. It treats the mean and variance of cumulative damage as time‐dependent values that dynamically vary with increase in usage life. The reliability can be easily calculated by limited data necessary from fatigue life samples. The applicability of the proposed method is demonstrated using the experimental data of two metallic materials under constant amplitude and two‐block loadings. The results show that the model predictions are in good agreement with the experimental observations under constant amplitude loading and L‐H loading sequence. In addition, the proposed method provides better predictive ability than the Miner rule under constant amplitude loading and H‐L loading sequence. Moreover, the predicted reliability plots can typically present a two‐stage fatigue characteristic during crack initiation and crack propagation periods.

Method of target damage probability distribution simulation and evaluation based on GPU parallel computing

Method of target damage probability distribution simulation and evaluation based on GPU parallel computing

Prediction model for sandstone strength based on Weibull distribution of micro-element strength and power-law distribution of crack length

It is of the great significance to construct the strength prediction model that considers the influence of the macro and micro defects in the rock in an overall manner to ensure the construction of smart mines and the safety of underground personnel and equipment. Based on the Weibull distribution of rock micro-element strength and the power-law distribution of crack length and the discrete element calculation model, the prediction model for strength of damaged rock specimens were established by numerical simulation and theoretical derivation respectively. Then the rationality of the model was verified by the calculated results. The results show that: 1) The weibull distribution of the micro-element strength and the power-law distribution of the crack length in the PFC2D calculation model are realized by programming, and the quantitative corresponding relationship between the macro, micro and micro damage in the rock and the corresponding distribution parameters is analyzed. 2) 400 sandstone specimens with macro, micro and micro damage are numerically established and loaded to achieve statistical analysis of the relationship between micro element strength, pre-crack information and rock strength. According to the simulation results, the four-dimensional space scatter points of uniaxial compressive strength of sandstone specimens are constructed, and the flow law of compressive strength of sandstone specimens under the influence of multiple damage parameters is obtained. 3) Combined with Mori Tanaka method and rock damage probability distribution theory, a 12 parameter rock strength prediction model is established. The model can both describe the influence of the micro-element strength and macroscopic crack information on the rock strength, and the model calculation results are highly consistent with the simulated results, with the correlation coefficient up to 0.991.

Monitoring fatigue cracks in rib-to-deck joints of orthotropic steel deck using ultrasonic Lamb waves

Fatigue cracks in rib-to-deck joints of orthotropic steel decks (OSDs) endanger the safety of bridges and are difficult to detect. This paper proposes to monitor fatigue cracks using ultrasonic Lamb waves. An OSD specimen instrumented with ultrasonic sensors was fabricated and tested to crack under fatigue loads. Ultrasonic Lamb waves were measured to detect, locate, visualize, and evaluate fatigue cracks using a probabilistic inspection of damage method. A finite element model was developed to understand wave propagation and crack growth process, and utilized to perform parametric studies on the type, position, and severity of cracks. The results indicated that fatigue cracks were effectively monitored by ultrasonic Lamb waves. Errors of crack positions were less than 5 mm. The damage probability distribution increased with the crack depth and crack length. The ultrasonic Lamb waves are more sensitive to toe-deck and root-deck cracks than other modes of cracks in rib-to-deck joints.

Fluvial Flood Losses in the Contiguous United States Under Climate Change

AbstractFlooding is one of the most devastating natural disasters causing significant economic losses. One of the dominant drivers of flood losses is heavy precipitation, with other contributing factors such as built environments and socio‐economic conditions superimposed to it. To better understand the risk profile associated with this hazard, we develop probabilistic models to quantify the future likelihood of fluvial flood‐related property damage exceeding a critical threshold (i.e., high property damage) at the state level across the conterminous United States. The model is conditioned on indicators representing heavy precipitation amount and frequency derived from observed and downscaled precipitation. The likelihood of high property damage is estimated from the conditional probability distribution of annual total property damage, which is derived from the joint probability of the property damage and heavy precipitation indicators. Our results indicate an increase in the probability of high property damage (i.e., exceedance of 70th percentile of observed annual property damage for each state) in the future. Higher probability of high property damage is projected to be clustered in the states across the western and south‐western United States, and parts of the U.S. Northwest and the northern Rockies and Plains. Depending on the state, the mean annual probability of high property damage in these regions could range from 38% to 80% and from 46% to 95% at the end of the century (2090s) under RCP4.5 and RCP8.5 scenarios, respectively. This is equivalent to 20%–40% increase in the probability compared to the historical period 1996–2005. Results show that uncertainty in the projected probability of high property damage ranges from 14% to 35% across the states. The spatio‐temporal variability of the uncertainty across the states and three future decades (i.e., 2050s, 2070s, and 2090s) exhibits nonstationarity, which is driven by the uncertainty associated with the probabilistic prediction models and climate change scenarios.

The use of fractional order statistics for estimating nonparametric confidence intervals for quantiles of the fatigue damage computed in service random loadings

This paper deals with the statistical variability of fatigue damage in random loadings as caused by the inherent randomness of the loading. It examines the use of a nonparametric method based on fractional order statistics as a tool for constructing confidence intervals for the quantile of fatigue damage, regardless of the knowledge of the damage probability distribution. The approach here discussed relies on a statistical method existing in the literature. After a short review of this method, with also an emphasis on possible advantages and limitations, the paper presents a numerical benchmark, followed by a practical application to time-histories measured on a mountain-bike in off-road tracks. The paper concludes with some critical remarks and an outlook.

Estimation of probability distribution of long-term fatigue damage on wind turbine tower using residual neural network

Fatigue is one of the most significant failure modes in structural and mechanical design. As for wind engineering, the fatigue issue on wind turbine towers is more critical since it concerns not only the structural safety but also the power production of the wind turbine. On the one hand, due to the complex fluid–solid interaction and the sophisticated control system of the wind turbine, it is impossible to predict the probability of fatigue-induced failure on wind turbine towers by analytical method. On the other hand, the structural reliability methods based on a numerical approach are usually time-consuming. To overcome these drawbacks, this work firstly proposes a probabilistic fatigue analysis framework to estimate the fatigue damage of wind turbine tower based on numerical simulations. Then, to reduce the computational cost of numerical approach, a residual neural network (ResNet)-assisted fatigue estimation approach is designed for the assessment of long-term fatigue loads under the proposed probabilistic fatigue analysis framework. The proposed probabilistic fatigue analysis framework estimates the cumulative fatigue damage on the cross-section of wind towers in a probabilistic pattern. The designed surrogate-assisted approach learns a model to approximate the relationship between wind speed and the fatigue damage. Then, this surrogate model can be used to predict fatigue damage under different wind speed so that a large number of simulation can be replaced by model prediction. Consequently, the efficiency of the proposed probabilistic fatigue analysis method can be significantly improved. Our proposed method is validated by numerical studies with a state-of-the-art wind turbine and has been applied in a wind turbine design with real-world wind loads.

Linear annular path damage probability distribution based ultrasonic guided wave method for position imaging and tracking of multi-damage on plate-like carbon fiber composite structure

Plate-like carbon fiber composite is an important component of the main bearing structure of spacecraft and high-speed trains, which has significant advantages in reducing the dead weight and energy consumption, and improving the carrying capacity. However, due to long-term exposure to complex service environments, material properties will be changed, these changes accumulated to a certain extent will lead to structural damage, threatening equipment operation and personal safety. To facilitate the attainment of mastering structural health states, this paper proposes a damage position imaging and tracking technology based on linear annular path damage probability distribution and ultrasonic guided wave for composite plate-like structures. Firstly, according to the dispersion curve, the propagation velocity characteristics of guided wave on composite structure are analyzed. Then, combined with the limited number of measured propagation velocities, the group velocity of the A0 mode in each direction is fitted. Based on the fitted velocity, the time-of-flight (TOF) map for all search points on each path can be pre-constructed. Subsequently, the damage TOFs and absolute TOF difference threshold are combined to obtain the annular damage probability distribution map of each sensing path. Ultimately, the total damage probability of the whole monitoring region is obtained by summing up the path damage probability, which can directly reflect the current damage position. Experimental results show that the proposed method has obvious advantages in imaging and tracking of single or multiple damage positions. It is hoped that the findings in this paper can provide new ideas for long-term damage state monitoring of the composite structures.

A simplified method for seismic assessment of unreinforced masonry buildings

ABSTRACT The paper presents a simplified vulnerability assessment method for unreinforced masonry buildings based on the evaluation of a few structural parameters, which can be determined from visual inspection and a geometry survey. The authors proposed an empirical approach with the aim to assess the in-plane vulnerability quickly by predicting the damage failure of bearing masonry walls. Field observations reveal different behaviours: out-of-plane and in-plane seismic responses. Several simplified assessments focus on out-of-plane behaviour. Few studies deal with in-plane seismic behaviour, which is also the expected response for more masonry buildings. The proposed seismic method provides a vulnerability index, which is evaluated as the weighted sum of 10 parameters markedly affecting the in-plane seismic performance. The reliability of the method is investigated through an application on buildings located in Central Italy, damaged by the 2016 earthquake. The mean damage and damage probability distributions were predicted for each building using the proposed method. Then, fragility functions were estimated from the results of non-linear static analysis, and the damage probability distributions were derived. The capability of the simplified method to foresee the damage probabilities was confirmed by a comparison between different approaches, confirming the reliability of the method in large-scale seismic assessment.

Rapid earthquake loss assessment based on machine learning and representative sampling

This article proposes a new framework for rapid earthquake loss assessment based on a machine learning damage classification model and a representative sampling algorithm. A random forest classification model predicts a damage probability distribution that, combined with an expert-defined repair cost matrix, enables the calculation of the expected repair costs for each building and, in aggregate, of direct losses in the earthquake-affected area. The proposed building representation does not include explicit information about the earthquake and the soil type. Instead, such information is implicitly contained in the spatial distribution of damage. To capture this distribution, a sampling algorithm, based on K-means clustering, is used to select a minimal number of buildings that represent the area of interest in terms of its seismic risk, independently of future earthquakes. To observe damage states in the representative set after an earthquake, the proposed framework utilizes a local network of trained damage assessors. The model is updated after each damage observation cycle, thus increasing the accuracy of the current loss assessment. The proposed framework is exemplified using the 2010 Kraljevo, Serbia earthquake dataset.

Analysis of probabilistic fatigue damage of mooring system for offshore fish cage considering long-term stochastic wave conditions

ABSTRACT This study deals with the probability distribution of fatigue damage of the mooring system for offshore fish cage considering the uncertainty of long-term wave conditions. A set of numerical simulations for offshore fish cage are performed to predict the fatigue damage of the mooring system. Through a virtual stochastic process model, the probability density function of the long-term fatigue damage of the mooring system is achieved by the generalized probability density evolution method, and the failure probability of the mooring system is predicted. The results demonstrate that the generalized probability density evolution method can effectively provide the fatigue damage distribution from the stochastic point of view. And the calibration of the engineering-based fatigue design factor of the current regulation can be conducted through the fatigue reliability analysis considering the uncertainty of the long-term wave conditions. This study provides a new understanding of the long-term fatigue damage distribution.

Comparative Investigation of Two Random Medium Models for Concrete Mesostructure

Concrete is intrinsically endowed with randomness on meso-scale due to the random distribution of aggregates, mortar, etc. In this paper, two random medium models of concrete mesostructure are developed and comparative studies are provided based on random field representation approach. In the first place, concrete is considered as a kind of one-phase random field, where stochastic harmonic function is adopted as the approach to simulate the random field. Secondly, in order to represent the stochastic distribution of the multi-phase of concrete such as aggregates and mortar, two-phase random field based on the Nataf transformation and the Hermite polynomials are introduced. Then, the proposed two random medium models are testified by the multi-scale simulation results, specifically, the mean value of the homogenized stress-strain relationship and the damage evolution curve. Meanwhile, the generalized density evolution equation is utilized to measure the consistency of these two random medium models by the probability distribution of damage.

Development of a reduced order model for severe accident analysis codes by singular value decomposition aiming probabilistic safety margin analysis

ABSTRACT Severe accident codes (e.g. MAAP, RELAP, and MELCORE) model various physical phenomena during severe accidents. Many analyses using these codes for safety margin evaluation are impractical due to large computational costs. Surrogate models have an advantage of quickly reproducing multiple results with a low computational cost. In this study, we apply the singular value decomposition to the time-series results of a severe accident code to develop a reduced order modeling (ROM). Using the ROM, the probabilistic safety margin analysis for the station blackout with a total loss of feedwater capabilities at a boiling water reactor is carried out. The dominant parameters to the accident progression are assumed to be the down-time and the recovery-time of the reactor core isolation cooling system, and decay heat. To reduce the number of RELAP5/SCDAPSIM analyses while maintaining the prediction accuracy of ROM, we develop a data sampling method based on adaptive sampling, which selects the new sampling data based on the dissimilarity with the existing training data for ROM. Our ROM can rapidly reproduce the time-series results and can estimate core conditions. By reproducing multiple results by ROM, a time-dependent core damage probability distribution is calculated instead of the direct use of RELAP5/SCDAPSIM.

Fatigue damage distribution and reliability assessment of grid mooring system for fish cage

This paper investigates the evolution of fatigue damage distribution with the loading cycle and predicts the annual fatigue damage distribution and system reliability of the grid mooring system under fatigue limit state for fish cage, employing the generalized probability density evolution method (GPDEM). A series of the hydrodynamic analysis for the grid mooring system of fish cage are performed to obtain the fatigue damage of the grid mooring system considering the long term environmental loading. The GPDEM equation is solved to determine the evolution of probability distribution of fatigue damage in term of the loading cycles, and the probability distribution of the annual fatigue damage of mooring lines is evaluated through the combination of the GPDEM and the virtual stochastic process model. In addition, the system reliability assessment of the grid mooring system under fatigue limit state is performed by the equivalent extreme-value event method. The results indicate that the probability distribution of the fatigue damage of the mooring component becomes more asymmetrical and platykurtic with the increase of the loading cycle and the annual fatigue damage distribution of the components in the grid mooring system can be estimated by the GPDEM from a stochastic point of view without any approximations or any asymptotic distributions. And it is necessary to conduct the uncertainty quantification of the Miner's sum at failure for the system reliability prediction of the grid mooring system under fatigue limit state to ensure the safety of fish farm.

Quantification of debris flow vulnerability of typical bridge substructure based on impact force simulation

Vulnerability analysis of engineering structures is an important aspect of risk assessment. It involves the probability that the structure meets or exceeds various set damage conditions under the influence of different risk levels. In order to quantitatively analyze the vulnerability of the typical bridge substructure under debris flow, four vulnerability curves with different damage levels under debris flow impact are obtained by numerical simulation of 150 damage conditions with the aid of three-dimensional finite element analysis software. The results show that the vulnerability curves of debris flow established in this paper are well fitted with data of numerical simulation. The acceleration is fastest in the middle of the curve, and high-intensity debris flow is more likely to cause high-level damage of bridge structure. By using the vulnerability curves established in this paper, the damage probability distribution under a certain debris flow intensity and damage control points of bridge substructure can be further obtained, which provides a basis for disaster prediction, risk management and reliability analysis of transportation system. The method and model presented can provide a reference for the vulnerability analysis of other types of structures under debris flow.

Modeling and calculation method of target damage based on multi-attitude flying projectile in space intersection

To study the damage correlation and damage efficiency of projectile fragment distribution for the target in space, a damage calculation modeling of multi-attitude projectile and target intersection is put forward in this paper. According to the spatial position of projectile and target, the triangular mesh method was used to establish the model of target damage probability and distribution under multi-attitude projectile fragment; calculate the spatial intersection parameters of different attitude fragment to triangular plane, analyze the correlation model of projectile and target intersection coordinate and the effective damage surface, set up the calculation function of target damage probability and projectile multi-attitude fragment distribution based on the vulnerable target characteristics and the triangular mesh distribution. The result shows that the closer space position of projectile explosion and target, the faster velocity of projectile, and the smaller dispersion density of fragment, the higher target damage probability.

Non-parametric prediction of the long-term fatigue damage for an instrumented top-tensioned riser

Marine risers are susceptible to sustained vortex-induced vibration (VIV) because of their slenderness and light damping. Commonly used tools for analyzing VIV and the associated fatigue damage are based on the finite element method and rely on simplifying assumptions on the riser's physical model, the flow conditions, and characteristics of the response. In order to assess the influence of VIV and to ensure the integrity of the riser, field monitoring campaigns are often undertaken wherein data loggers such as strain sensors and/or accelerometers are installed on such risers. Given the recorded riser's dynamic response, empirical techniques can be used in VIV-related fatigue estimation. These empirical techniques make direct use of the measurements and are intrinsically dependent on the actual current profiles. Damage estimation can be undertaken for the different current profiles encountered and can account explicitly even for complex riser response characteristics. With a significant amount of data, “short-term” fatigue damage probability distributions, conditional on current, can be established. If the relative frequency of different current types is known from a separate metocean study, the short-term fatigue damage distributions can be combined with the current distributions to yield an integrated “long-term” fatigue damage model, which then can be used to predict the long-term cumulative fatigue damage for the instrumented riser. Non-parametric statistical techniques (that do not assume a specific function for the underlying distribution as parametric techniques do) are employed to describe the short-term fatigue damage data. In this study, data from the Norwegian Deepwater Programme (NDP) model riser experiments are used to demonstrate the effectiveness of empirical procedures and non-parametric statistics applied to field measurements to predict long-term fatigue damage, life, and probability of fatigue failure.

Comparing the ISO-recommended and the cumulative data-reduction algorithms in S-on-1 laser damage test by a reverse approach method.

We compare the ISO-recommended (the standard) data-reduction algorithm used to determine the surface laser-induced damage threshold of optical materials by the S-on-1 test with two newly suggested algorithms, both named "cumulative" algorithms/methods, a regular one and a limit-case one, intended to perform in some respects better than the standard one. To avoid additional errors due to real experiments, a simulated test is performed, named the reverse approach. This approach simulates the real damage experiments, by generating artificial test-data of damaged and non-damaged sites, based on an assumed, known damage threshold fluence of the target and on a given probability distribution function to induce the damage. In this work, a database of 12 sets of test-data containing both damaged and non-damaged sites was generated by using four different reverse techniques and by assuming three specific damage probability distribution functions. The same value for the threshold fluence was assumed, and a Gaussian fluence distribution on each irradiated site was considered, as usual for the S-on-1 test. Each of the test-data was independently processed by the standard and by the two cumulative data-reduction algorithms, the resulting fitted probability distributions were compared with the initially assumed probability distribution functions, and the quantities used to compare these algorithms were determined. These quantities characterize the accuracy and the precision in determining the damage threshold and the goodness of fit of the damage probability curves. The results indicate that the accuracy in determining the absolute damage threshold is best for the ISO-recommended method, the precision is best for the limit-case of the cumulative method, and the goodness of fit estimator (adjusted R-squared) is almost the same for all three algorithms.