Probabilistic Damage Research Articles

Probabilistic damage evaluation of base-isolated reinforced concrete structures under near-fault pulse-like bidirectional seismic excitations

In this article, seismic fragility of a base-isolated special Reinforced Concrete (RC) moment frame is investigated under near-fault pulse-type ground motion records. The vulnerability of the displacement-dominated performance of isolator devices to a likely vibration resonance caused by such records is the focus of the study. For this purpose, Lead-Rubber Bearings (LRBs) and Triple Friction Pendulum Bearings (TFPBs) are utilized to represent various isolator behaviorisms in different period ranges. The structures are modelled in three dimensions to account for the axial-bending-bending interaction in the isolator devices. The models are then subjected to IDAs under three sets of near-fault pulse-type ground motion records with different pulse periods. Four different damage states are considered and the IDA results are used for deriving fragilities that express probabilities of exceeding these states at various intensity levels. The study revealed that despite the amplifying effects of the employed records, using isolators is still feasible. That is, even for pulse periods near to the effective period of isolators, resonance has not led to higher failure probabilities in the isolated buildings compared to their fixed-base counterparts. Furthermore, at longer pulse periods, the gradual yielding behavior of TFPBs made them more effective than the LRBs. Results also disclosed that at lower intensities, damage of base-isolated structures is mainly caused due to excessive floor acceleration while at higher intensities the maximum inter-story drift plays the dominant role. This suggest these two response parameters to be alternatively used as the Engineering Demand Parameter (EDP) when defining damage states at the medium and high intensity levels.

A Probabilistic Framework for the Fatigue Damage Assessment of Ships Navigating through Level Ice Fields

For ships navigating in ice-covered waters, fatigue damage due to ice loads is an important issue. The purpose of this paper is to provide ship researchers and engineers with a simulation-based procedure for a probabilistic fatigue damage assessment of ships moving through a level ice field. A novel procedure for fatigue damage assessment using numerical simulations is developed, and a hypothetical scenario with the Xuelong 2 icebreaker is used to illustrate the procedure. Long-duration time-domain simulations are performed to generate samples of the ice-load peaks due to ship-ice interactions. Based on the average conditional exceedance rate (ACER) method, the extreme value statistics of the line load peaks are predicted, and subsequently, the fatigue stresses caused by ice loads are estimated by means of beam theory. Several analytical models are applied to describe the probability distribution of the stress amplitudes, and the fatigue damage is calculated based on S-N curves and the Palmgren-Miner formula. Furthermore, a quantification of the effects of uncertainties related to discretization errors (mesh size, reference period), ship-model properties, choice of boundary conditions, and S-N curves is performed.

Tropical cyclone damage assessment of distributed infrastructure systems under spatially correlated wind speeds

Probabilistic damage evaluation and loss estimation of spatially distributed infrastructure systems (e.g. an electric power system or a building portfolio) under a scenario tropical cyclone must consider the spatial correlation of cyclone wind speeds to estimate their impact on the built environment statistically. Previous studies have seldom considered the impact of this spatial correlation on damage assessments of distributed civil infrastructure. In this paper, a stochastic field model is developed to capture the uncertainty of cyclone wind speeds and their spatial correlation for the North Atlantic region. A series of recorded wind speed fields of historical cyclone events are examined. The bias values between the recorded wind speeds and computed wind speeds based on a widely used cyclonic wind field model are obtained. The statistics of the wind field bias are estimated using geostatistical tools. The effect of wind speed uncertainty and spatial correlation on performance assessment of distributed infrastructure systems is illustrated using an electric power system, where the metrics of performance are damage ratio, outage ratio and outage cost.

Nonlinear static and dynamic analyses of Costa Rican reinforced concrete masonry structures

In Costa Rica, typical dwelling constructions are generally built with reinforced concrete masonry walls. This construction practice became one of the most common during the second half of the last century in Costa Rica. These kinds of structures exhibit high lateral stiffness and shear capacity, which makes them susceptible to semi-ductile failure or torsion if they are not correctly designed and constructed or the walls are not well distributed. However, recent research has shown that this type of masonry exhibits adequate capacity to dissipate plastic energy if the latter requirements are controlled. In this study, the seismic behavior of a recently designed and built reinforced concrete masonry structure is studied from a probabilistic perspective. Experimental results have been used to calibrate the probabilistic model. This structure was designed using the response spectrum method according to the Costa Rican Seismic Code. To verify its expected behavior considering more advanced analysis, it is analyzed through probabilistic incremental nonlinear static and dynamic computational-based methods. The aim is to obtain probabilistic damage curves in a series of permutations between the mechanical properties and the nonlinear behavior of the walls. Three different Damage Indices are estimated. Specifically, the Park & Ang damage index is used as a reference for two approximations that employ the capacity curve as input. Results indicate that the behavior of the analyzed structure is suitable for the seismic demand provided by the Costa Rican Seismic Code. Finally, correlations between input and output variables are calculated to analyze what are the variables governing the structural response. A strong relationship between masonry compression strength, Young’s module, and the post yielding slope (input variables) and all the output variables has been observed.

Research on probabilistic diagnosis-based structural damage identification using two-phase fusion of multi-source information

Several de-noising techniques have been proposed previously. However, in structural damage identification, it is still difficult to effectively eliminate the influence of noise by using any de-noising technique due to the complexity of environmental noise. This difficulty leads to the failure of some damage identification indices when used in practical applications, despite their high sensitivity to damage in simulation analyses. This paper proposes a probabilistic diagnosis-based method involving the fusion of two-phase multi-source information. First, local decision results of structural damage were obtained by using the improved element damage variable and the element stiffness reduction factor. Then, the Dempster-Shafer(D-S) evidence theory was used to fuse the local decision results to obtain the final decision results. By performing a simulation analysis and dynamic tests of a reinforced concrete beam and steel beam, it was confirmed that the proposed procedure demonstrated good stability and noise resistance.

Probabilistic damage simulation for strengthening design of concrete structures

AbstractShape memory alloy (SMA) is a smart material that can be applied as an internal and external reinforcement of reinforced concrete flexural elements in order to increase ductility and strength of the members. Column‐beam joint is a critical section of a concrete structure which under seismic and unexpected heavy loads may lead to failure of entire of the structure. Therefore, this numerical investigation aims to increase strength and mitigate risk of failure of the joint by employment of SMA plate. To do so, an experimentally investigated joint under 1000 load combinations has been simulated in Ansys APDL. Each load combo contained two axial loads and one bending moment; load values have been randomly selected through a procedure in MATLAB. Some nodes in plastic hinge region of the joint were chosen as control points. Generated load values were applied in the simulation, and stress of the control nodes was recorded. This process continued for all 1000 combos. Then, obtained results were imported into MATLAB for a probabilistic analysis. Probability of 0.95 quantile of stress of each node was calculated in order to design the required plate thickness at each node. Some numerical examples were applied on the designed plate. Results demonstrated that the designed SMA plate gets the risk of failure from the joint away and increase strength of the joint.

Performance-based wind-induced structural and envelope damage assessment of engineered buildings through nonlinear dynamic analysis

Performance-based wind engineering (PBWE) is undergoing a period of rapid development with numerous procedures and frameworks being proposed over the past few years. Notwithstanding these advancements, there is still a knowledge gap concerning the relative severity, dependency and rate of occurrence of structural and envelope damage in extreme wind events. This work is focused on investigating this problem for engineered buildings. In particular, envelope damage is estimated through a recently introduced PBWE framework that explicitly includes the effects of demands originating from dynamic net pressure and the structural responses. Structural damage is estimated through both fragility analysis as well as material yielding/hysteresis modeled through the adoption of a nonlinear fiber-based finite element formulation. Structural responses include the effects of large deformations through solving the finite element model in a corotational environment. To investigate the relative severity and dependency between the damages, a carefully calibrated archetype 45-story steel building located in Miami, FL, and subject to hurricane winds is studied. Probabilistic damage metrics are estimated for both the envelope and structural systems and are subsequently discussed in terms of relative severity, occurrence rates and nonlinear structural behavior.

Limited Sensor-Based Probabilistic Damage Detection Using Combined Normal–Lognormal Distributions

A methodology for probabilistic damage detection in Bayesian framework without any requirement of mode matching is presented with detailed formulations on finite element model updating using incomplete modal data measured using limited number of sensors. Multiple modal measurement/data sets from multiple different sensor set-ups can be used in the proposed methodology with further scope for using repeated measurements from any single sensor set-up. Combined normal–lognormal multivariate distribution is considered in the Bayesian framework. Strictly positive random parameters are assigned with lognormal distribution, while the remaining random parameters are assigned with normal distribution. In this work, the normal distribution is incorporated for the likelihood function, which consists of the eigen-system equation error and the error between the system mode shapes and experimental mode shapes. On the other hand, mass and stiffness parameters are assigned with the lognormal distribution. Detailed formulations for probabilistic identification of changes/damages are also developed. The proposed approach is validated using a three-dimensional building structure considering multiple simulated damage cases. Performance in updating and damage detection is evaluated based on multi-set-up and multi-dataset considerations. Besides, the proposed technique is compared with the similar Bayesian updating solely based on normal distribution and the Gibbs sampling.

Extended mean-field homogenization of viscoelastic-viscoplastic polymer composites undergoing hybrid progressive degradation induced by interface debonding and matrix ductile damage

In this contribution, a probabilistic micromechanics damage framework is presented to predict the macroscopic stress–strain response and progressive damage in unidirectional glass-reinforced thermoplastic polymer composites. Motivated by different failure modes observed experimentally, the damage mechanism in the vicinity of the fibers (namely, the interphase) is characterized by initiating and growing voids. The mechanisms can be formulated through a Weibull probabilistic density function. In contrast, the ductile progressive degradation of matrix initial stiffness is analyzed via the continuum damage theory. To accommodate different damage mechanisms in the matrix and the interphase, a three-phase Mori-Tanaka (MT) method and transformation field analysis approach (TFA) are established within a unified framework that allows simulation of both ductile and discrete damages in different phases. Moreover, the rate-dependent viscoelastic and viscoplastic response of the polymer matrix phase is modelled through a phenomenological model consisting of four Kelvin-Voigt branches and a viscoplastic branch under the thermodynamics framework. The reliability and efficiency of the modified mean-field damage model, based on TFA and Mori-Tanaka scheme, are assessed by comparing the simulated stress-strain response against full-field Abaqus simulations under both unidirectional and multiaxial nonproportional loading paths at different loading rates. The developed model provides an efficient alternative to the finite-element based full-field homogenization schemes or other mean-field micromechanics techniques that may be compared, as well as a framework for a potential extension of the theory for simulating damage evolution in composites with random reinforcement orientations.

A multiscale modeling of damage accumulation and permeability variation in shale rocks under mechanical loading

This paper presents a hierarchal multiscale model to simulate the damage behavior of transversely isotropic shales, where the damage mechanism is attributed to microcrack growth under mechanical loading. An anisotropic damage model is presented in which the state of damage is described by a scalar crack density parameter. Furthermore, a simplified permeability model is incorporated to couple the evolution of damage to permeability variation through the damage density parameter. The Maximum Entropy principle is employed to account for uncertainty in the main parameters of the multiscale model representing the subscale structural and compositional features. This probabilistic multiscale damage model provides a framework to simulate the probabilistic descriptions of poromechanical and damage properties and the subsequent variation in microcrack-induced permeability. This framework is used to simulate nonlinear stress-strain behavior in uniaxial compression tests for varying loading directions with respect to the bedding plane of transversely isotropic shale rocks. The outcome of this study includes probabilistic characteristics of stiffness degradation, crack growth, and permeability variation under different loading conditions.

Degradation analysis on high-cycle bending fatigue for woven SiC/SiC composites based on Wiener process model

A comprehensive investigation of degradation analysis under high-cycle bending fatigue (HCBF) loading for composite materials was conducted based on the Wiener process model. Degradation data are generated by conducting the probabilistic progressive damage analysis of composite materials considering the variability of material properties including mechanical properties and strength. Based on the degradation data, the Wiener process model is established with the power time transformation function and linear time-scale functions. The HCBF tests of composite cantilever beam specimen (CBS) and turbine guide vane (TGV) are conducted to evaluate the degradation process of composite materials. Compared with the experimental data and Monte Carlo simulation (MCS) method, the proposed methodology has the promising potentials to improve computational efficiency with acceptable computational accuracy for the CBSs. As for the TGV, the maximum relative errors for mean fatigue life are within 17.89%, while the degradation tendency from experiments is similar to the simulated degradation curves, verifying the rationality of the proposed method based on Wiener process model. Moreover, reliability analysis is conducted based on the stochastic degradation process, which can be used to determine whether the performance of the structure meets the design requirement.

Digital twin approach for intelligent operation planning and health management of mechanical systems

The digital twin paradigm aims to fuse information obtained from sensor data, physics models, and operational data for a mechanical component in use to make well-informed decisions regarding health management and operations of the component. In this work, we discuss a methodology for digital-twin-based operation planning in mechanical systems to enable: a) cost-effective maintenance scheduling, and b) resilient operations of the system. As properties of mechanical systems, as well as their operational parameters, loads and environment are stochastic in nature, our methodology includes probabilistic damage diagnosis, probabilistic damage prognosis, and system optimization under uncertainty. As an illustrative example, we consider the problem of fatigue crack growth in a metal component. We discuss a probabilistic, ultrasonic-guided-wave-based crack diagnosis framework that can handle both aleatory and epistemic uncertainties in the diagnosis process. We build a high-fidelity, finite element model to simulate the piezoelectric effect and ultrasonic guided wave propagation. We use test data obtained by conducting diagnostic experiments on the physical twin to calibrate the error in the diagnosis model. We perform Bayesian diagnosis of crack growth using the corrected diagnosis model, considering data corrupted by measurement noise, and fuse the information from multiple sensors. We build a finite-element-based high-fidelity model for crack growth under uniaxial cyclic loading, and calibrate a phenomenological (low-fidelity) fatigue crack growth model using the high-fidelity model output as well as data from fatigue loading experiments performed on the physical twin. We use the resulting multi-fidelity model in a probabilistic crack growth prognosis framework; thus achieving both accuracy and computational efficiency. Lastly, we utilize the damage diagnosis framework along with the damage prognosis model to optimize system operations under diagnostic and prognostic uncertainty. We perform simulation as well as laboratory experiments that show how the digital twin of the component of interest can be used for intelligent health management and operation planning for mechanical systems.

A novel mode-dependent and probabilistic semi-discrete damage model for progressive failure analysis of composite laminates - Part I: Meshing strategy and mixed-mode law

A novel semi-discrete damage model (SD2M) is proposed for the progressive failure analysis (PFA) of composite structures. The presented method utilizes a separation of fiber and matrix failure modes and introduces a material strength distribution to thin strips of matrix-splitting elements in order to capture the progression of transverse crack density. With the proposed meshing strategy, the discreteness is greatly enhanced, while the model remains efficient and simple by using solely continuum elements. The SD2M approach aims to unify desirable features of both smeared and discrete methods and utilizes a practical and simple mesh generation procedure. In addition, a novel mixed-mode law is proposed to capture the damage evolution of matrix cracks. The proposed mixed-mode formulation ensures smooth and simultaneous vanishing of traction components and is suitable for generic softening laws. Applications of SD2M to several examples are presented in part II [1] of this two-part paper.

A novel mode-dependent and probabilistic semi-discrete damage model for progressive failure analysis of composite laminates - Part II: Applications to unnotched and open-hole tensile specimens

A new method is introduced in part I of this two-part paper [1] to model the progressive failure of composite laminates. In this second part, the method is applied to unnotched (UNT) and open hole tensile (OHT) specimens. With semi-discrete meshing features and a randomized material distribution, the proposed model is capable of capturing both ultimate failure and damage progression. The increase of crack density and splitting as well as fiber failure localization are demonstrated on the basis of the cross-ply tensile specimen. Similar mechanisms, including free edge cracking, are predicted in the more complex (50/40/10) layup. With a simple technique, the meshes are efficiently generated for unnotched and notched specimens using Abaqus CAE/ Python scripting. As a result, the model is able to capture the discrete cracking near the hole as well as stress concentrations using a locally refined mesh region. By unifying features of both smeared and discrete methods, the presented semi-discrete damage model (SD2M) is seen to provide a pathway to model a variety of failure mechanisms and their interactions fairly accurately and efficiently, leading to very good predictions of ultimate strengths.

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.

A reliability-based sieve technique: A novel multistage probabilistic methodology for the damage assessment of structures

A novel multistage probabilistic methodology called the “Reliability-Based Sieve Technique (RBST)” is presented in this paper for the reliable assessment of the functionality of structures. In this method, the structural damagedetectionproblem is defined as a multistage probabilistic optimization problem. The Holistic Objective Function (HOF) based on the combination of the inherent characteristics of the structure (i.e., the vibration frequencies and mode shapes) is incorporated into the Interactive Autodidactic School (IAS) optimization algorithm, for the first time, to solve the problem. In addition, the Latin Hypercube Sampling (LHS) techniqueis used to simulate and analyzethe probabilistic damage assessment problem. In each stage of the proposed methodology,the Probability of Damage Existence (PDE) is computed in each of the structural elementsthrough a probabilistic damage detection analysis. According to the results of the PDE inthe structural elements in each stage, the elements with low PDEsare gradually sieved inthe subsequent steps. The sifted elements ineach stage are considered asintactones in the next stage. This systematic filtration of the design variables can simultaneously decrease the dimensions and increase the speed of the optimization problem. To improve the performance of the RBST, the sizesof the sieves are regularly reduced for the next stages. This multistage procedure iscontinueduntil convergence to a precise structural damage location diagnosis and intensity prognosis is achieved. Finally, to investigate the efficiency and robustness of the proposed technique, it is examined on three benchmark structures by taking the high level of uncertainties associated with both finite element modeling errors and vibration data noises into account. The obtained results confirmed that the proposed technique correctly identifies the damage indices and has consummate capability compared with the single-stage probabilistic analysis. Likewise, it is observed that the RBST accurately sieves the intact elementsfromthe vector of the design variables in highly noisy conditions. Consequently, in the presence of both mentioned uncertainty sources, the RBST not only assesses the damage site and extent properly, but also shows a reliable performance in terms of PDE.

Identification of Structural Stiffness and Mass using Bayesian Model Updating Approach with Known Added Mass: Numerical Investigation

The Bayesian model updating approach (BMUA) has been widely used to update structural parameters using modal measurements because of its powerful ability to handle uncertainties and incomplete data. However, a conventional BMUA is mainly used to update stiffness with the assumption that structural mass is known. Because simultaneously updating stiffness and mass leads to unidentifiable case or coupling effect of stiffness and mass, this assumption in conventional BMUA is questionable to update stiffness when the mass has significantly changed. This study proposes a new updating framework based on two structural systems: original and modified systems. A modified system is created by adding known mass to the original system. Different from the conventional Bayesian approach, two sets of measured vibration data in the proposed Bayesian approach are obtainable to address the coupling effect existing in the conventional Bayesian approach. To this end, a new approach reformulates the prior probability distribution function and the objective function. Two numerical simulations are considered to demonstrate the performance of the proposed approach, including (1) parameter identification, (2) posterior uncertainties, (3) probabilistic damage detections. The proposed BMUA outperforms a conventional BMUA in identifying both stiffness and mass.

Earthquake evacuation simulation of multi-story buildings during earthquakes

Through combining a network-based pedestrian dynamics simulation model, simplified probabilistic structural damage assessment, and structural random vibration analysis, a fully random evacuation model is proposed for simulating and analyzing earthquake evacuation processes of multi-story buildings during earthquakes. The model simplifies the simulation of three-dimensional pedestrian dynamics, couples the emergency evacuation processes and damage processes of structures, and takes into account the randomness of pedestrian dynamics, structural damage, and earthquake excitation. The model can be used for the fast pre-evaluation or evaluation of the earthquake evacuation capabilities of multi-story buildings. The simulation and analysis of the earthquake evacuation process of a three-story office building, in which a total of 60 persons work in the first and second stories, illustrates the effectiveness and implementation of the proposed model.

Research of Method for Improving Antifreeze-Thaw Performance Based on Asphalt Mixture Freeze-Thaw Damage Development Process

To improve the antifreeze-thaw performance of asphalt pavement in the seasonal freezing regions, the temperature and the time of freeze-thaw test were redesigned based on the climatic characteristics of the regions, and the splitting tensile strength tests were carried out to determine the low-temperature performance of the asphalt mixture under the influence of the gradation and the asphalt-aggregate ratio. A mathematical model was built to investigate the freeze-thaw damage law. According to the test results of splitting tensile strength of the asphalt mixture under freeze-thaw cycles, the probabilistic damage variable of the asphalt mixture was redefined and a physical probability model was built to analyse the freeze-thaw damage. Based on the freeze-thaw damage development process and the mechanism of the asphalt mixture, the effective measures to improve the antifreeze-thaw performance were provided and demonstrated through the correlations among the damage parameters (the shape parameter α, the scale factor λ, and the gradient factor ν) and the freeze-thaw resistance of the asphalt mixture. The test results showed that the splitting tensile strength decreased with the increase of the number of the freeze-thaw cycles. With the same gradation, the splitting freeze-thaw damage degree of the asphalt mixture with 5.8% asphalt-aggregate ratio is about 6% less than others after the 18th freeze-thaw cycle. The freeze-thaw resistance increases with the asphalt-aggregate ratio. With the same asphalt-aggregate ratio, the splitting freeze-thaw damage degree of S-grade mixtures is about 11.8% higher than that of Z-grade mixtures. S-grade mixtures have positive effects on the freeze-thaw resistance. The results suggest new measures for further investigation on the design and maintenance of the asphalt mixture in the seasonal freezing regions.

Stochastic nonlocal damage analysis by a machine learning approach

A machine learning aided stochastic nonlocal damage analysis framework is proposed for quasi-brittle materials. The uncertain system parameters, including the material properties and loading actions, have been incorporated and analysed within a unified safety assessment framework against various working conditions. A three-dimensional integral-type nonlocal damage model through finite element method (FEM) has been adopted. For the purpose of investigating the probabilistic damage analysis problems, a freshly established machine learning approach, namely the capped-extended-support vector regression method (C-X-SVR), is proposed to eliminate the influences of random outliers in the first step, then establish the relationship between the uncertain systemic inputs and structural responses. Such that the training robustness and computational adaptability of the proposed regression model can be reinforced. Moreover, the proposed approach is competent of efficiently predicting the statistical information (i.e., means, standard deviations, probability density functions and cumulative density functions) of structural behaviours under continuous information update of the uncertain working condition from mercurial environment. One real-life experimental validation and two numerical investigations are implemented to further verify the effectiveness and efficiency of the uncertainty quantification framework against probabilistic damage analysis.