Reliability-based Structural Design Research Articles

Robustness and reliability of composite structures: effects of different sources of uncertainty

A study to evaluate the effects of different sources of uncertainty in the Reliability-based Robust Design (RBRDO) of composite laminate structures is performed. The goal is to understand how the set of Pareto-optimal solutions will change and the interaction between the design search and the reliability constraint. The RBRDO is executed by a newly proposed methodology exclusively based on Genetic Algorithms (GA), to guarantee higher levels of accuracy in the optimization procedure, avoiding local minima, common to gradient methods. Design optimization is considered as the bi-objective minimization problem of the weight (optimality) and the determinant of the variance–covariance matrix (robustness). Reliability assessment is made by a mathematical reformulation of the Performance Measure Approach, suitable for GA’s, as an inner-cycle of the design optimization. A numerical example of a fuselage-like composite laminate structure is presented. In the reliability assessment, the uncertainty of the system is considered only through the group of mechanical parameters. It is plausible that there exists an implicit functional relationship between feasibility robustness and the reliability constraint, on which the latter constrains the former, at least for the evaluated numerical example. Optimized weights vary between the same values. Tsai numbers and reliability indexes have similar distributions, for different sources of uncertainty. Only the thickness variables and the ply-angle seem to be affected by the structural feasibility robustness assessment. The distribution the Tsai numbers is affected by the reliability constraint, to respect the imposed reliability level.

Reply to Giannakos, K. Comment on: Toughness of Railroad Concrete Crossties with Holes and Web Openings. Infrastructures 2017, 2, 3

This paper responds to the discussion [1] by Dr. K. Giannakos over our technical note [2].[...]

System Reliability Based Multi-Objective Design Optimization of Bridges

Continuous progress in structural reliability theory and methods, in addition to the evolving advances in optimization solution techniques, drives the steady development of reliability-based structural design process. The integration of system reliability in the design optimization of structures, especially bridges, improves the allocation of available, and usually scarce, budgets. However, the complexity in the determination of system reliability of large structural systems renders the consideration of system reliability in design optimization computationally prohibitive. This issue is even exacerbated when discrete design variables are considered. Furthermore, the optimization of structural systems typically requires using linked-discrete design variables. The recently developed matrix-based system reliability method (MSR) enables the computation of system reliability efficiently and accurately through convenient matrix calculations. The non-dominated sorting genetic algorithm with controlled elitism (NSGA-II) has proven its effectiveness and efficiency in numerous multi-objective optimization applications. The objective of this paper is to propose an approach for the system reliability-based multi-objective design optimization of bridges using the MSR method and NSGA-II and considering linked-discrete design variables. The approach is illustrated by redesigning an actual bridge in order to compare the results of the proposed approach with those of conventional bridge design.

Reliability-based structural design framework against accidental loads – ship collision

As civil infrastructures become highly complex and interconnected, accidental events such as fire, explosion, dropped objects and collision tend to occur more frequently, and are causing critical structural damage and socio-economic costs. Therefore, accidental loads should be considered appropriately during the structural design. To achieve this goal, the paper presents a reliability-based structural design framework against accidental loads. The proposed framework employs a scenario-based simulation in which the occurrence of an accidental load event and the resulting structural loads are modelled probabilistically. The probabilistic distribution of accidental loads is then determined based on the occurrence probabilities of identified scenarios and the conditional probability of structural loads given each accident scenario. In order to estimate the structural responses under accidental loads, an appropriate type of structural analysis is carried out for the given limit states of the structural resistance at the critical sections. The proposed framework is illustrated by an example of a cable-stayed bridge whose piers are under ship collision risk. To consider the dynamic amplification of bridge response caused by ship–bridge collision, time history analysis is performed for the equivalent static ship collision loads. The paper also identifies research needs and challenges in applying the proposed framework to other accidental loads.

Reliability-based durability design and service life assessment of reinforced concrete deck slab of jetty structures

Reinforced concrete (RC) structures in a marine environment deteriorate with time due to chloride-induced corrosion of reinforcing bars. Since the RC deck slabs of jetty structures are exposed to a very aggressive environment, higher deterioration rates can develop. In this paper, a reliability-based durability design and service life assessment of RC jetty structures are presented. For new RC jetty structures, the concrete quality and concrete cover necessary to prevent the chloride-induced reinforcement corrosion causing the deterioration of structural performance during the whole lifetime could be determined. Based on the airborne chloride hazard depending on the vertical distance from the sea level surface to the RC deck slab, the probability associated with the steel corrosion initiation is estimated. The water to cement ratio and concrete cover to satisfy the target reliability level are provided. For evaluating the service life of existing structures, the condition state based on the visual inspection of RC structure can be provided. The deterioration process of the RC jetty structure can be modelled as a Markov process. Therefore, the transition probability matrix at time t after construction can be updated by visual inspection results. A procedure to update the transition probability matrix by the Sequential Monte Carlo Simulation method is indicated. In an illustrative example, the effect of the updating on the life-cycle reliability estimate of existing RC deck slab in a jetty structure subjected to the chloride attack is presented.

Reliability-Based Optimal Design of Steel Box Structures. II: Ship Structure Applications

AbstractTraditional design of ship structures relies on a combination of experience, sound judgment, and deterministic approaches and typically ignores the potential for design improvement and other benefits offered through the use of reliability methods and structural optimization strategies. Part I of this article outlines the underlying theories involved in incorporating reliability methods and structural optimization strategies into the initial design of ship structures, whereas Part II (this paper) discusses their application to two case studies, namely, (1) a simple ship structure and (2) a more complex ship structure in an attempt to achieve weight reduction in the face of constraints on ultimate strength and buckling capacity. Using the approach outlined in the companion paper, a weight reduction of 5.6% was realized in the case of the simple vessel, whereas a 2.0% reduction was achieved in the case of the more complex vessel. A reduction in weight reduction has the potential to minimize the lifec...

Reliability-Based Structural Design of Concrete Pipes

Concrete pipes are widely used for transferring water in urban infrastructure facilities. The current design standard of concrete pipes in Australia is based on the deterministic indirect-design method. However, there is uncertainty in pipe performance during service life due to assumed design parameters, installation error, changed operational environments, and pipe deterioration. This study aims to assess the reliability of structural performance of concrete pipes at the design stage. The reliability assessment is based on the use of Markov chain theory for modeling pipe deterioration during service life and coefficient of variation for representing uncertainty in design, installation, and operational parameters. The results of a case study show that increasing pipe strength from class 2 as per current design to class 3 as per reliability assessment can significantly reduce the likelihood of structural failure during service life and delay inspection and structural rehabilitation by 10 years. There is a difference in structural deterioration between pipe cohorts, which should be taken into account for reliability-based design.

Size effect on reliability indices and safety factors of quasibrittle structures

Many modern engineering structures are made of brittle heterogenous (quasibrittle) materials, such as concrete, composites, and tough ceramics. Recent studies have shown that the strength distribution of quasibrittle structures varies from a Gaussian distribution modified by a power-law tail to a Weibull distribution as the structure size increases, and such size dependence can be well captured by a finite weakest link model. This paper investigates the implication of the size-dependent strength distribution on the reliability-based analysis and design of quasibrittle structures by considering a linear failure limit state. The size effect on the statistical properties of structural strength directly leads to a size-dependent Cornell index, which could give a reasonable estimation of the failure risk in some cases. To improve the prediction of the structural failure risk, the size dependence of the strength distribution is further incorporated into the computation of the Hasofer–Lind index, where it is shown that the transformation method for the non-Gaussian random structural strength is dependent on the structure size and geometry. By assuming that the applied load follows a Gaussian distribution, approximate size effect equations are developed for the central and nominal safety factors through asymptotic matching. The proposed formulation of the size effect on reliability indices and safety factors is applied to analyze the failure of the Malpasset arch dam.

On the effect of near-field excitations on the reliability-based performance and design of base-isolated structures

This work explores the effect of near-field excitations on the reliability-based performance and design of base-isolated systems. In particular base-isolated buildings under uncertain excitation are considered in this work. A probabilistic logic approach is adopted for considering the variability of future excitations. Isolation elements composed by rubber bearings are used in the present formulation. The non-linear behavior of the bearings is characterized by a biaxial hysteretic model which is calibrated with experimental data. The performance of the isolated system is defined in terms of the isolators deformations and the superstructure interstory drifts and absolute accelerations. First excursion probabilities are used as measures of system reliability. Two example problems involving large finite element building models are presented to illustrate the ideas set forth.

Reliability-Based Analysis and Design of Wide-Span Structures under Stochastic Wind Loads

AbstractThe objective of this paper is to present a reliability-based method for structural analysis and design under stochastic wind loads so that nominal wind pressure coefficients p′* (associated with the covariance matrix Cp′) can be defined for use in the context of the load and resistance factor design (LRFD) method. The novelty of the formulation presented in this paper is based on the approach used to solve the problem of considering simultaneously the wind load as random variables (the maximum mean wind pressure outside the influence of the structure on the life cycle of the facility) and the wind load as a space and time random process defined by the covariance matrix Cp′ (i.e., a second moment approximation for the non-Gaussian process) and the peak factor q. The nominal wind pressure coefficients p′, associated with the covariance matrix Cp′, are defined so that the three sources of wind randomness can be independently considered: (1) the randomness in the peak factor q (which depends on the m...

Reliability analysis of structures with complex limit state functions using probability density evolution method

In reliability-based structural analysis and design optimization, there exist some limit state functions exhibiting disjoint failure domains, multiple design points and discontinuous responses. This study addresses this type of challenging problem of reliability assessment of structures with complex limit state functions based on the probability density evolution method (PDEM). Probability density function (PDF) of stochastic structures under static and dynamic loads can be acquired, which is independent of the specific form of limit state functions. Numerical results of several typical examples illustrate that, the time-invariant and instantaneous PDF curves and failure probabilities of stochastic structures with disjoint failure domains, multiple design points and discontinuous responses are calculated effectively and accurately. Moreover, the PDEM is validated to be more efficient than the Monte Carlo simulation and the subset simulation, and is a feasible and general approach to tackle the reliability analysis of complicated problems. In addition, the influence of random design parameters of structures on uncertainty propagation is also scrutinized.

Reliability-based optimal design of linear structures subjected to stochastic excitations

In this paper the problem of reliability-based optimal design of linear structures subjected to stochastic excitations is considered. A global optimization method based on Transitional Markov chain Monte Carlo (TMCMC) is used to address the problem, where the optimization problem is converted into the task of generating sample points (designs) according to a probability density function (PDF) suitably constructed on the feasible space of designs satisfying all the constraints. TMCMC is used for generating sample points, in order to get higher convergence rate of the stationary distribution of the Markov chain states to the constructed PDF. The generation of sample points uniformly distributed in the feasible space, which is required at the initial stage of TMCMC, is achieved by using Subset Simulation. To apply Subset Simulation and TMCMC in the concerned reliability-based optimization problem, Domain Decomposition Method (DDM) is used to examine the reliability constraint, that is, whether the failure probability at a given design exceeds a specified threshold. Based on the statistical properties of the failure probability estimator given by DDM, a ‘minimum’ computational effort, in terms of providing a reliable judgment on the reliability constraint, is defined so that a further reduction in the computational cost can be achieved in the proposed reliability-based optimization (RBO) algorithm. Illustrative examples are presented to show the application and the advantages of the proposed global RBO algorithm.

Expanded reliability-based design of piles in spatially variable soil using efficient Monte Carlo simulations

Inherent spatial variability is considered as a major source of uncertainties in soil properties, and it affects significantly the performance of geotechnical structures. However, research that considers, directly and explicitly, the inherent spatial variability in reliability-based design (RBD) of geotechnical structures is limited. This paper develops a RBD approach that integrates a Monte Carlo Simulation (MCS)-based RBD approach, namely the expanded RBD approach, with random field theory to model, both directly and explicitly, the inherent spatial variability of soil properties in RBD of drilled shafts. The proposed approach is implemented in a commonly-available spreadsheet environment to effectively remove the hurdle of reliability computational algorithms and to provide a user-friendly graphical user interface to practicing engineers. To improve the efficiency and resolution of MCS at small probability levels, the expanded RBD approach is enhanced with an advanced MCS method called “Subset Simulation”. Equations are derived for the integration of the expanded RBD approach and Subset Simulation. The proposed approach is illustrated through a drilled shaft design example, and is applied to explore the effects of inherent spatial variability (including the scale of fluctuation and correlation structure) and to evaluate systematically the equivalent variance technique that is commonly used to indirectly model inherent spatial variability in current RBD approaches. It is found that inherent spatial variability significantly affects the RBD of drilled shafts, and its effects are considered in RBD using the proposed approach in a direct and explicit manner. In addition, the results show that the indirect modeling of inherent spatial variability using the equivalent variance technique with the simplified form of variance reduction function in RBD might lead to relatively conservative designs in design practice.

Reliability-based optimum seismic design of structures using simplified performance estimation methods

We present an algorithm for the reliability-based seismic design of structures incorporating approximate performance estimation methods and structural optimization. The proposed algorithm allows the automatic design of steel moment-resisting frames using reliability-based criteria and more specifically design criteria based on the mean annual frequency (MAF) that a limit-state is exceeded. Such criteria allow setting constraints with a clear engineering meaning and help to obtain building designs of improved performance and reduced cost. In this work, we propose a simplified approach that allows to quickly calculate the limit-state mean annual frequencies without significant loss of accuracy. More specifically, we use the static-pushover-to-incremental-dynamic-analysis (SPO2IDA) method, which in essence is a R–μ–T relationship with improved properties. SPO2IDA extracts information from the static pushover curve and produces estimates of the limit-state response statistics that are necessary to implement the reliability-based criteria on the limit-state MAF. The optimization problem at hand is solved with a specifically tailored genetic algorithm. A three and a nine-storey steel moment-resisting frame are used to demonstrate the efficiency of the proposed procedure, leading to efficient building designs within reasonable computing time.

Reliability design optimization of composite structures based on PSO together with FEA

The present work aims to develop a method for reliability-based optimum design of composite structures. A procedure combining particle swarm optimization (PSO) and finite element analysis (FEA) has been proposed. Numerical examples for the reliability design optimization (RDO) of a laminate and a composite cylindrical shell are worked out to demonstrate the effectiveness of the method. Then a design for composite pressure vessels is studied. The advantages and necessity of RDO over the conventional equi-strength design are addressed. Examples show that the proposed method has good stability and is efficient in dealing with the probabilistic optimal design of composite structures. It may serve as an effective tool to optimize other complicated structures with uncertainties.

Non-probabilistic reliability-based structural design optimization based on the interval analysis method

Using interval variables to describe uncertain parameters in structural systems and their complex environments, a non-probabilistic reliability-based optimization model, which can give optimized design to meet certain reliability requirements, is proposed based on the interval reliability analysis method. Two levels are included in the non-probabilistic reliability optimization process for structures. The outer layer uses different global optimization algorithms according to the characteristics of the specific issues. The inner layer evaluates the upper and the lower bounds of the structural responses using the interval analysis method based on the Taylor expansion or the collocation interval analysis method according to the sensitivities of the responses with respect to the uncertainties. The optimization process which has strong portability, can not only avoid the two nested optimization which reduces the computational efficiency, but also take full advantage of existing mature optimization algorithms. Two different improved practical interval reliability models, which named 1-formula model based on interval possibilistic method and 2-formula chart-based model, are used in the optimization model. Two numerical examples in the paper show the effectiveness of the proposed method.

Integration of the effects of airborne chlorides into reliability-based durability design of reinforced concrete structures in a marine environment

In this paper, the hazard curve associated with airborne chlorides in a marine environment and the computational procedure to obtain the probability of occurrence of corrosion cracking in reinforced concrete (RC) structures are presented. A method for integration of the effects of airborne chloride into reliability-based durability design of RC structures in a marine environment is proposed. By using this method, it is possible to determine the probability of corrosion cracking due to airborne chlorides, regardless of region, distance from coastline, and the properties of the concrete controlled by the water to cement ratio.

On the reliability-based design of structures including passive energy dissipation systems

Abstract This contribution presents a methodology for stochastic design of structures including vibration protection systems. The approach is then used to investigate the effect of uncertain model parameters on the reliability-based optimal design of structures with a class of passive energy dissipation systems. The uncertainty of structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. The optimal design problem is formulated as a non-linear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability measures. A sequential optimization approach based on global conservative, convex and separable approximations is implemented for solving the optimization problem. The effects of uncertain model parameters on the performance, robustness and reliability of protected systems is illustrated by two example problems that consider multi-story buildings under stochastic ground excitation.

Reliability-Based Design and Heuristic Optimization MPSO-SA of Structures

In this paper, we present a probability study about spring of clutch structure. In the structure problems, the randomness and the uncertainties of the distribution of the structural parameters are a crucial problem. In the case of Reliability Based Design Optimization (RBDO), it is the objective is to play a dominant role in the structural optimization problem introducing the reliability concept. The RBDO problem is often formulated as a minimization of the initial structural cost under constraints imposed on the values of elemental reliability indices corresponding to various limit states. This paper proposes a new method for a modified particle swarm optimization algorithm (MPSO) combined with a simulated annealing algorithm (SA) and RBDO. MPSO is known as an efficient approach with a high performance of solving optimization problems in many research fields. It is a population intelligence algorithm inspired by social behavior simulations of bird flocking. Numerical results show the robustness of the MPSO-SA algorithm and RBDO.

Dynamic Reliability-Based Seismic Optimal Design of Base-Isolated Structures

This paper presents a dynamic reliability-based optimization technique for the seismic design of base-isolated structures. Firstly, the governing equation of multi-degree-of-freedom base-isolated structures is established. Then, the superstructure is unfolded by the first mode. Considering that the damping is non-classical and the total base-isolation system is un-symmetric, the complex modal analysis is adopted to uncouple the governing equation and the analytical solutions of stochastic seismic response under the Kanai-Tajimi spectrum loading are obtained. Taking the ratio between the first-order modal displacement standard deviation of the superstructure with base- isolated system and the fixed-base structure as the optimal objective function, the dynamic reliability of the isolated system displacement as the constraint, the optimal design parameters of the isolated system are obtained through the penalty function method. A 3-story building with isolated system illustrates the proposed dynamic reliability-based optimization method. It is believed that such an optimization technique provides an effective tool for the seismic design of base-isolated structures.