Reliability Analysis Of Structural Systems Research Articles

Seismic reliability analysis of energy-dissipation structures by combining probability density evolution method and explicit time-domain method

Hysteretic dampers such as buckling restrained braces (BRBs) have been widely used for improving the performance of civil structures exposed to seismic hazard. In this study, a hybrid approach, which combines the probability density evolution method (PDEM) and the explicit time-domain method (ETDM), is proposed for system reliability analysis of energy-dissipation structures with hysteretic dampers under seismic excitations. The PDEM can capture the probability density function (PDF) of system limit-state function for a structure by constructing a virtual random process associated with the limit state. The system failure probability of the structure can be directly evaluated through the integration of the PDF of system limit-state function over the failure domain. However, hundreds of deterministic nonlinear time-history analyses corresponding to the selected representative points need to be conducted in the solution procedure of PDEM, leading to high computational cost when applied to large-scale energy-dissipation structures. To enhance the efficiency of PDEM, the ETDM with dimension-reduced iteration scheme is incorporated into PDEM to conduct the required nonlinear time-history analyses with high efficiency, in which only a small number of degrees of freedom associated with the hysteretic dampers are considered in the iteration process. A real engineering building with 32 BRBs is investigated to illustrate the accuracy and efficiency of the proposed method and its feasibility to practical structures.

New reliability modeling methods for structural systems with hybrid uncertainty

AbstractThe present study investigates the hybrid reliability modeling of structures in which the inputs contain both random variables and interval variables. Hybrid uncertainty is divided into three categories, including random variables mixed with random variables, interval variables mixed with interval variable, and random variables mixed with interval variables. In order to perform the reliability analysis of structural systems, first, the Bayes method is proposed in the present study to obtain distribution parameters of random variables. Moreover, the self‐sample method is introduced to obtain the interval boundaries based on the least available measuring data. Then, the reliability models are established for three situations and the reliability indices are defined and derived accordingly. The abovementioned three types of reliability indices outline the general situation of structural systems. Finally, the specific calculation process is described in details through different examples. Furthermore, the accuracy and efficiency of the proposed method is discussed by comparing the results obtained from the Monte Carlo simulation and those of other methods. The obtained results indicate that the performance of the proposed model in solving reliability modeling problems is better.

System-based calibration of offshore Malaysia environmental action factors for the ISO 19902 PETRONAS offshore fixed platforms

Previously, the action factors, which are generally used in the region of Malaysia is based on the data from the Gulf of Mexico (GoM) or the North Sea, where the environmental condition is much harsher than the offshore Malaysia. Direct application of the high load factors in these regions can result in a waste of economic resources. Based on a reliability-based Load and Resistance Factor Design approach, the current study is carried out for the provision of system-based approach for the calibration of Offshore Malaysia Annex Extreme Environmental Action Factors based on the data from Malaysian waters. With the accessible SEAFINE and HYCOM hindcast database, long-term statistics of extreme environmental load have been derived for six platform locations in Malaysian waters, following the response-based Load Statistics Module (LSM) process. The Generic Load Model (GLM) including the wave-in-deck forces, which has been employed for transferring the wave motion statistics to structural response statistics, is developed in the paper. The structural resistance uncertainty is characterised by the minimum reserve strength ratios (RSRs) derived from a theoretical model that relates with environmental load factor. A structural system reliability analysis based on the FORM method has been performed for a range of minimum values of theoretical RSR for jacket structures fully designed to ISO Code 19902. Partial action factors associated with extreme environmental loads are calibrated to achieve a target reliability level in terms of reliability index.

Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables

The reliability analysis of structural systems with multiple failure modes and mixed variables is a critical problem because of complex nonlinear correlations among failure modes (or components), huge computational burden of time-consuming implicit functions, and complex failure regions. In this paper, aleatory and epistemic uncertainties are considered simultaneously, and an efficient adaptive kriging-based reliability method is proposed for structural systems with multiple failure modes and mixed variables. Two new learning functions are developed as guidelines for selecting new training samples at each iteration. The proposed learning functions and corresponding stopping criteria are directly linked to system probability of failure; this allows the proposed method to select new training samples efficiently To determine the lower and upper bounds of system probability of failure, the limit-state functions in the entire uncertainty space of interest are accurately constructed while avoiding complicated nested optimizations. The proposed method has the following advantages: (1) the learning functions and stopping criteria are directly linked to system probability of failure, and the structure importance of components is also considered; (2) it requires fewer samples to achieve accurate results, and can be applied to small system probability of failure; (3) it is easy to use for extremely complex systems (e.g., bridge systems); (4) it can be applied to a system with multiple failure modes and mixed variables (e.g., mixture of random and p-box variables). The capabilities and efficiency of the proposed method are validated through four numerical examples; results show that it has high applicability and accuracy.

AKOIS: An adaptive Kriging oriented importance sampling method for structural system reliability analysis

A major issue in the structural reliability analysis is to determine an accurate estimation result of the failure probability ideally based on a small number of model evaluations. In this regard, the active-learning Kriging based importance sampling method has been received considerable attentions. However, the utility of the most probable failure point (MPP) as the unique sampling center has limited its potential applications for multi-MPP problems. To this end, the paper presents an adaptive Kriging oriented importance sampling (AKOIS) approach. The outer active-learning loop of the AKOIS procedure is used to identify importance sampling centers, whereas its inner-loop is realized based on a rather small subregion centering at the sampling center to gain new training samples. Besides, numerical convergence of local active-learning iterations will immediately trigger another round of outer global search for a new importance sampling center. In this regard, the determined importance sampling centers are able to adaptively cover all branches of the investigated limit-state surface for structural system reliability analysis. Engineering applications of the data-driven importance sampling approach are demonstrated by several system reliability examples in the literature.

An improved reliability analysis approach based on combined FORM and Beta-spherical importance sampling in critical region

The reliability analysis of structural systems is generally difficult when limit state function (LSF) is implicitly defined especially by black-box models in engineering. To balance analysis efficiency and accuracy, an improved approach named BIS-FC is proposed in this paper based on the Beta-spherical importance sampling (BIS) framework with the innovative concept of critical region defined by combination with First Order Reliability Method (FORM). The critical region is defined by the hyper-tangent plane of LSF at the Most Probable Point (MPP) and its parallel hyperplanes according to the convex or concave features of LSF, wherein the samples are of both high occurrence probability and high misjudgment risk due to the linearization assumption of FORM. BIS-FC only conducts LSF analysis for the BIS samples located in the critical region, and the other samples are directly identified as safe or failure according to the linearized hyperplanes. Thus large computational cost can be saved compared to the original BIS, and meanwhile, the analysis accuracy can be greatly enhanced compared to FORM. An iterative process is proposed to properly define the critical region, based on which reliability is analyzed sequentially until the stopping criteria for desired estimation error level and stable convergence are satisfied. The algorithms of BIS-FC for both single and multiple MPP situations are developed and testified with six numerical examples and one satellite structural engineering problem. The results demonstrate the effectiveness of BIS-FC regarding good balance between efficiency and accuracy.

Multi-scale Dynamic System Reliability Analysis of Actively-controlled Structures under Random Stationary Ground Motions

This paper proposes a multi-scale dynamic system reliability analysis approach to assess the failure probability of an activelycontrolled structure subject to random stationary ground motions. The proposed approach employs a multi-scale hierarchical framework where a lower-scale system reliability analyses compute the failure probabilities of the structural members during the earthquakes and a higher-scale system reliability analysis computes the failure probability of the structural system based on results of the lower-scale analyses. The multi-scale framework facilitates the system reliability analysis of the large-sized complex system by decomposing the complex system into the manageable-sized subsystems. It also enables us to deal with statistical dependence both in spatial and temporal senses through the decomposition of the reliability analysis in space and time aspects. In these regards, the proposed approach performs a reliability analysis with the dynamic responses in time domain. This dynamic reliability analysis approach can consider uncertainties in system parameters and earthquake excitations simultaneously. In addition, the peak response over a time duration is used to describe the limit state of the structural system, which provides a more realistic measure of the failure probability of a structural system than instantaneous probability. In order to demonstrate the proposed approach, a 3-story shear-type building equipped with an optimal active control device is considered. The control performance under uncertainties is investigated through the reliability assessment by the proposed approach and the Monte Carlo Simulation (MCS) approach, respectively. The numerical study also investigates the influence of the uncertainties in the system parameters and the earthquake excitations on the system failure probability. The results of the numerical examples demonstrate that the proposed approach can efficiently estimate the system reliability and the failure probability of an actively-controlled structure.

A Novel Nonparametric Estimation for Conditional Copula Functions Based on Bayes Theorem

Conditional copula which measures the conditional dependence among variables, possesses a special position in copula field. In this article, based on Bayes theorem, we derive three kinds of conditional copula functions as the product of the corresponding conditional copula density functions and the corresponding unconditional copula functions (or the cumulative distribution functions). Then, a novel nonparametric method for estimating these conditional copula functions is proposed by the classification of the Monte Carlo Simulation (MCS) samples and by the kernel density estimation. In contrast to other estimation methods for conditional copula functions, the proposed method needs only a set of samples without any parameter or distribution assumption, or other complicated operators (such as estimation of the weights, integral operator, etc.). Therefore, the proposed nonparametric method reduces the computational complexity and possesses more universality for estimating the conditional copula functions. A 2-dimensional normal copula function, a numerical example, a structural system reliability analysis considering the common cause failure and an astrophysics model based on real data are employed to validate the effectiveness of the proposed method. Results show that the proposed nonparametric method is accurate and practical well.

Reliability and reliability-based importance analysis of structural systems using multiple response Gaussian process model

In the context of structural system reliability, quantifying the relative importance of random input variables and failure modes is necessary for improving system reliability and simplifying the reliability-based design problems. We firstly introduce the reliability-based variable importance analysis (VIA) indices to structural systems for quantifying the individual, interaction and total effects of each random input variable on the system failure probability, and propose two new reliability-based mode importance analysis (MIA) indices for measuring the effects of each failure mode on the failure and safety of structural systems. Then, an active learning procedure, which combines the multiple response Gaussian process (MRGP) model and the Monte Carlo simulation (MCS), is introduced to efficiently and adaptively produce surrogate models for the failure surfaces of systems, and three learning functions are compared. Based on the well-established surrogate models, the system failure probability as well as the VIA and MIA indices are estimated without calling the limit state functions in addition. Results of six test examples demonstrate the significance of the VIA and MIA indices, and show that the developed MRGP-based methods are effective in estimating both the system failure probability and the proposed importance indices.

Structural System Reliability Analysis Based on Improved Explicit Connectivity BNs

The study proposes an improved Explicit Connectivity Bayesian Networks (ECBNs) for system reliability assessment. The framework combines Analytic Hierarchy Process (AHP) with the traditional ECBNs. AHP is adopted to consider probabilistic dependencies between system components. Judgment matrix is constructed and weight vector, which meets the requirement of a random consistency check, is extracted to describe a conditional probability information of BNs intermediate nodes. The framework is especially suitable for the system with rare damage filed data. In addition, considering the multiple failure modes for the system component, the multi-dimensional Performance Limit State (PLS) function is proposed to estimate the marginal probability for the BNs root nodes. PLSs are properly modeled as interdependent random variables instead of deterministic quantities. Failing to properly account for the dependencies between PLSs, the non-conservative failure probability results will be obtained. Finally, the system reliability can be calculated through the BNs Junction Tree forward inference algorithm, and the most vulnerable components in the system can be identified through backward diagnose inference. The improved ECBNs theory is first applied to the system reliability evaluation for a reinforced concrete bridge to verify its validity.

An adaptive cubature formula for efficient reliability assessment of nonlinear structural dynamic systems

Abstract Extreme value distribution (EVD) evaluation is a critical topic in reliability analysis of nonlinear structural dynamic systems. In this paper, a new method is proposed to obtain the EVD. The maximum entropy method (MEM) with fractional moments as constraints is employed to derive the entire range of EVD. Then, an adaptive cubature formula is proposed for fractional moments assessment involved in MEM, which is closely related to the efficiency and accuracy for reliability analysis. Three point sets, which include a total of 2 d 2 + 1 integration points in the dimension d, are generated in the proposed formula. In this regard, the efficiency of the proposed formula is ensured. Besides, a “free” parameter is introduced, which makes the proposed formula adaptive with the dimension. The “free” parameter is determined by arranging one point set adjacent to the boundary of the hyper-sphere which contains the bulk of total probability. In this regard, the tail distribution may be better reproduced and the fractional moments could be evaluated with accuracy. Finally, the proposed method is applied to a ten-storey shear frame structure under seismic excitations, which exhibits strong nonlinearity. The numerical results demonstrate the efficacy of the proposed method.

A method for estimating the reliability of structural systems with moment-matching and copula concept

ABSTRACTIt is aimed to propose a copula based systematic quantitative method for system reliability analysis of engineering structures considering multiple dependent failure modes. The principles of the moment matching method, the copula theory and the bound theory are combined to achieve the purpose. As the very first step, the moment estimation of the limit state function of each component is calculated by anchored ANOVA (Analysis of Variance) expansion. The third moment saddle point approximation is then applied to derive the distribution of each performance function and evaluate the reliability index with obtained moments. By introducing copula functions into the narrow bounds theory, the traditional reliability method is improved. The best-fitting copula function is determined to ensure the accuracy of the joint probabilistic modeling between the dependent failure modes. A novel feature of the proposed method is the use of the copula concept, instead of traditional numerical integration commonly used in the joint failure probability estimation. Examples are presented to illustrate the accuracy and applicability of the presented method.

A probabilistic framework based on statistical learning theory for structural reliability analysis of transmission line systems

This paper describes a novel application of statistical learning theory to structural reliability analysis of transmission lines considering the uncertainties of climatic variables such as, wind speed, ice thickness and wind angle, and of the resistance of structural elements. The problem of reliability analysis of complex structural systems with implicit limit state functions is addressed by statistical model selection, where the goal is to select a surrogate model of the finite element solver that provides the value of the performance function for each conductor, insulator or tower element. After determining the performance function for each structural element, Monte Carlo simulation is used to calculate their failure probabilities. The failure probabilities of towers and the entire line are then estimated from the failure probabilities of their elements/components considering the correlation between failure events. In order to quantify the relative importance of line components and provide the engineers with a practical decision tool, the paper presents the calculation of two types of component importance measures. The presented methodology can be used to achieve optimised design, and to assess upgrading strategies to increase the line capacity.

An improved high-order statistical moment method for structural reliability analysis with insufficient data

The fourth-order moment method for reliability analysis of structural systems can be practically applied to effectively address the problem of reliability calculation and analysis with insufficient probability data. For complicated reliability analysis problems, however, this method can lead to inaccurate and unstable reliability calculation results. In this paper, an improved high-order statistical moment method for structural reliability analysis with insufficient data is presented. The presented method is inferred using the properties of statistical moment of standard normal distribution parameter and therefore is possible to obtain more stable and accurate calculation of the reliability indexes of a structural system with insufficient probability data. Two numerical examples are provided to show the performance of the presented method. The example results have shown that the method proposed in this paper not only improves the calculation accuracy and stability, but also brings the calculation results closer to the project conditions. The developed high-moment method for reliability calculation of structural systems provides a practical and effective theoretical base and technical support for the reliability design of structural systems.

Dominant failure modes identification and structural system reliability analysis for a long-span arch bridge

Failure of a redundant long-span bridge is often described by innumerable failure modes, which make the structural system reliability analysis become a computationally intractable work. In this paper, an innovative procedure is proposed to efficiently identify the dominant failure modes and quantify the structural reliability for a long-span bridge system. The procedure is programmed by ANSYS and MATLAB. Considering the correlation between failure paths, a new branch and bound operation criteria is applied to the traditional stage critical strength branch and bound algorithm. Computational effort can be saved by ignoring the redundant failure paths as early as possible. The reliability of dominant failure mode is computed by FORM, since the limit state function of failure mode can be expressed by the final stage critical strength. PNET method and FORM for system are suggested to be the suitable calculation method for the bridge system reliability. By applying the procedure to a CFST arch bridge, the proposed method is demonstrated suitable to the system reliability analysis for long-span bridge structure.

A new approach to system reliability analysis of offshore structures using dominant failure modes identified by selective searching technique

The reliability analysis of offshore structures, as conceived by current design practice, is typically carried out at the component level with an implicit assumption that the structural system will be safe as long as all its members are safe according to the corresponding limit state equations. However, it is widely accepted that a more general and rigorous approach to the risk assessment of offshore structures based on system reliability analysis is needed, in which the reliability of a structure is estimated with respect to the system-level failure caused by potential failure modes consisting of component failures with their statistical dependence considered. To this end, the merits of a new risk assessment framework, originally developed for truss and frame structures, are investigated in this paper in view of an extensive application of this method to the offshore structural systems. The main advantage of the proposed method is that the identification process of dominant failure modes is decoupled from the evaluation process of the probabilities of failure modes and the system failure event. The identification phase consists of a multi-point parallel search employing a genetic algorithm, and it is followed by the evaluation phase, which performs a multi-scale matrix-based system reliability analysis where the statistical dependence among both components and failure modes is fully considered. In order to demonstrate the applicability of the proposed method to the offshore field, the problem of a jacket platform under an extreme sea state is considered, in which the uncertainties are assumed both in the wave and hydrodynamic models and in the material properties of the structural members. The computational efficiency and accuracy of the proposed approach are successfully demonstrated through comparison with Monte Carlo simulations.

Compressive sensing with an adaptive wavelet basis for structural system response and reliability analysis under missing data

The challenge of determining response and reliability statistics of large-scale structural systems under earthquake induced stochastic excitations is considered where the source load data records are incomplete. To this aim, a compressive sensing based framework in conjunction with an adaptive wavelet basis is presented for reconstructing the samples with missing data and estimating the underlying process EPS. In this regard, novel insights are provided whereas certain conceptual, numerical, and practical implementation aspects of the technique are presented in detail. A numerical example pertaining to the stochastic response and reliability analysis of an eight floor reinforced concrete building structural system demonstrates the effectiveness of the proposed methodology.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

Reliability analysis of structures using stochastic response surface method and saddlepoint approximation

Stochastic response surface method (SRSM) is a technique used for reliability analysis of complex structural systems having implicit or time consuming limit state functions. The main aspects of the SRSM are the collection of sample points, the approximation of response surface and the estimation of the probability of failure. In this paper, sample points are selected close to the most probable point of failure and the actual limit state surface (LSS). The response surface is fitted using the weighted regression technique, which allows the fitting points to be weighted based on their distance from the LSS. The cumulant generating function (CGF) of the response surface is derived analytically. The saddlepoint approximation (SPA) method is utilized to compute the probability of failure of the structural system. Finally, four numerical examples compare the proposed algorithm with the traditional quadratic polynomial SRSM, Kriging based SRSM and direct MCS.

Reliability block diagram methods for system reliability analysis of spatial structures

The safety of complex spatial structures in operation depends highly on the reliability of the whole system and its structural components. In order to determine the relationship between system reliability and reliability of its components, reliability block diagram (RBD) method, which emphasises depicting the connection mode among all the components of a system, is employed for system reliability analysis of spatial structures. With the assumption of geometric stability, a new approach, aiming at finding out key elements where damage could lead to overall collapse of the structure, is adopted here for the logic relationship identification among components. The logic relationship, which is considered as the core component of the reliability block diagram, is utilised for reliability analysis of the system and the predetermined components. Finally, a large-span latticed grid spatial structure is investigated to validate the applicability of the RBD method for analysing the system reliability of spatial structures.