Structural Reliability Assessment Research Articles

Post-earthquake reliability assessment of segmental column structures based on nonlinear model updating

In this study, a Bayesian based nonlinear model updating approach is developed to enhance the post-earthquake reliability assessment of posttensioned segmental column structures. According to the proposed procedure, dynamic global sensitivity analysis (DGSA) approach is firstly performed to analyze the sensitivity of the model outputs to the model parameters, which aims to select the appropriate parameters for model updating, and then, the likelihood function of Bayesian estimation is constructed based on the residual errors between the measured and simulated dynamic responses of segmental column structures. Since the decomposed structural dynamic responses are conducted for model updating, the simulated error variance parameters are also considered as unknown. To simultaneously estimate the unknown model parameters and variance parameters, the maximum likelihood estimation approach is employed in this study. Then, the Cram-Rao lower bound (CRLB) analysis method is applied to estimate uncertainty of the identified model parameters that caused by measurement noise. Once nonlinear model updating is completed, the earthquake-induced failure probability of segmental column structure can be evaluated by performing reliability analysis. In numerical simulations, the feasibility of the proposed reliability assessment approach is validated by using a planar posttensioned segmental column model subjected to seismic loads. Furthermore, a scaled posttensioned segmental column structure subjected to bi-directional earthquake exactions is applied to verify the effectiveness of the proposed approach. Both numerical and experimental results have shown that the proposed strategy is accurate and effective for nonlinear model updating of segmental column structures, and the updated results are capable of using to evaluate the failure probability of such type of structures subjected to strong external excitations.

Development of Performance-Based Fragility Curves of Coastal Bridges Subjected to Extreme Wave-Induced Loads

A number of coastal bridges faced significant damage due to recent natural hazards, inducing extreme waves. The fragility function is the basic step for assessing the resilience of a structure, thereby allowing the designers to alleviate post-event structural disasters and develop improved design methods for new structures. The majority of the focus of fragility functions developed in literature are concentrated on superstructure components and wave load on bridge decks. This paper presents a simplified methodology for the definition of damage states of the substructure component (pier drift) due to wave loads acting on piers as well as the bridge deck. The hazard intensity parameters representing the extreme wave loads chosen for this study are wave period, wave height, and still water depth. The Latin hypercube sampling technique is applied to consider the uncertainties in the intensity parameters as well as the material properties for the finite-element bridge models. Results indicate that the wave period is the most dominant factor affecting the wave-load intensity. The deck-level loading caused a higher probability of failure compared with the pier-level wave loading scenario. In both loading scenarios considered, the elastomeric bearing and shear keys are found to be one of the most vulnerable components in the system-level fragility curves developed. The system-fragility curves generated in this paper can be used to assess the resiliency of coastal bridges subjected to extreme wave-induced loads. The findings of this paper will also add to the risk mitigation and reliability assessment of coastal structures under multi-hazard conditions.

Structural Time-Dependent Reliability Assessment: Advanced Approaches for Engineered Structures

Structural Time-Dependent Reliability Assessment: Advanced Approaches for Engineered Structures

Structural reliability and partial safety factor assessment of unreinforced masonry in vertical bending

ABSTRACT This paper focuses on a structural reliability-based assessment of clay brick unreinforced masonry (URM) walls subjected to uniformly distributed out-of-plane loads in one-way vertical bending. Stochastic models combining finite element analysis (FEA) and Monte Carlo simulations (MCS) are used to account for spatial variability of the flexural tensile bond strength when estimating the wall failure loads. The strength of URM walls is known to be influenced by the flexural tensile bond strength, which is subject to high spatial variability as batching, workmanship, and environmental exposure alter the strength of this bond. For this assessment, single skin walls have been considered with bond strength statistics seen in typical construction. The model error statistics available for similar walls are combined with the results of the spatial stochastic FEA and probabilistic load models to determine the reliability index corresponding to the Australian Standard for Masonry Structures AS 3700 design of members in vertical bending. It was found that existing levels of reliability exceed target reliabilities, and the capacity reduction factor can be increased from 0.60 to 0.65 for URM walls in one-way vertical bending while still providing an acceptable level of reliability. A sensitivity analysis showed this finding to be robust.

Structural health monitoring and fatigue life reliability assessment of a flexible structure in extreme wind

Structural health monitoring and fatigue life reliability assessment of a flexible structure in extreme wind

Generalized first-order second-moment method for uncertain random structures

<abstract> <p>In this paper, a new reliability assessing method for structures influenced by both aleatory and epistemic uncertainty simultaneously is developed. To handle hybrid types of uncertainties, chance theory is introduced to define a new hybrid reliability index. By mathematical derivation and theorems proofs, the new index is showed to be effective and compatible with hybrid types of uncertainties. Correspondingly, a generalized first-order second-moment (GFOSM) algorithm is established for practical reliability assessment of structures with hybrid uncertainties. Based on the first two moments of basic variables, the GFOSM method can perform fast and effective reliability assessment without large-scale integration operations and can be considered as an extension and expansion of the traditional FOSM method. Two numerical cases further illustrate the effectiveness and practicability of the proposed method from different perspectives.</p> </abstract>

A note on peak inelastic displacement as a proxy for structural damage in seismic sequences

Structural reliability assessment for a building that may experience damage accumulation during a seismic sequence can play an important role in decision making for post-earthquake repair operations or demolition and rebuilding. This typically requires the integration of the aftershock ground motion hazard at the site with the probabilistic description of the damaged building's capacity to withstand the shaking of the seismic sequence. This is usually quantified as the conditional probability that the structure, starting from a specific damage state and for given shaking intensity, will reach a more severe one. In sequence-based seismic risk studies, an analytically-derived estimate of the peak inelastic displacement is often used as a proxy for structural damage. This paper investigates the issues behind this choice and the ability of inelastic displacement demand to adequately describe structural damage due to a seismic sequence, when compared with more direct metrics of damage, such as stiffness and strength degradation. To reach this objective, a series of inelastic single-degree-of-freedom systems, having different natural period, backbones and post-elastic behavior, were subjected to sequential dynamic analysis, while considering a series of arbitrarily chosen damage states, conventionally defined by displacement demand thresholds. The investigation showed that maintaining the attractive simplicity of deformation-based damage proxies in sequence-based risk analysis, can lead to some counterintuitive representations of seismic vulnerability. Some results suggest that such problems could be alleviated if one were to consider some dependence of damage state transition thresholds on the current state of the structure.

An Application of Relative Entropy in Structural Safety Analysis of Elastoplastic Beam under Fire Conditions

The main aim of this work is to propose a new algorithm of reliability assessment for steel civil engineering structures subjected to fire temperatures. This new algorithm is based upon the relative probabilistic entropy concept elaborated by Bhattacharyya, and this probabilistic distance is sought in-between extreme and admissible deformations of some structural beam subjected to higher temperatures. Similar to the First Order Reliability Method, this approach uses the first two probabilistic characteristics of the structural response, when structural output may be modelled with the use of Gaussian distribution. The probabilistic structural response is found here using hybrid computational technique–the Finite Element Method system ABAQUS with its fully coupled thermo-elastic analysis with 3D solid elements and probabilistic modules implemented in the computer algebra system MAPLE. The probabilistic response is determined via a triple stochastic analysis, which is based on the classical Monte-Carlo simulation, iterative generalized stochastic perturbation technique, and also using semi-analytical probabilistic calculus. Final determination of the relative entropy in the Serviceability Limit State of the given structure and its comparison with the results obtained using the FORM analysis enables to calibrate this new technique to numerical values proposed in the engineering designing codes. Hence, a more accurate probabilistic method may use some experimental-based admissible values included in the existing design of legal provisions.

Simulation Analysis and Experimental Study of the Strength of Aluminum Alloy Suspension Structure

High-speed trains have a large amount of ancillary equipment, which is suspended from the underside of the train by means of a suspension structure. Due to the large mass of the ancillary equipment, the suspension structure is subjected to various loads during train operation and there is a risk of fatigue failure. In this paper, the stress distribution at the suspension point and the lo-cation of the maximum stress point under load are investigated in detail based on actual test loads at the suspension point and finite element simulation analysis. In order to further investigate the fracture failure of the suspension points, experimental studies were carried out. Firstly, static strength tests were carried out to obtain the load-displacement curves of the structural members and to determine the fracture strength of the structure based on the displacement sensors, and secondly, fatigue tests at different stress levels were carried out to obtain the load-life curves of the structural members and to investigate the probabilistic load-life curves at different reliability levels. The test results show that the structural component has a high fracture strength of 65kN, while the conditional fatigue strength is relatively low, corresponding to a load level of 12.5kN at a median life of 106 cycles. The above research work provides the necessary basis for the design, optimization and reliability assessment of the suspension structures of high-speed trains.

Reliability Analysis and Life Prediction of Aging LNG Unloading Arms Based on Non-Destructive Test Data

Unloading arms (ULAs) among seaport infrastructures are susceptible to deterioration posed by the effects of harsh marine environmental conditions. During infrastructure’s service life, the deterioration of structural integrity may increase the risk of failure of infrastructure, and should be taken into account during structural reliability assessment. In this study, a simple non-destructive test (NDT) was employed to examine the structural deterioration of ULAs which were installed over 30 years ago. Then, these aging ULAs were modeled by the finite-element program, using non-destructive test data to update the thickness dimensions of structural members. Next, a reliability assessment was conducted based on the stress distribution of the main structural components under external loads, which are calculated by their relation to wind speed. Moreover, the time-dependent reliability index curve was also built by considering the deterioration function to predict the failure probability of the particular components during the remaining lifetime. The study revealed that the present condition of the ULA system was satisfactory for current loading conditions. A reliability index predicted with deteriorations factors may be a rational and appropriate approach for the assessment of aging structures needed for efficient infrastructure management.

Mechanical and Morphological Characterizations of Laminated Object Manufactured 3D Printed Biodegradable Poly(lactic)acid with Various Physical Configurations

Mechanical behavior of 3D-printed poly(lactic) acid material is an open topic for research on the reliability assessment of structures in marine and offshore industries. This article presents the mechanical and morphological properties of poly(lactic) acid specimens using the laminated object manufacturing technique. The effect was experimentally investigated on 3D-printed discs joined together to make a laminated test specimen. The specimen was prepared and tested under different infill patterns, viz. linear, triangular, and honeycomb structure, 50–90% infill density, and under varying disc thickness ranging from 3.4–5.6 mm. The maximum compressive strength of 42.47 MPa was attained for the laminated specimen with 70% infill, honeycomb pattern, and disc thickness of 3.4 mm (six discs), whereas the linear infill pattern has shown the least compressive performance of 22.40 MPa. The result of the study suggested that the honeycomb infill pattern with 90% infill density and six discs provides the optimum set of parameters for the 3D printing of PLA samples for maximization of compressive strength, especially for laminated object manufactured specimens. The Taguchi L9 orthogonal analysis (OA) suggested a significant influence on the infill pattern and the number of discs, contributing 51.60% and 48.29%, respectively, towards the compressive strength. Scanning Electron Microscopy (SEM) and toolmaker microscopic images have supported the observed experimental mechanical results for the laminated object manufactured specimens. The used technique of laminated object-manufactured components in the current study may have effective usage in marine and structural engineering fields.

Seismic collaborative reliability evaluation of slopes using subset simulation via support vector machine

The computational effort places a limit on the low failure probability estimate of geotechnical engineering exposed to seismic stimulation. In this research, a novel method is proposed for the seismic reliability assessment of complicated geotechnical engineering slope structures with low failure probability. First, an improved subset simulation (SS) approach is provided for the low-failure events with high-dimensional indirect cross-correlation parameters. This method expands the usefulness of SS by using the support vector machine (SVM) method. Then, in order to reduce computing effort, the seismic collaborative reliability evaluation (SCRE) framework for seismic reliability assessment based on SS and the response conditioning method (RCM) is constructed. Finally, the accuracy of SCRE is verified by comparison with the standard Monte Carlo simulation based on 2D slope. The results show that SCRE's computational effort is approximately 2% that of Monte Carlo simulation. Meanwhile, SVM does a good job of preserving the significant indirect cross-correlation that occurs in the subspace samples that were split by SS. The time-saving benefit of SCRE is further enhanced when the aforementioned situations are expanded to 3D, and the findings demonstrate that the failure probability and sliding surface of the slope are different in 2D and 3D.

Improved estimation on seismic behavior of RC column members: A probabilistic method considering dynamic effect and structural parameter uncertainties

To acquire more accurate and reliable seismic behavior of reinforced concrete (RC) column members, a probabilistic estimation method for considering both the impacts of loading rate-sensitivity of materials and randomness in structural parameters is proposed in this paper. The previously developed dynamic modified coefficient (DMC) models are extended to include different sources of uncertainties by using the Monte-Carlo (MC) simulation with the Latin hypercube sampling (LHS) technique. The influences of variations in key structural parameters on the DMC estimates are investigated through sensitivity analysis. Moreover, the accuracy and effectiveness of the proposed method are verified by qualitatively and quantitatively comparing the probabilistic predictions with the available dynamic loading test results. Furthermore, the computation procedure of the dynamic skeleton model cluster (DSMC) is put forward and typical cases of skeleton line are also discussed. The impacts of randomness in structural parameters and skeleton line number on the DSMC predicted results are presented. This research shows that more reasonable estimate on the seismic behavior of RC column members can be obtained by employing the proposed probabilistic method, which can be further applied into the seismic reliability assessment of RC frame structures in future research works.

The Inverse Transformation of L-Hermite Model and Its Application in Structural Reliability Analysis

In probabilistic analysis, random variables with unknown distributions are often appeared when dealing with practical engineering problem. A Hermite normal transformation model has been proposed to conduct structural reliability assessment without the exclusion of random variables with unknown probability distributions. Recently, linear moments (L-moments) are widely used due to the advantages of stability and insensitivity. In this paper, the complete expressions of the inverse transformation of L-moments Hermite (L-Hermite) model have been proposed. The criteria are proposed to derive the complete inverse transformation of performance function and the complete expressions of the inverse transformation of L-Hermite model are formulated. Moreover, a first-order reliability method for structural reliability analysis based on the proposed inverse transformation of L-Hermite model is then developed using the first four L-moments of random variables. Through the numerical examples, the proposed method is found to be efficient for normal transformations since the results of the proposed L-Hermite are in close agreement with the results of Rosenblatt transformation. Additionally, the reliability index obtained by the proposed method using the first four L-moments of random variables provides a close result to the reliability index obtained by first-order reliability method with known probability density functions in structural reliability assessment.

Novel Nonprobabilistic Bayesian Uncertainty Quantification Method for Structures with Interval Parameters

Structural reliability analysis is a crucial task in structural safety analysis. Owing to insufficient data information, traditional probabilistic methods do not accurately quantify input or output variables and the resultant assessment of structural reliability. Considering the development of engineering technology, a quantitative model of uncertainty based on improbability method is urgently needed. Herein, a novel nonprobabilistic Bayesian-inference-based interval uncertainty quantification model is developed with a user-specified credibility level. On the contrary, limited samples are introduced to update the bounds of the interval, and the conservativeness is decreased compared to the traditional unbiased interval estimation based on uniform distribution. Moreover, it can provide more conservative quantification than the extreme values-based interval model. Consequently, two examples are implemented to demonstrate the feasibility and effectiveness of the proposed model.

Two multifidelity kriging-based strategies to control discretization error in reliability analysis exploiting a priori and a posteriori error estimators

This paper presents two approaches to tackle the issue of discretization error in the reliability assessment of structures. The first method (AGSK-MCS for Adaptive Guaranteed State Kriging Monte Carlo Sampling) uses discretization error bounds to guarantee the state safe or failed of the points used to build the Kriging metamodel of the limit state function. Two kriging metamodels interpolating lower and upper bounds can be constructed. These metamodels allow to compute discretization error bounds on the probability of failure through Monte Carlo sampling, which can then be used to validate the choice of the mesh. However, discretization error bounds are not available for any solver and any mechanical problem. In that case, a Mesh Size parameterized Kriging (MSK) metamodel can be used to check mesh convergence of the probability of failure. First, finite element simulations are spread on different mesh sizes. Second, the metamodel is used to compute the probability of failure for a given set of mesh sizes using Monte Carlo estimation. The mesh convergence of the probability of failure can be checked and may guide the user toward remeshing. These two strategies are illustrated on two 2-D mechanical problems.

Time-Dependent Sensitivity of Structural Reliability Assessment to Multi-Source Uncertainties Using Lamb Wave

Abstract This article investigates the time-dependent sensitivity of structural reliability assessment to multisource uncertainties using Lamb wave. To precisely model the influence of local damage on the structure in the course of damage growth, a surface damage effect model is proposed to obtain the equivalent elasticity modulus, which can be coupled with the structure model. The evolution of the surface damage is modeled using the fatigue crack propagation model. Furthermore, by setting up the component and structure failure criteria, the time-dependent reliability model of the structure under multisource uncertainties from Lamb wave detection and material properties is established. The method of score function is employed to evaluate the sensitivity index, which is defined as the derivative of the reliability with respect to the distribution parameters of uncertain variables. A spatial truss structure is used to demonstrate the overall procedure. Numerical results show that the sensitivities indices are time and damage size dependent. The sensitivity contributions from Lamb wave quantification model and the material properties are comparable when the crack size is relatively small. When the crack grows to a larger size, the reliability assessment result is much more sensitive to uncertainties associated with material properties.

Time-dependent structural reliability under nonstationary and non-Gaussian processes

With the increasing recognition of random and time-variant nature in structural responses, time-dependent reliability methods have become popular for structural reliability assessment in recent decades. This paper proposes a method that can determine the time-dependent reliability with accuracy and robustness under general stochastic processes, which are neither stationary nor Gaussian. It presents a detailed derivation of the first passage probability and upcrossing rate with a view to better understanding the time-dependent reliability theory. An idea is proposed to determine the upcrossing rate for any stochastic processes by combining the Rice formula with transformation of the stochastic processes. The proposed method is verified with both analytical solution and Monte Carlo simulation, and further tested with two practical examples. It is found in the paper that the proposed method is more accurate than the only existing analytical solution and yet more efficient than the Monte Carlo simulation with the same accuracy. It is also found that the proposed method is robust for any type of stochastic processes with a range of barrier levels and band widths. The significance of this proposed method is that it widens the application of time-dependent reliability methods to the assessment of practical structures during their service life.

An Alternative Probabilistic Approach for Reliability Assessment of Rotorcraft Structures

An alternative probabilistic approach is proposed to assess the reliability of rotorcraft structures. According to the approach, safe boundaries of reliability predictions (i. e., conservative ones with additional safety margins) are calculated instead of exact values of the reliability as usually estimated in conventional analysis. Due to additional safety margins, these boundaries are suggested for practical engineering applications. The proposed approach is based on two main ideas, namely (a) prediction of a relatively small population of independent coarse estimations of reliability and (b) application of sampling methods to predict reliability for each individual coarse estimation. Robustness and convenience of the developed approach and its computational implementation are demonstrated for four scenarios considering two problems (simplified analytical and realistic finite element analysis–based ones) under two sets of input data providing the probability of failure (POF) close to 1e-6 and 1e-9, respectively. High accuracy of predictions according to the developed approach is independently verified by comparison with known "exact" references: closed-form solutions for the analytical problem and by direct Monte Carlo simulation for the numerical one. The proposed approach can be recommended as an efficient practical solution for a broad range of reliability assessments of rotorcraft structures requiring both (i) low POF (e. g., below 1e– 6) and (ii) relatively complex time-consuming structural definitions (e. g., compute times in hours for each quasi-deterministic simulation).

Investigation on out-of-plane displacement measurements of thin films via a mechanical constraint-based 3D-DIC technique

Thin film is functioning as a key material in surface engineering, and accurate measurement of its deformation are particularly important for the reliability and stability assessment of coating-substrate structures. However, the displacement field measured by the conventional three-dimensional subset-based digital image correlation (3D-DIC) method has no spatial continuity; thus, it cannot precisely reflect the true deformation of thin films. To improve the measurement accuracy, a 3D-DIC method considering mechanical constraints (3DMC-DIC) was proposed in this paper. In this method, a mesh with 8-noded quadrilateral shell elements satisfying spatial continuity was employed to determine the out-of-plane displacements of all nodes based on trusted points, which are the speckle points with higher measurement accuracy obtained by the conventional subset-DIC method. The whole out-of-plane displacement field was then inversely obtained based on the optimized displacements of these nodes. A blister test was performed, and the results show that the out-of-plane displacement field of thin film with spatial continuity and high accuracy on specimen edge can be obtained by the 3DMC-DIC method.