Failure Probability Of Structural System Research Articles

Analysis on Reliability of Wind Barrier on High-speed Railway Bridge under Wind Load

In order to guarantee the safety of wind barrier structure on the railway bridge and to prevent the overturning of wind barrier in the strong wind impacting on the normal operation of the train, the study on reliability of wind barrier is conducted. Taking the single side 4m wind barrier installed on the Lanzhou-Xinjiang second double-line railway bridge as an example, considering the randomness of natural wind velocity and train speed, based on the probabilistic theory analyze the reliability of the wind barrier structure system under the static wind load and dynamic wind load, and evaluate the wind barrier safety with the reliability index and failure probability of structural system. And parameter sensitivity analysis is performed to find out which factors are more important to the reliability of the wind barrier system. The research results show that the reliability index of the wind barrier system meets the requirements of the design specification, and the failure probability is small; the reliability index of the wind barrier system under the static wind load and dynamic wind load is more sensitive to the wind velocity than the train speed.

An efficient reliability analysis method for structures with hybrid time-dependent uncertainty

Performing time-dependent reliability analysis is an effective way to estimate the failure probability of structural system throughout its lifetime. In the engineering practices, uncertain parameters with sufficient sample and limited sample may exist simultaneously. The uncertain parameters with limited sample data are difficult to construct its precise probabilistic characteristics during estimating the accurate time-dependent reliability. To address this issue, this paper first develops a new hybrid time-dependent reliability model involving interval processes. Then, to reduce the high dimensionality, an extension method based on equivalent stochastic process transformation approach is proposed to transform the stochastic processes and the interval processes into corresponding equivalent random variables respectively. In particular, an instantaneous reliability model is constructed to envelope all potential system failures that may occur during the time interval. In order to identify the instantaneous failure surface accurately, an active learning method is proposed based on the deep neural network model and the weighted sampling method. With the constructed deep neural network model, the new hybrid time-dependent reliability can be evaluated by performing the Monte Carlo Sampling. Three numerical examples are used to verify the accuracy and efficiency of the proposed method.

Failure Probability of Structural Systems in the Presence of Imprecise Uncertainties

Structural reliability evaluation is considered to be the solution for modern complex engineering systems possessing uncertain parameters. Reliability estimation involves probabilistic theory when the uncertainties are defined as random variables, whereas with limited resources, it is strenuous to estimate precise parameters in the structural model. Therefore, for such cases, imprecise parameters should be treated appropriately in the design and analysis stage for the improvement of serviceability of the system. On the other side, analyses involving multi-dimensional, computationally expensive, and highly nonlinear structures are formidable in simulation-based methods in the presence of uncertainties. An efficient uncertainty analysis procedure is presented in this paper for analysing the systems with imprecise uncertainties defined as probability-box variables. The estimated bounds of failure probability for the numerical examples from structural mechanics are compared with the traditional approaches to demonstrate the efficiency of the methodology.

Nonlinear finite-element-based structural system failure probability analysis methodology for gravity dams considering correlated failure modes

The structural system failure probability (SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams. Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions, namely, limit state functions of failure modes. Several problems are to be solved in the use of traditional methods for gravity dams. One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode; another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined. Performing SFP analysis for a gravity dam system is a challenging task. This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams. Firstly, reasonable nonlinear constitutive modes for dam concrete, concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms. Meanwhile the response surface (RS) method is used to model limit state functions of main failure modes through the Monte Carlo (MC) simulation results of the dam-interface-foundation interaction finite element (FE) analysis. Secondly, a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations. Then, the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed. Finally, a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool (FERUM). This methodology is demonstrated by a case study of an existing gravity dam analysis, in which the dominant failure modes are identified, and the corresponding performance functions are established. Then, the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.

110 限界状態曲面上に初期値を定めるRF法に基づく設計点探索法の研究 : 設計点情報を用いたシミュレーションに基づく構造信頼性解析法(GS1,3 材料力学(1),研究討論セッション)

This study describes an efficient application of Rackwitz Fiessler algorithm to search out all of design points, utilized in the multimodal importance sampling simulation to estimate structural failure probabilities. The initial points to execute Rackwitz Fiessler algorithm are proposed to set in the respective quadrants of the basic random variable space and all of possible design points are determined. Numerical examples to estimate the failure probability of structural system with multiple and nonlinear limit state function by using multimodal importance sampling using all of design points determined are presented to illustrate that the proposed method gives accurate estimations effectively.

Reliability Assessment and Reliability-Based Design Optimization of Large Scale Box-Girder Structural System

Reliability analysis and reliability-based design optimization of large scale box-girder structural system is an interesting topic in the field of structural design. Structural resistance, loading, plating thickness and cross-sectional area of beam are considered as stochastic variables. Safety margin equations of both beam and plate element are constructed. Since the safety margin equations are implicit function of random variables, the stochastic finite element method (SFEM) is adequate for sensitivity analysis. The advanced first order second moment (AFOSM) method is used to calculate the safety indices of structural components. In addition to this, branch and bound method is used to identify the dominant failure paths. Probabilistic Network Evaluation Technique (PNET) method is used to assess failure probability of structural system. The optimization problem of structure is formulated as a nonlinear programming problem that aims at minimizing structural weight with constraints on reliability and range constraints of design variables. An optimum vector algorithm is applied to solve the optimization problem. One illustrative example is carried out to elucidate present process of reliability assessment and reliability-based design optimization.

Probabilistic importance analysis of the input variables in structural systems

To measure the effects of input variables’ realization on variance of the output performance function and on the failure probability of structural system, two new probabilistic importance measures (PIMs) are defined. As an input variable takes its realization according to its probability distribution, the two PIMs can quantify the possibility of reducing the variance of the output performance function and the possibility of improving the structural system reliability, respectively. After the properties of the PIMs are illuminated and proved in detail, a solution based on the probability density function evolution method (PDEM) is constructed to evaluate the PIMs. The solution is used to solve the PIMs with correlated input variables based on the Copula transformation. Examples demonstrate that the proposed solution on the PDEM can improve the computational efficiency greatly with acceptable precision, and the solution based on the conjunction of the PDEM and the Copula transformation can effectively solve the PIMs with correlated input variables.

A Novel Computational Methodology for Uncertainty Quantification in Prognostics Using The Most Probable Point Concept

This paper develops a novel computational approach to quantify the uncertainty in prognostics in the context of condition- based monitoring. Prognostics consists of two major steps; first, it is necessary to estimate the state of health at any time instant, and then, it is required to predict the remaining useful life of the engineering component/system of interest. While the topic of estimation has been addressed through different types of Bayesian tracking techniques, this paper primarily focuses on the second aspect of future prediction and remain- ing useful life computation, which is influenced by several sources of uncertainty. Therefore, it is important to identify these sources of uncertainty, and quantify their combined ef- fect on the remaining useful life prediction. The computation of uncertainty in remaining useful life can be treated as an uncertainty propagation problem which can be solved using probabilistic techniques. This paper investigates the use of the Most Probable Point approach (which was originally developed to estimate the failure probability of structural systems) for calculating the probability distribution of the remaining useful life prediction. The proposed methodology is illustrated using a battery which is used to power an un- manned aerial vehicle.

Reliability Analysis of Two-Dimensional Series Portal-Framed Bridge System Based on Mixed Copula Functions

In this paper, several commonly-used Elliptical copulas and Archimedean copulas were introduced, and their application in the correlation analysis were also described in detal. For the two failure modes of two-dimensional series portal-framed bridge system, the performance function values with respect to the failure modes were considered as the analysis variables of the chosen copula functions, and the Baysian copula selection method was applied to select the proper copula functions. And then, the two-dimension mixed copula function was built. Thereinto, the uncertain parameters of copula function were determined with Monte Carlo Sampling (MCS) method, so the numerical modeling of the mixed copula fuction about the failure mode of two-dimensional series portal-framed bridge system was achieved. Finally the reliability of this system was analyzed with the built mixed copula function, and the structural system failure probability was obtained.

Reliability analysis of structural system with multiple failure modes and mixed uncertain input variables

In the design of engineering structure, uncertainties can be modeled as randomness or fuzziness depending on the amount of information available. In this article, the estimation of failure probability of structural system with multiple failure modes and mixed (random and fuzzy) inputs is considered. We firstly review the addition law of failure probability and a linear programming based bound method, and then these two techniques are combined to deal with structural system with multiple failure modes and only random inputs. Eventually, this method is extended for estimating the membership function of the failure probability of structural system with both random and fuzzy inputs. This method is computationally cheap, especially for the structural system with a large number of failure modes. Several numerical examples are introduced for demonstrating the efficiency and accuracy of the proposed method.

MEMBERSHIP FUNCTION OF FAILURE PROBABILITY USING MULTICUT-HIGH DIMENSIONAL MODEL REPRESENTATION

The structural reliability analysis in the presence of mixed uncertain variables demands more computation as the entire configuration fuzzy variables needs to be explored. Moreover the existence of multiple design points deviate the accuracy of results as the optimization algorithms may converge to a local design point by neglecting the main contribution from the global design point. Therefore, in this paper a novel uncertainty analysis method for estimating the membership function of failure probability of structural systems involving multiple design points in the presence of mixed uncertain variables is presented. The proposed method involves Multicut-High Dimensional Model Representation technique for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability analysis involving any number of fuzzy and random variables. The accuracy and efficiency of the proposed method is demonstrated through three examples.

System failure probability of offshore jack-up platforms in the combination of fatigue and fracture

As it is known, fatigue is the process of damage accumulation in material due to the stress fluctuation. The failure occurs when accumulated damage exceed critical level. In practice, uncertainties are incorporated in fatigue estimation especially in the loads and in the capacity of structures. Reasonably these uncertainties can be incorporated within reliability framework or probability context. It is possible to estimate the fatigue reliability based on crack propagation in fracture mechanics and also using reliability context. However the first failure of structural element under fatigue degradation may not lead to the collapse of system, an approach to combine in the system failures is needed. This paper presents a new approach to estimate structural system failure probability of jack-up platforms in combination of fatigue and fracture. The probability of failure for each component is initially estimated using typical fatigue and fracture failure scenario. But for the second element failure in combination of fatigue and fracture, a new approach is presented. This method is based on the Monte Carlo Simulation of crack size in accordance with the crack growth approach in fracture mechanics. Important sequences leading to the structural collapse are identified within the branch and bound technique. Finally the system failure probability through combination of important paths leading to the structural collapse is obtained. Advantage of this method in addition to its simplicity in application is possibility of using the FORM technique to estimate each failure path individually and finally combine them together to determine system reliability. It is shown the system failure under combination of fatigue and fractures has higher probability of occurrence than the purely first or in combination with the second fatigue failures only.

Discussion of Reliability Analysis for Aircraft Wing Box Structural System

It is very complex problem that the reliability of aircraft wing box structural system with many random variables (such as area, thickness, material modulus, load etc.) is analyzed. In the paper, the reliability analysis method of aircraft wing box structural system is proposed based on the theory of structural reliability and stochastic finite element. The explicit expression of safe margin and the sensitivity of safe margin to each random variable are given, which improves the accuracy and efficiency of reliability calculation. The relationship of the level of failure path with structural system failure probability is discussion. The failure probability of element is calculated by using first order second moment method, and the main failure path of structural system is identified by using the advanced branch and bound method, and the failure probability of structural system is evaluated by using probabilistic network evaluation technique method. Numerical examples show that the method is of efficient and accurate, and the 3 or 4 level of failure path is acceptable for wing box structural system considering efficiency and accuracy.

A technique for computing failure probability of a structure using importance sampling

In this paper, based on the probability formula of the union of events and the concept of the importance sampling, a technique for computing structural system failure probability is developed. In Melcher's method, all importance sampling functions corresponding to the structural significance failure modes should be combined by some criteria, and they would affect the precision of results or computational efficiency. In this paper, the developed technique is based on the multiple simulation using every importance sampling function in turn, the criterion for combination is not necessary, so, the shortcomings of Melcher's method is overcome. Several examples illustrate the developed technique of this paper.

Time-Dependent Structural Reliability Analysis Based on Directional Simulation.

This paper outlines an improved simulation method for a time-dependent reliability analysis of structural systems subjected to stochastic loads. Strengths of structural elements are assumed to degrade with time proportionally during the life cycle of the structural system, and stochastic load events are modeled as Poisson processes. The structural failure probabilities are estimated through the life cycle simulation, in which the directional simulation method is applied just to sample random load variables to execute each life cycle simulation efficiently. Numerical examples are presented and results are compared with those obtained by the crude Monte Carlo simulation to show the effectiveness of the proposed method. It is shown that the proposed method is effective for the assessment of the time-dependent failure probability of structural systems.

Approximated Evaluation of Failure Probability for Structural System Using Conditional Safety Indices.

This paper deals with the approximated evaluation method for failure probability of structural systems using conditional safety indices. In general, it is difficult to compute an exact solution of the structural reliability problem with correlations of design variables and limit state functions. It is expected that the conditional safety index proposed will be a useful measure for the safety of complicated structural systems. The merit of this new measure is that the characteristics of statistics and geometry are identical on standardized space. Therefore the conditional safety index yields a practical effective interval of system reliability. When the high-order product sets of a failure event is obtained, the new assessment of the bounds for the estimation of failure probability is also significant. However, the evaluation process of conditional safety indices requires a sequential conditional correlation matrix so that it is the complicated process to calculate high-order simultaneous probability. This paper also proposes the method for transforming the vector of original safety indices into the vector of conditional safety indices using cholesky decomposition of the correlation matrix. In addition, it is suggested that the multi-integral can be approximated by the product of simple integrals using conditional safety indices.

System reliability analysis and optimization of stiffened panels under compression

Abstract A system reliability analysis method and an optimization method of stiffened panels are presented in this paper. The correlations among the system resistances of failure modes are considered to increase computational accuracy. By taking the allowable structural system failure probability as a constraint, the mathematical model of structural optimization is established and the feasible direction method is used to solve it. The effectiveness and efficiency are shown by the illustrative examples.

A numerical integration method in affine space and a method with high accuracy for computing structural system reliability

In this paper, a numerical integration method in affine space for computing structural system failure probability is presented. This method has the advantage over the method in orthogonal space in that the integration grid can be easily generated because of the very simple integration domain. Furthermore, by using it to compute the two- and three-order joint failure probabilities, the computational accuracy of Feng's method for combining system failure probability is increased.

Reliability analysis of structure and control mechanism of aircraft flap

The aircraft flap structure and its control mechanism are considered as an entire system for analysis of the system's reliability. The significant failure modes of a flap structure are based on the following engineering criteria: the magnitude of the computational safety factors of different structural members and the possible patterns that compose failure modes. According to these significant failure modes, the failure probability of a single failure mode can be computed, and the failure probability of the flap structural system can then be solved based on these single failure probabilities. For the flap control mechanism, besides the static strength reliability, it is necessary to compute the function reliability. The reliability of the control mechanism can be synthesized from the above two kinds of reliabilities. Finally, the entire flap system failure probability can be solved by synthesis of the flap structural system failure probability and the flap control mechanism failure probability.

Stochastically Dominant Modes of Frames by Mathematical Programming

Most important in calculating the failure probability of structural systems is the search for the stochastically most relevant failure mechanism of ductile structural systems—particularly framed structures. For this reason an automatic method for finding all modes can be employed, but for very large systems these procedures may become intractable. Mesh and nodal methods for frames are formulated with particular attention to simple data preparation. The generalized mesh description leads to the simpler and more efficient formulation of the mechanism compatibility equations. Two nonconvex problems, one with bilinear constraints and the other with a fractional objective function, have been derived. The latter formulation can be solved quite effectively when cast in the form of the maximization of a quadratic convex function over a linear domain. This is followed by mathematical programming techniques that are more appropriate for nonconvex optimization problems. The paper concludes with a discussion of the methodologies for finding other important modes.