Structural Reliability Assessment Research Articles

Prediction of the Mean Time to Failures of a Complex System Using the Monte Carlo Simulation Method

This paper presents a Monte Carlo-based algorithm for predicting the Mean Time to Failure (MTTF) of complex structures, specifically a “Bridge-type network” with five elements exhibiting various failure distributions. The proposed algorithm involves generating element lifetimes through the inverse of their failure distribution functions, providing a robust approach to evaluating MTTF for systems beyond traditional series or parallel configurations. The approach was implemented in MATLAB, and the software underwent extensive testing across different scenarios, including both exponential and Weibull distributions. The results demonstrated the method’s accuracy and its capability to handle diverse failure distributions with minimal error. This tool offers reliability engineers a versatile solution for predicting and improving the reliability of complex systems. In summary, the proposed method and software significantly advance the reliability assessment of intricate structures and offer a solid foundation for further research and practical applications in the field of reliability engineering.

Surrogated modelling for structural reliability and safety assessments of high-strength concrete beams with industrial and recycled steel fibers

As a secondary material recycled from tyres, Recycled Steel Fibre Reinforced Concrete (RSF) aims to replace industrial steel fibres (ISF) to improve concrete matrix‘s severability, fracture toughness, and residual tensile stress. Despite the increasing attention on the mechanical properties of this material, RSF concrete’s influence on structural component strength is still neglected due to a lack of sufficient and reliable experimental data. This study looks into existing Crack mouth opening displacement (CMOD) experiment results of both types of steel fibre reinforced concrete beams together with nonlinear finite element model (FEM) simulations using the RILEM TC 162-TDF crack damage model(CDP) proposed for ISF in ABAQUS. Meanwhile, an additional parameter analysis of the experimental data related to shear capacity also examines the shear span ratio, fibre content, and fibre type of the two types of fibre reinforced concrete beams. Moreover, Kriging surrogate models (KSM) and Sobol global sensitivity analysis have been conducted. For the reference concrete beams with a fibre content of 0.4 %, the prediction accuracy ratios of ultimate strength, corresponding displacement, and stiffness between the FEM and the experiment results are 98 %, 88 %, and 100 %, respectively. This paper has been proved that the CMOD-based CDP model effectively elucidates the shear contribution of different steel fibres, which can be used in structural analysis of ISF or RSF concrete for structure components. Utilizing FEMs, a series of modified flexural strength prediction formulas based on TR63 standards are proposed to enhance structural applications with ISF and RSF. Moreover, the prediction ability of the proposed formulas is validated using the results of 183 real flexural capacity experiments of ISF reinforced concrete beams, achieving an improved R² value of 0.97.

Global Sensitivity Analysis and Surrogate Models for Evaluation of Limit States in Steel Truss Structures

This article presents the global sensitivity analysis of the serviceability limit state of a steel truss using Monte Carlo simulations. The focus is on the probabilistic assessment of deflection, with failure probability defined as the likelihood of exceeding the deflection limit. Deflection is computed using the beam finite element method. A surrogate model is introduced to reduce computational costs. By integrating the surrogate and original models, significant CPU cost reductions are achieved. Furthermore, classical Sobol sensitivity analysis is used to examine the model outputs and analyze the significance of member loading and stiffness on the deflection. This study advances the use of surrogate models in global sensitivity analysis, enhancing computational efficiency and the understanding of interactions between input variables in the reliability assessment of steel truss structures.

A physical stochastic model of near-surface fluctuating wind fields

Modeling and simulation of atmospheric turbulence in coastal areas has emerged as a prominent area of research in recent years. This study presents a physical stochastic model to describe the horizontal coherence of fluctuating wind fields within the physical stochastic modeling frame. Based on the one-dimensional stochastic Fourier spectrum and isotropic turbulence theory, the horizontal coherence for fluctuating wind fields is expressed as a random function, with its probability information determined by the physical mechanism/background. The proposed physical stochastic model directly depicts the stochastic time series thereby enabling it to capture all probability information in detail comprehensively. The proposed model is numerically validated with the measured data obtained from an observation array constructed in Southeast China. This investigation holds significant potential for its application in wind-resistance design and reliability assessment of long-span structures.

On application of the relative entropy concept in reliability assessment of some engineering cable structures

The main research problem studied in this work is an uncertain response and reliability assessment of the spatial cable structures due to the environmental stochasticity as well as material and geometrical imperfections. Some popular cable structures are analyzed for this purpose using the Stochastic Finite Element Method (SFEM) implemented with the use of three different techniques, namely the iterative generalized perturbation method, semi-analytical approach as well as the Monte-Carlo simulation. Uncertainty quantification delivered in this study is based on the series of FEM analyses of both static and dynamic structural problems. They enable the Least Squares Method determination of the structural polynomial responses linking extreme stresses and deformations with several uncorrelated uncertainty sources. Reliability assessment, fundamental in durability and Structural Health Monitoring, is completed using a comparison of the First Order Reliability Method (FORM) with probabilistic distance formulated by Bhattacharyya. Input uncertainties are assumed to be Gaussian according to the Maximum Entropy Principle. They have specific expected values following engineering design demands or the provisions of designing codes, whereas their standard deviations do not exceed the 10% level. The methods presented and the results obtained in this study may serve for further reliability analyses of large-scale civil engineering structures completed with both steel cables and also reinforced concrete plates like suspended bridges, for instance.

Quantified active learning Kriging model for structural reliability analysis

A quantified active learning Kriging-based (qAK) methodology for structural reliability analysis is presented. The proposed approach is based on an updated probability density function (PDF), which is dominant in the vicinity of the limit-state surface. This PDF is created using weights based on an improved learning function called the most probable misclassification function. This function is used as a metric for efficiently updating the Kriging model, as it symmetrically quantifies the uncertainty of candidate points in terms of the model’s accuracy. The proposed approach accurately approximates the points that lie on the limit-state surface. Moreover, a probabilistic-based stopping criterion is proposed. The new support points are selected using the weighted K-means algorithm and the sample from the updated PDF. Thus, the method does not require solving an optimization problem or using a sampling algorithm. The proposed qAK methods are more reliable and robust than previous implementations of the Kriging method for structural reliability assessment. The proposed approach is presented within the framework of standard reliability methods, i.e., the Monte Carlo and the Subset Simulation methods. The efficiency of the proposed qAK methods is demonstrated with the aid of six case studies.

Forecasting bridge damage within a predictive Structural Reliability-based DSS

Nowadays there is urgent need for expeditious and efficient approaches to assess the structural reliability of widespread aging bridge stocks. As such, a shift towards predictive maintenance measures is required. This paper addresses such pressing necessity for efficient methods to assess the structural state of aging bridges, centring its research question on developing a Decision Support System (DSS) that integrates an innovative reliability model with Markov Chain projections to prioritize bridge interventions. The proposed DSS effectively forecasts structural risks and computes a Priority Index to guide maintenance decisions. This tool empowers infrastructure managers with timely insights, enhancing bridge safety and optimizing resource allocation. The study's practical example underscores the DSS's applicability, demonstrating its capacity to streamline decision-making in real-world scenarios. By providing a sophisticated yet accessible approach to structural reliability assessment, this research lays the groundwork for future enhancements, including the incorporation of additional risk factors and refined calibration methods.

Data-driven fast reliability assessment of offshore structures based on real-time sensor data

With the advancement of monitoring technologies for offshore structures, sensor data are becoming increasingly available in real-time. The objective of this paper is to develop fast methods for reliability assessment of offshore structures for the extreme and fatigue failure modes, based on the latest real-time sensor data, assumed to be four months. The continuously updated assessment informs operators on the failure probability over the next few years. Reliability analysis using real-time data is challenging owing to the need to extrapolate the observed data to more severe sea states and across many orders of magnitudes of probabilities, and there is a lack of related studies. Here, the environment comprises the short-term and long-term wave characteristics. Three data-driven reliability approaches are developed for three types of wave sensor data. The first approach applies statistical models to the response when wave data are unavailable. The second relies on Gaussian Process Regression (GPR) when only the wave spectral parameters are known. The third applies the Gaussian-experienced NARX network to predict the response time series when the wave time series are recorded. The proposed approaches are applied to a jack-up platform, and implementation of benchmark reliability analysis is enabled by establishing an emulator trained from dynamic simulations for fast generation of synthetic sensor data. The GPR approach is found to show good extrapolation capabilities and able to provide relatively accurate and robust reliability predictions.

Buckling Instability of Monopiles in Liquefied Soil via Structural Reliability Assessment Framework

Buckling Instability of Monopiles in Liquefied Soil via Structural Reliability Assessment Framework

Time-variant reliability assessment for bridge structures based on deep learning and regular vine copula models

This study proposes a novel method for assessing the time-variant reliability of bridge structures by combining deep learning and regular vine (R-vine) copula models. The sample convolution and interaction network (SCINet) model, which is a deep learning algorithm, is established to predict future structural responses at different control-monitoring points. The R-vine copula model captures the complex correlations of the failure modes associated with different control-monitoring points and models their dependence structure. By integrating the SCINet and R-vine copula models, the SCINet-pair-copula model (SCINet-PCM) is established, and a framework based on SCINet-PCM is proposed to forecast the time-variant reliability of bridge structures. The results for a practical bridge reveal that the calculated results obtained using the proposed SCINet-PCMs satisfy the quality-inspection results of the bridge and are closer to the benchmark results of importance sampling, indicating that the proposed method is accurate and reasonable.

Comparison of probabilistic structural reliability methods for ultimate limit state assessment of wind turbines

The probabilistic design of offshore wind turbines aims to ensure structural safety in a cost-effective way. This involves conducting structural reliability assessments for different design options and considering different structural responses. There are several structural reliability methods, and this paper will apply and compare different approaches in some simplified case studies. In particular, the well known environmental contour method will be compared to a more novel approach based on sequential sampling and Gaussian processes regression for an ultimate limit state case study on the maximum flapwise blade root bending moment. For one of the case studies, results will also be compared to results from a brute force simulation approach. Interestingly, the comparison is very different from the two case studies. In one of the cases the environmental contours method agrees well with the sequential sampling method but in the other, results vary considerably. Probably, this can be explained by the violation of some of the assumptions associated with the environmental contour approach, i.e. that the short-term variability of the response is large compared to the long-term variability of the environmental conditions. Results from this simple comparison study suggests that the sequential sampling method can be a robust and computationally effective approach for structural reliability assessment.

Structural Risk and Reliability Assessment of Offshore Aquaculture Floating System for Seaweed Cultivation

Structural Risk and Reliability Assessment of Offshore Aquaculture Floating System for Seaweed Cultivation

A novel multiple linearization method for reliability analysis based on evidence theory

Evidence theory has been applied in structural reliability assessment to address epistemic uncertainties, given its capability to deal with imprecise, incomplete and even contradictory information. An important challenge in structural reliability assessment based on the framework of evidence theory is its expensive computational cost in multidimensional problems. In this work, a modified multiple linearization method is proposed to identify a set of hyperplane approximations to the limit state function. It provides a clear guidance for the hyperplanes by evaluating curvature magnitude of the original limit state at the most probable point along each axis in the rotated standard normal space, and shows good stability and satisfactory accuracy in nonlinear reliability analysis based on evidence theory. The belief measure and plausibility measure of the structure are assessed by the hyperplanes through the intersection or union of the failure domains. In the meantime, the classification and division of focal elements in failure set, safety set and uncertain set will be made through the segment edge of the failure and safety domain to reduce the computation burden. Finally, four mathematical examples and engineering cases are explored to illustrate the methodology and show its benefits.

Approaches to estimate global safety factors for reliability assessment of RC structures using non-linear numerical analyses

The study is focused on the comparison and discussion of different approaches within the use of the global resistance method (GRM) for safety assessment of reinforced concrete (RC) systems using non-linear numerical analyses (NLNAs). With this purpose, a benchmark dataset, comprising 56 experimental results obtained from tests on 40 RC columns with variable slenderness and 16 non-slender RC elements including walls, deep beams and shear walls, is considered. The NLN models for all the 56 members adopt solution strategies able to optimize the agreement between numerical predictions and experimental outcomes. Then, probabilistic hypotheses have been defined regarding both aleatory (i.e., materials and geometry) and epistemic uncertainties (i.e., model) associated with all the 56 RC members. These assumptions form the basis for developing a comprehensive set of probabilistic analyses of the global structural resistance for each RC member. The results of these probabilistic analyses offer valuable insights into the impact of the different sources of uncertainties on the global structural response. In detail, three distinct approaches for estimating the global safety factors within the GRM are outlined and compared. The purpose is to address the effectiveness of the different approaches for the reliability evaluation of RC members within the GRM together with the relevance of both aleatory and epistemic uncertainties. Ultimately, recommendations are provided regarding the adoption of the GRM in the upcoming generation of design codes.

A clustering-based partially stratified sampling for high-dimensional structural reliability assessment

Assessing structural reliability problem with high-dimensional random inputs is still challenging due to the “curse of dimensionality”. In this paper, this challenge is addressed by extending the Generalized Distribution Reconstruction Method via Characteristic Function Inversion (GDRM-CFI). Specifically, a clustering-based partially stratified sampling method is proposed for selecting high-dimensional points to numerically evaluate the characteristic function (CF) curve of complex high-dimensional problems. An improved number-theoretical method (i-NTM) is used to establish a uniform, efficient point set, ensuring determinism and reducing variability. Subsequently, a partial stratification approach partitions the high-dimensional space into orthogonal two-dimensional subspaces. The fundamental point set is projected into each subspace, and the k-means clustering algorithm identifies centroids within each, acting as representative points. The complete set of representative points from all subspaces formulates the high-dimensional point set. Numerical examples are investigated, which demonstrate the proposed method is effective for high-dimensional structural reliability assessment.

Reliability Assessment of RC Structures: Progress of the Failure Probability Calculating Methods

Reliability Assessment of RC Structures: Progress of the Failure Probability Calculating Methods

Electric current stressing enhanced damping properties in Sn5Sb solder

PurposeThe purpose of this paper is to investigate the effects of electric current stressing on damping properties of Sn5Sb solder.Design/methodology/approachUniformly shaped Sn5Sb solders were prepared as samples. The length, width and thickness of the samples were 60.0, 5.0 and 0.5 mm, respectively. The damping properties of the samples were tested by dynamic mechanical analyzer with a cooling system to control the test temperature in the range of −100 to 100°C. Simultaneously, electric current was imposed to the tested samples using a direct current supply. After tests, the samples were characterized using scanning electron microscope, electron backscatter diffraction and transmission electron microscope, which was aimed to figure out the damping mechanism in terms of electric current stressing induced microstructure evolution.FindingsIt is confirmed experimentally that the increase in damping properties is due to Joule heating and athermal effects of current stressing, in which Joule heating should make a higher contribution. G–L theory can be used to explain the damping properties of strain amplitude under current stressing by quantitative description of geometrically necessary dislocation density. While the critical strain amplitude and high temperature activation energy decrease with increasing electric current.Originality/valueThese results provide a new method for vibration reliability evaluation of high-temperature lead-free solders in serving electronics. Notably, this method should be also inspiring for the mechanical performance evaluation and reliability assessment of conductive materials and structures serving under electric current stressing.

Safety Assessment of Brazilian Concrete Bridges Through Reliability Analysis

This paper addresses the need for accurate and objective safety assessments of bridges in Brazil taking into account the increase in traffic load and limited funding for infrastructure. In Brazil, the usual method of ensuring bridge safety involves strengthening based on design codes using deterministic analysis and partial safety factors. This method leads to an increase in the maintenance cost of the bridges. Structural reliability assessment, a higher-tier assessment method, is recommended globally for assessing the safety of existing bridges beyond current deterministic methods. This paper presents a study that evaluates the structural safety of existing road bridges in Brazil using the semi-probabilistic method defined in Brazilian standards and the full probabilistic method. The study selected six case studies of existing reinforced and prestressed concrete bridges to evaluate their structural safety concerning current normative loads. The results suggest that the partial safety factors defined in the Brazilian standards are consistent with international standards. The reliability analysis can guarantee the bridges’ safety, even with increased traffic loads, without additional costs for structural strengthening. Therefore, the paper highlights the importance of promoting reliability analysis in Brazil to ensure the safety of existing bridges and promote cost-effective and objective safety assessments.

Multi-sensor data fusion reconstruction method for vibration dynamic responses of aerospace structures

The dynamic responses of key locations are important inputs for the life and reliability assessment of spacecraft structures. Due to the limited sensing resources, most critical responses are difficult to measure directly. A structural dynamic response reconstruction method is necessary. The responses of target locations can be reconstructed based on the empirical mode decomposition (EMD) of measured signals and the modal superposition. However, the structural modal information contained in the measured signal of a single sensor is limited, affecting the reconstruction accuracy. In this paper, a response reconstruction method based on multi-sensor data fusion is proposed. It is applied to a main load-bearing structure of a spacecraft and its typical components to verify its strain response reconstruction effect under random vibration loads. The experimental results show that multi-sensor data fusion improves the strain reconstruction accuracy. The maximum reduction in reconstruction error is from 8.7% to 1.3%. The reconstruction accuracy is further improved with the increase in the number of sensors. The optimal weighted fusion strategy for this problem is the weights defined by the Euclidean distance (EUC) or the dynamic time warping distance (DTW). The fusion results show a better performance with the increase in the power of the defined distance. The proposed multi-sensor fusion method improves the reconstruction accuracy via supplementing structural information to each other and eliminating the instability of single measured signals. More accurate dynamic responses via reconstruction reduce the large input uncertainty in life prediction and lay the foundation for building structural digital twins and managing structural health more effectively.

AK-SYS-IE: A novel adaptive Kriging-based method for system reliability assessment combining information entropy

Structural reliability assessment is a popular topic in engineering problems, particularly for the larger and more complex systems with implicit performance functions, also called black-box problems. The reliability assessment for a black-box problem must continuously be computed using simulation models, such as the finite element model, a highly time-consuming process with a high computational cost. The adaptive Kriging has gained considerable attention over the past decade. The Kriging-based reliability assessment method reduces the computational cost to a great extent, on the premise of ensuring the accuracy of reliability assessment. However, many of the currently published system reliability assessment methods, construct adaptive Kriging models by reducing the probability of incorrect prediction of the system state, and do not make full use of the uncertainty of the system state prediction information. To this end, a new Kriging-based method for structural system reliability assessment is proposed in this study. First, the probabilities of incorrect or correct system state predictions were understood from the perspective of information entropy. Second, an active learning strategy is proposed based on information entropy theory. Finally, the advantages of the proposed method are demonstrated and highlighted through several numerical examples. The results show that the proposed method achieves a good balance between the accuracy and computational cost, and the numerical magnitude effect does not affect the computational cost. Moreover, this is an effective method for assessing the reliability of complex systems.