Structural Reliability Index Research Articles

Seismic Fragility and Reliability of Base-Isolated Structures with Regard to Superstructure Ductility and Isolator Displacement Considering Degrading Behavior

ABSTRACT The present study investigates the effects of the degradation of mechanical properties (pinching, stiffness degradation, and strength degradation) in load-deformation relationship of the superstructures equipped with friction pendulum systems on the seismic fragility and reliability results. An equivalent two-degree-of-freedom model is employed, in which the Bouc-Wen hysteretic model characterizes the inelastic behavior of both the superstructure and the isolator. To examine a wide variety of system combinations with different structural properties and degradation severity, a comprehensive parametric study is performed. Incremental dynamic analyses are carried out to develop fragility functions. Subsequently, the seismic reliability of both the superstructure and the isolation level is assessed. Results indicate that the negative effects of degrading behavior are more prominent in stiff superstructures as it significantly decreases structural capacity and reliability indices. It is demonstrated that the system is primarily influenced by pinching behavior rather than degradation in strength and stiffness, especially at low intensity levels that correspond to lower limit-states. In the majority of investigated systems, the seismic demand in the isolator decreases when superstructures undergo degrading behavior. Overall, such effects should be considered in the reliability-based design procedure to attain design consistency in terms of reliability. The results of this paper that account for the degrading effects enable reliable estimations of key parameters essential for the design of the superstructure and the isolator.

Theory and Empirical Analysis of Bridge Load Limitation Under the Action of Typical Heavy-Duty Vehicles

Abstract With the continuous growth of transportation demands, in-service highway bridges face greater challenges in their long-term operational lifespans, and bridge collapse accidents caused by vehicle overloading occur from time to time. Additionally, under the influence of loads and environmental factors, various wear patterns inevitably lead to degraded reinforced concrete bridges. In view of this problem, it is reasonable and feasible to limit the vehicle loads passing over highway bridges, and the key basis for limitation is determining the load limit value of a bridge. To determine a reasonable load limit value of a bridge, this paper has carried out the following research: Based on a classification of vehicle types, this paper explores the load parameters of several heavy-duty vehicles with large traffic volumes through traffic flow information and summarizes the load spectra of typical heavy-duty vehicles. On the basis of the theory of structural reliability, a method for determining the limit load of bridges is proposed. Given a structural target reliability index, the theoretical load limit value of a bridge can be calculated. To ensure the rationality of the theory of bridge load limit value, by relying on the engineering example, the theoretical load limit value is calculated. By comparing actual bridge load test data with the finite element model results, the rationality of the bridge load limiting theory is verified. Finally, the paper notes that it is safer and more reliable to define the load limit value according to the bending stress state for bridges.

Reliability assessment of ship hull girders considering pitting corrosion and crack

The current study aims to investigate the combined effect of cracking and pitting damage on the ultimate strength of ships. The well-known Smith’s approach is modified considering the random number and distribution of cracked-pitted plates in the ship cross-section. Using the Monte Carlo approach, the structural reliability index of the cracked-pitted ship is determined. A single-bottom oil tanker’s ultimate strength is computed, and it turns out that the reliability indices for various damage scenarios are nearly identical when the ship is at its early age. When the ship ages, its reliability index rises to its maximum if the damage is concentrated at the bottom under sagging conditions and at the sides and longitudinal bulkheads in hogging conditions. The reliability indices in the hogging conditions are often greater than those in the sagging conditions. Furthermore, it is determined that, while the ship is at its early age, the detrimental effect of pitting, cracking, or a combination of both on the reduction of the ship’s hull girder ultimate strength is equal. The lowest reliability index is seen in aged ships when cracking and pitting are combined, followed by cracking and pitting damage separately. It is shown that pitting corrosion has a lower reliability index than the general type of corrosion.

Research on the application of high performance concrete and steel structure combination in civil engineering

Abstract The increase in complexity and quality standards of civil engineering projects continues to drive the innovation of construction materials from the traditional ordinary concrete-steel structure combination to the combination of high-performance concrete and steel structure. In this paper, the application of the combination of high-performance concrete and steel structures in civil engineering projects is investigated based on the mechanical properties of the two structures. The structural reliability index and the corresponding functional function are used to measure the structural reliability of the combination of high-performance concrete and steel structures. After measuring its reliability, a finite element simulation is carried out to investigate the application value of the high-performance concrete-steel structure combination in civil engineering projects. Considering the reliability index of resistance and load time-varying effects decreases with the service time of the combined structure, if the reliability index of the components during the service period is not allowed to be lower than the target reliability index, the time to reach the limit state of the selected high-performance concrete-steel combined building in this paper is about 75 years. The ultimate load-carrying capacity of the high-performance concrete-steel structure combination is increased by 28.74% compared with that of the ordinary concrete-steel structure combination, and the end slip of the high-performance concrete-steel structure combination is smaller than that of the ordinary concrete-steel structure combination under the same load. It shows that the advantages of high-performance concrete-steel structures in civil engineering are much more than ordinary concrete-steel structures.

Reliability-based design optimization of post-tensioned self-centering rocking steel frame structures

This paper reports the Reliability-Based Design Optimization (RBDO) of post-tensioned self-centering rocking steel frame structures with buckling-restrained bracing systems. The objective was to investigate the reliability index, optimization of self-centering structures to reach minimum weight using metaheuristic algorithms, and their application in linear and nonlinear reliability problems. For this purpose, three steel structures (10-, 15-, and 20-storey structures) were each evaluated with three steel framing systems (buckling-restrained bracing, post-tensioned self-centering multiple rocking steel frame with buckling-restrained bracing, and post-tensioned self-centering single rocking steel frame with buckling-restrained bracing), making a total of nine models. Subsequently, specific 2D frames of the structural models were numerically simulated using nonlinear dynamic analysis (NDA) in OpenSees software. Optimization was carried out in two stages: with and without considering the uncertainties. Finally, for calculating the failure probability and structural reliability index, Monte-Carlo Simulation (MCS) was employed. Results indicate that, although considering the reliability index leads to heavier structures, structural safety was increased and failure probability was reduced to even lower specified levels. Furthermore, among the incorporated algorithms, the Colliding Bodies Optimization (CBO) and Charged System Search (CSS) algorithms proved to have superior performances in terms of accuracy and converging time. On average, using these two algorithms for cases without uncertainty resulted in maximum weight reductions of 36%, 30%, and 32% for 10-, 15-, and 20-storey structures. In addition, for cases with uncertainty, these two algorithms with reliability index (β) of 2 respectively reduced the weight of 10-, 15-, and 20-storey structures by 21%. Also, it was shown that not considering the uncertainties can increase the failure probability by up to 23%.

Towards optimal reliability-based design of wind turbines towers using artificial intelligence

Metaheuristic Optimization Techniques and Artificial Neural Networks (ANNs) have proven to be useful tools to find the best design solutions for different structural systems. However, the application of both techniques oriented toward the optimal design of wind turbine towers still requires further research. A methodology is presented to obtain the best design solutions for onshore wind turbine steel towers using the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm and ANNs. The proposed methodology is applied to steel towers with heights of 70, 75, 80, and 85 m. Case studies are assumed to be located in La Ventosa, Oaxaca. Three design objectives are defined: minimize the mass of the structure, maximize the structural reliability, and maximize the wind power. In order to avoid high computational costs, ANNs are trained and used to obtain the structural reliability index β. First, the design variables and constraints are defined; subsequently, a metaheuristic swarm intelligence-based optimization (MOPSO) technique is implemented. As a result of the optimization process using the MOPSO algorithm, a Pareto Front that includes the best design solutions is efficiently obtained. Finally, graphs are generated in order to recommend initial parameters for pre-design of steel towers, satisfying three design objectives.

Integrating Energy-Based Limit State Functions to Optimize Target Reliability of Bridge Pile for Seismic Events

The target reliability index is a safety and economic measure used to stipulate the optimal reliability level for structural elements. The conventional load and resistance factor design (LRFD) philosophy is premised on limit state functions that ignore structural performance by disregarding the structural stored energy capacity. Indeed, two significant concerns have yet to be adequately addressed within structural failure and safety analysis. The first pertains to the careful consideration of failure modes. The second involves the relationship between target reliability and hazard intensity. The main goal of this research is to propose a new energy-based limit state function to incorporate the performance-based design and LRFD philosophies concerning the target reliability of bridge substructure systems, including piles. The proposed energy-based limit state function can thoroughly examine a structure’s behavior in the presence of a natural disaster. This study’s reliability analysis corresponds to the seismic performance levels. The elastic and plastic energy resistance of pile elements is quantified concerning the various performance levels subjected to the loading scenarios. The uncertainties of soil and structural resistance and the structure’s dynamic response are considered and a new energy-based limit state function established. To validate the proposed limit state function, several finite element method models are examined to capture the probability energy distribution for structural resistance and loading conditions. Finally, the structural target reliability indices for the bridge piles are delineated using the proposed optimization approaches.

L-Moments-Based FORM Method for Structural Reliability Analysis Considering Correlated Input Random Variables

Leveraging the properties of the first three linear moments (L-moments), this study proposes an effective normal transformation for structural reliability analysis considering correlated input random variables, in which the admissible range of the initial correlation matrix when employing this transformation is also presented. Subsequently, a practical procedure for structural reliability analysis, grounded in the proposed transformation and first-order reliability method (FROM), is proposed, accommodating instances wherein the joint probability density functions (PDFs) or marginal PDFs of the relevant random variables remain unknown. In comparison to the technique premised on the first three central moments (C-moments), the proposed method, based on the first three L-moments, exhibits a more extensive applicability. Various practical scenarios showcase the method’s effectiveness and precision in calculating the structural reliability index, considering diverse distributions, numerous variables, and complex structures.

Performance-based system reliability analysis for steel moment frames

This study aims to bridge the gap between two major design philosophies in structural design: load and resistance factor design (LRFD) and performance-based design (PBD). While LRFD prioritizes the design of structural members, PBD starts by controlling the system's target parameter. The main area for improvement of LRFD is paying attention to the structure's performance. At the same time, PBD needs to pay attention to the sufficiency of internal members in the presence of local damages. To bring these two attitudes closer together, the study proposes a system-reliability-performance-based design analysis to simultaneously measure the entire structure's safety level associated with the reliability of elements. As a state-of-the-art, new performance-based limit state functions are introduced to measure structural reliability indices corresponding to desired performance levels. Multi-story frames were designed and evaluated based on incremental dynamic analysis. The entire structure was designed and controlled using the linear static analysis method, and static and dynamic nonlinear analyzes were performed to evaluate its behavior. Dynamic analysis of acceleration mapping was also performed to investigate the performance of the structural components. The proposed combined design algorithm aims to develop a new set of performance-based load combinations and provide a strong interlock between LRFD and PBD. The study's results show that the IO level has the lowest performance-based system reliability index, while the CP level has the highest. It was observed that as the number of story levels increases, the performance-based system reliability index decreases due to an upsurge in the possibility of failure patterns. Therefore, the current LRFD practices are unlikely to provide the IO's perfect reliable level for the entire system. The study concludes that the new approach can enhance the safety of structures and prevent catastrophic failure.

A Digital Twin Assisted and Embedded Strain Gauge Monitoring System

In this work, a strain monitoring system (strip) for assessing the road pavement distress under vehicle loads was developed. The system consists of the sensing element, the data processing and storage unit, and a graphical user interface with post- processing features. The sensing elements were designed to be adhesively bonded on the pavement and are protected by an encapsulating plastic strip. Strain data are sent to a digital reconstruction (the Digital Twin) of a real-life asset (the pavement model) that is frequently and automatically updated through data sampling. This tool provides functionalities to monitor and optimize assets and make informed and data-based decisions, in the context of day-to-day operative conditions and after extreme events. These data not only include sensor data, but also regularly revalidated structural reliability indices formulated on the grounds of the frequently updated Digital Twin model.

Kehandalan Struktur Anjungan Lepas Pantai Terpancang Empat Kaki di Perairan Natuna

The design of offshore platforms in Indonesia generally uses Working Stress Design (WSD) method rather than Load and Resistance Factor Design (LRFD) method. Whereas the LRFD method produces designs that better describe real conditions with load and capacity factors. The load and capacity factors are obtained from consideration of the uncertainty or randomness of their values. One of the load factors used is the environmental load factor. The environmental load factor of LRFD method is obtained based on environmental characteristics not in Indonesian waters. There are differences in the environmental characteristics of each water. Uncertainty of environmental loads in the offshore platforms design is wave height, current velocities, and wind speed. To get a structure designed according to the characteristics of the waters in Indonesia, an environmental load factor is needed in accordance with the characteristics of Indonesian water. To achieve that, structural reliability analysis is needed. S tructure s reliabilty represents the possibility of the structure's performance criteria being met which is expressed by the reliability index. The reliability index of structures designed using the WSD method used as a reference for LRFD method. In this study, reliability analysis was carried out using the reserve strength ratio value from the pushover analysis on WSD method. The reliability index of the structure model is 4.10. This value is categorized as high reliability . Th is results can be used as a reference to determine the environmental load factor of Indonesia n water in the future.

Probabilistic Collapse Design and Safety Assessment of Sandwich Pipelines

This paper presents an approach for probabilistic design and safety assessment of sandwich pipelines under external pressure. The methodology consists of the categorisation of sandwich pipeline collapse strength models based on interlayer adhesion conditions. The models are validated by comparing their predictions against collapse test data of sandwich pipelines. The accuracy of the strength models and their prediction uncertainty are used to select the best model in each category. Regarding interlayer adhesion categories, uncertainty propagation of models’ predictions over a wide range is assessed by the Monte Carlo simulation method. The proposed methodology is demonstrated using a case study of a sandwich pipeline with adequate probabilistic modelling of the basic random variables. Different limit states are defined for three categories of sandwich pipelines, based on which structural reliability indices are estimated. In employing the First Order Reliability Method for sensitivity analysis, the importance of basic variables of the limit states is evaluated. Later, a parametric analysis is conducted, presenting reliability variations for several design and operational scenarios of sandwich pipelines. Finally, to achieve a uniform level of structural reliability of sandwich pipelines, a few suggestions are provided, and practical partial safety factors are calculated. The results of the present analysis can provide guidance on the probabilistic design and operational safety assessment of sandwich pipelines.

An Iterative Two-step Lagrangian-based Method for Evaluation of Structural Reliability Index

In structural reliability analysis, Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method is a widely used approximation method for evaluating the reliability index. However, by increasing the nonlinearity or complexity in the limit state function of a structure, HL-RF may get in trouble for convergence. This paper represents an iterative algorithm that tries to minimize the Lagrange function, associated with the reliability problem. In each iteration of this method, two steps are followed, to satisfy the minimization condition and the existing constraint. In the first step, a movement for minimization in a descent direction is followed. In the second step, another search direction contributes to approach limit state surface, and therefore the next iteration can start from the vicinity of the surface. Employing Lagrange reliability function and limit state function simultaneously in the proposed two-step Lagrangian-based method (TSLB) can help to control the numerical instability in highly nonlinear problems. The accuracy and robustness of the proposed algorithm are shown in illustrative examples of the literature.

Approach for the structural reliability analysis by the modified sensitivity model based on response surface function - Kriging model

The sensitivity analysis model is widely used to describe the impacts of condition parameters on structural reliability. However, the classical sensitivity analysis model is limited to the small number of influence parameters and has no high prediction accuracy. Integrating the response surface function - Kriging model with Sobol sensitivity algorithm, a revised sensitivity model is proposed in this paper. And the quantitative sensitivity analysis for the influence of condition parameters on structural reliability are achieved through combining the revised sensitivity model with the experimental design of coupling parameters, range verification, the multi-body dynamics analysis and the structural statics analysis. The proposed analysis model is mainly applied in large structures with multiple influence parameters. Finally, a typical port crane is adopted to verify the accuracy and effectiveness of the proposed model. The results reveal that among the multiple parameters, the biggest sensitivity influence is the trolley position, while the least one is the lifting speed. The average prediction accuracy of the quantitative structural reliability index for the influencing parameters is up to 95.91%. The revised sensitivity model enables the accurate assessment of structural relativity with plenty of coupling condition parameters.

A Wiener degradation process with drift‐based approach of determining target reliability index of concrete structures

AbstractIn this paper, a novel approach is proposed to determine target reliability index based on modeling performance degradation of concrete structures as a stochastic process. First, the Wiener process with drift is used to simulate the degradation process of relative dynamic elastic modulus of concrete, and the drift coefficient and diffusion coefficient of Wiener process are estimated according to the experimental data of degradation of relative dynamic elastic modulus. Then, based on the relations between concrete compressive strength, dynamic elastic modulus, and relative dynamic elastic modulus, the relationship between compressive strength and the amount of degradation of relative dynamic elastic modulus are deduced, and then, the statistical parameters of concrete compressive strength under different service time can be calculated. Finally, based on the established limit state equation of flexural capacity of the weak section and the statistical parameters of compressive strength at different times, the reliability index of a structure under different service life is calculated. On the other hand, according to the drift Wiener process model of relative dynamic elastic modulus degradation of concrete, the time‐varying failure probability of structural durability degradation is calculated based on the first‐passage failure probability formula of drift Wiener process. Taking a concrete plant structure as an example, the time‐varying reliability index calculated based on the limit state equation and the time‐varying failure probability obtained based on the first‐passage failure probability analysis of drift Wiener process are compared, and then the recommended values of target reliability index of structural bearing capacity are comprehensively determined.

Use of Artificial Neural Networks and Response Surface Methodology for Evaluating the Reliability Index of Steel Wind Towers

The estimation of structural reliability is a process that requires a large number of computational hours when statistical data are not available since it is necessary to perform a large amount of analysis or numerical simulations to estimate parameters related to the reliability. A methodology is proposed for estimating the structural reliability index, as well as the demand and structural capacity factors inherent to the structure, given the fundamental vibration period and the height of the structure, by using artificial neural networks (ANN) and, alternatively, the response surface method (RSM). Both approaches are applied to steel wind turbine towers. For the cases studied, ANN allow evaluating the reliability index and both the demand and structural capacity factors with greater accuracy than when using RSM.

Structural Reliability Analysis and Reliability Index Calculation Method Based on Measurement Uncertainty

Structural reliability is a probabilistic measure of structural reliability. Reliability indicators can be calculated from the average and standard deviation. The standard deviation only reflects the degree of dispersion of the series of measured values such as structural resistance and load effects. However, the acquisition of measurement values is related to the measurement objects, instruments, methods, conditions, and measurement personnel. It is difficult to reflect the impact of these five aspects on the measurement values of structural resistance and load effects using standard deviation. Based on this, this article deeply analyzes the measurement uncertainty evaluation theory and method and proposes to use the synthetic standard uncertainty instead of the standard deviation to calculate the standard value of the structural resistance and load effect. This article establishes the structural performance function, structural reliability calculation formula, the reliable index calculation formula, the calculation formula of variation coefficient and the calculation formula of the safety factor based on the measurement uncertainty. The conclusion of this article provides a new application approach for China national standard “Measurement Uncertainty Evaluation and Representation” and also builds a new bridge for the measurement uncertainty evaluation theory to enter the field of structural reliability analysis.

Nonsingular fast terminal sliding mode-based robust adaptive structural reliable position-mooring control with uncertainty estimation

This paper addresses a novel robust structural reliable position mooring scheme for a turret-moored floating production storage and offloading (FPSO) vessel subject to system uncertainties, environmental disturbances and unmeasurable velocity. A realistic mooring tension model considering buoys and different cable materials that can improve the capacity of the mooring system is derived. A sigmoid tracking differentiator (STD) is employed as a state observer to estimate the unmeasurable velocity. A structural reliability index is introduced to design a position mooring control law so that an FPSO vessel adequately uses a mooring system on the premise of safety to maintain position in an allowable region. It provides strong robustness and a fast transient response and suppresses chattering by merits of a backstepping method and an integral nonsingular fast terminal sliding mode surface (INFTSMS). An adaptive estimator is proposed to address the required unknown uncertainties and disturbances. Theoretical analysis proves the globally asymptotic stability of the whole system. Finally, comparative simulations on an FPSO vessel are conducted to illustrate the effectiveness and superiority of the proposed position mooring control scheme.

Digital Twin for Civil Engineering Systems: An Exploratory Review for Distributed Sensing Updating.

We live in an environment of ever-growing demand for transport networks, which also have ageing infrastructure. However, it is not feasible to replace all the infrastructural assets that have surpassed their service lives. The commonly established alternative is increasing their durability by means of Structural Health Monitoring (SHM)-based maintenance and serviceability. Amongst the multitude of approaches to SHM, the Digital Twin model is gaining increasing attention. This model is a digital reconstruction (the Digital Twin) of a real-life asset (the Physical Twin) that, in contrast to other digital models, is frequently and automatically updated using data sampled by a sensor network deployed on the latter. This tool can provide infrastructure managers with functionalities to monitor and optimize their asset stock and to make informed and data-based decisions, in the context of day-to-day operative conditions and after extreme events. These data not only include sensor data, but also include regularly revalidated structural reliability indices formulated on the grounds of the frequently updated Digital Twin model. The technology can be even pushed as far as performing structural behavioral predictions and automatically compensating for them. The present exploratory review covers the key Digital Twin aspects—its usefulness, modus operandi, application, etc.—and proves the suitability of Distributed Sensing as its network sensor component.

HUT‐based method for structural reliability considering the non‐normal and unknown distributions

AbstractStructural reliability analysis involving the non‐normal random variables are commonly encountered in practical engineering. Furthermore, some random variables are often unknown probability distributions, and the probabilistic characteristic of these variables may be expressed using only statistical moments. In this contribution, an efficient algorithm for structural reliability analysis considering the random variables with non‐normal and unknown probability distributions is proposed, in which high‐order unscented transformation (HUT) and fourth‐moment methods are adopted to efficiently evaluate the structural reliability index. By introducing the Rosenblatt transformation and third‐order polynomial transformation (TPT) techniques, random variables with non‐normal or unknown distributions are transformed into standard normal distributions. Accordingly, the performance functions can be reconstructed using standard normal random variables, and HUT is then employed to efficiently estimate the first four moments (i.e., mean, standard deviation, skewness, and kurtosis) of the performance function. Based on the Hermite polynomial model, the complete expression of fourth‐moment reliability index is derived for estimating the reliability index using the first four moments of the performance function. The efficiency and accuracy of the proposed algorithm are demonstrated through six numerical examples. The results show that the proposed algorithm is applicable to estimating reliability index of both static and dynamic reliability problems involving explicit and implicit performance functions.