A novel study of structural reliability analysis and optimization for super parametric convex model

Owing to the severe technological competition and high demand for safety estimation in complex physic and engineering systems, reliability analysis has drawn more and more attention. The regular non-probabilistic reliability analysis assumes that experimental data are enclosed by ellipse and rectangle; however, this appears inconsistent with various types of uncertain sources. In this article, a novel definition for non-probabilistic reliability is provided for structures based on super parameteric convex model, which is formulated as the ratio of the multidimensional volume located in the safety domain to that of the total super parametric volume. Subsequently, a sampling method is proposed based on Monte Carlo simulation as a reference algorithm. To improve the efficiency, a first-order calculation method is developed to solve the reliability model using a linear approximation of the limit state function. Furthermore, a second-order calculation method is constructed to improve the reliability calculation precision with high nonlinearity, and a new non-probabilistic reliability-based design optimization method is established accordingly. Six numerical examples are tested to demonstrate the effectiveness of the proposed method.     

Response surface method based on uniform design and weighted least squares for non-probabilistic reliability analysis

The non-probabilistic reliability theory is a promising methodology for implementing structural reliability analysis in case of scarce statistical data. One of the main obstacles to implement non-probabilistic reliability analysis is the implication of the limit state function (LSF) for complex structures. This paper aims to establish a surrogate model of the LSF with higher simulation precision, and whereby proposes a response surface method based on the combination of uniform design (UD) and weighted least squares (WLS). At first, the UD method is selected as the sampling method of interval variables to realize the uniform space-filling of the initial samples, and the sample set is updated by gradually adding the approximate optimal points to increase the sampling density of critical domain. Then, the WLS method is applied to improve the precision of the response surface by adjusting the importance of samples to the function fitting. Finally, a method of constructing sample weights is developed. Two examples are applied to validate the feasibility and efficiency of the proposed method. Results show that the proposed method is effective for non-probabilistic reliability analysis of complex structures owning to high computational precision and low computational cost in both numerical and case study.     

A response surface method based on weighted regression for structural reliability analysis

Approximation methods such as the response surface method (RSM) are widely used to alleviate the computational burden of engineering analyses. For reliability analysis, the common approach in the RSM is to use regression methods based on least square methods. However, for structural reliability problems, RSMs should approximate the performance function around the design point where its value is close to zero. Therefore, in this study, a new response surface called ADAPRES is proposed, in which a weighted regression method is applied in place of normal regression. The experimental points are also selected from the region where the design point is most likely to exist. Examples are given to demonstrate the benefit of the proposed method for both numerical and implicit performance functions.     

A time-variant reliability analysis method for structural systems based on stochastic process discretization

In this paper, we propose a new method for analyzing time-variant system reliability based on stochastic process discretization, which provides an effective tool for reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system reliability problem, we can obtain the structural reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the method.     

压杆稳定的非概率可靠性凸集合模型分析方法

 针对概率可靠性模型对原始数据要求高的局限性,用凸集合模型来描述影响压杆稳定可靠性分析中的不确定参数,利用一阶Taylor展开式基于凸集合模型讨论了压杆稳定分析中不确定性参数对压杆稳定响应的影响,提出了压杆稳定的非概率可靠性度量的指标.此方法对数据的要求低,不用求概率密度函数而且计算简便.通过对工程实例的计算,其结果表明所提出的方法是一种简便而实用的分析方法.     

A non-probabilistic prospective and retrospective human reliability analysis method — application to railway system

The paper describes a method to analyze human reliability. It defines human reliability as a degradation function related to deviations of both human behavioral state and system state due to this behavior. The method is called ACIH, a French acronym for Analysis of Consequences of Human Unreliability. It is a non-probabilistic approach, which aims at identifying both tolerable and intolerable sets of human behavioral degradations, which may affect the system safety. The corresponding scenarios of degradations are characterized by a behavioral model of unreliability including three main factors: acquisition related factors, problem solving related factors, and action related factors. Both prospective and retrospective analyses are taken into account to specify error prevention tools. They are applied to the railway system.     

The interval estimation of reliability for probabilistic and non-probabilistic hybrid structural system

The aim of this paper is to improve evaluation of the reliability of probabilistic and non-probabilistic hybrid structural system. Based on the probabilistic reliability model and interval arithmetic, a new model of interval estimation for reliability of the hybrid structural system was proposed. Adequately considering all uncertainties affecting the hybrid structural system, the lower and upper bounds of reliability for the hybrid structural system were obtained through the probabilistic and non-probabilistic analysis. In the process of non-probabilistic analysis, the interval truncation method was used. In addition, a recognition method of the main failure modes in the hybrid structural system was presented. A five-bar statically indeterminate truss structure and an intermediate complexity wing structure were used to demonstrate the new model is more suitable for analysis and design of these structural systems in comparison with the probabilistic model. The results also show that the method of recognition of main failure modes is effective. In addition, range obtained through interval estimation is shown to be more credible than certain results of other reliability models.     

基于非概率模型的星载天线展开机构中同步齿轮系防卡滞研究

对某周边桁架式大型星载天线展开机构中的齿轮运动副的卡滞失效形式进行了研究。从齿轮啮合的极限位置出发,推导出了同步齿轮副不发生卡滞的条件。综合考虑齿轮加工误差、装配误差和太空环境温度等因素,利用优化算法,构建了齿轮副防卡滞的非概率可靠度计算公式。对同步齿轮副在不同装配误差和不同温度环境下的防卡滞的非概率可靠度进行了预测,并与将运动功能函数中的变量视为正态分布的概率模型下的可靠度相比较,比较结果显示两者的变化趋势相同,而且与数值仿真过程比较吻合,说明本文的方法是合理有效的。     

Efficient structural reliability analysis via a weak-intrusive stochastic finite element method

This paper presents a novel methodology for structural reliability analysis by means of the stochastic finite element method (SFEM). The key issue of structural reliability analysis is to determine the limit state function and corresponding multidimensional integral that are usually related to the structural stochastic displacement and/or its derivative, e.g., the stress and strain. In this paper, a novel weak-intrusive SFEM is first used to calculate structural stochastic displacements of all spatial positions. In this method, the stochastic displacement is decoupled into a combination of a series of deterministic displacements with random variable coefficients. An iterative algorithm is then given to solve the deterministic displacements and the corresponding random variables. Based on the stochastic displacement obtained by the SFEM, the limit state function described by the stochastic displacement (and/or its derivative) and the corresponding multidimensional integral encountered in reliability analysis can be calculated in a straightforward way. Failure probabilities of all spatial positions can be obtained at once since the stochastic displacements of all spatial points have been known by using the proposed SFEM. Furthermore, the proposed method can be applied to high-dimensional stochastic problems without any modification. One of the most challenging problems encountered in high-dimensional reliability analysis, known as the curse of dimensionality, can be circumvented with great success. Three numerical examples, including low- and high-dimensional reliability analysis, are given to demonstrate the good accuracy and the high efficiency of the proposed method.     

A structural reliability model for composite materials

This work is a part of a project aimed at developing a model and procedure to evaluate the structural reliability of a laminate whose laminae properties are statistically known. The inputs consist of the laminae's elastic properties (deterministic in that they are not as closely related to manufacturing technology) and the derived allowable strengths (aleatoric variables), as well as the sequence (number, orientation, position) of the laminae in the laminate. The output, the laminate's structural reliability, allows determination of the laminate's collapse process, with the most probable lamina failure sequence.     

Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation

International Journal of Mechanics and Materials in Design - The traditional ellipsoid convex set is a kind of basic non-probabilistic model to measure uncertainties. However, it is difficult or...     

Sensitivity based reduced approaches for structural reliability analysis

In the reliability analysis of a complex engineering structures a very large number of system parameters can be considered to be random variables. The difficulty in computing the failure probability increases rapidly with the number of variables. In this paper, a few methods are proposed whereby the number of variables can be reduced without compromising the accuracy of the reliability calculation. Based on the sensitivity of the failure surface, three new reduction methods, namely (a) gradient iteration method, (b) dominant gradient method, and (c) relative importance variable method, have been proposed. Numerical examples are provided to illustrate the proposed methods.     

A method of human reliability analysis and quantification for space missions based on a Bayesian network and the cognitive reliability and error analysis method

Analyses of human reliability during manned spaceflight are crucial because human error can easily arise in the extreme environment of space and may pose a great potential risk to the mission. Although various approaches exist for human reliability analysis (HRA), all these approaches are based on human behavior on the ground. Thus, to appropriately analyze human reliability during spaceflight, this paper proposes a space‐based HRA method of quantifying the human error probability (HEP) for space missions. Instead of ground‐based performance shaping factors (PSFs), this study addresses PSFs specific to the space environment, and a corresponding evaluation system is integrated into the proposed approach to fully consider space mission characteristics. A Bayesian network is constructed based on the cognitive reliability and error analysis method (CREAM) to model these space‐based PSFs and their dependencies. By incorporating the Bayesian network, the proposed approach transforms the HEP estimation procedure into a probabilistic calculation, thereby overcoming the shortcomings of traditional HRA methods in addressing the uncertainty of the complex space environment. More importantly, by acquiring more information, the HEP estimates can be dynamically updated by means of this probabilistic calculation. By studying 2 examples and evaluating the HEPs for an International Space Station ingress procedure, the feasibility and superiority of the developed approach are validated both mathematically and in a practical scenario.     

A new artificial neural network-based response surface method for structural reliability analysis

This paper presents a new artificial neural network-(ANN)based response surface method in conjunction with the uniform design method for predicting failure probability of structures. The method involves the selection of training datasets for establishing an ANN model by the uniform design method, approximation of the limit state function by the trained ANN model and estimation of the failure probability using first-order reliability method (FORM). In the proposed method, the use of the uniform design method can improve the quality of the selected training datasets, leading to a better performance of the ANN model. As a result, the ANN dramatically reduces the number of required trained datasets, and shows a good ability to approximate the limit state function and then provides a less rigorous formulation in the context of FORM. Results of three numerical examples involving both structural and non-structural problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Compared with the conventional ANN-based response surface method, the proposed method is much more economical to achieve reasonable accuracy when dealing with problems where closed-form failure functions are not available or the estimated failure probability is extremely small. Finally, several important parameters in the proposed method are discussed.     

结构时变可靠度计算的全随机过程模型

为了对既有结构的可靠性进行正确评估,必须考虑时间变化的影响,对目前可靠度分析中采用的只考虑荷载随时间变化的半随机过程模型进行改进。基于结构抗力和作用效应相互独立的基本假设,充分依据作用效应和抗力的时变特性,考虑结构抗力为独立增量过程,并计算了抗力的自相关系数,得到了计算结构失效概率的近似算法,建立了结构时变可靠度计算的全随机过程模型。通过实例验证,该方法简单易行,便于工程应用,为基于时变可靠度理论的既有结构评估和寿命预测提供理论依据。     

基于风险分析的可靠性指标加速验证方法研究

传统的可靠性验证试验由于一般在使用条件下进行,且只利用失效数据进行判定,往往需要大量的时间和费用。这对于高可靠长寿命船舶设备可靠性指标的验证是不可接受的。本文提出一种基于风险分析的可靠性指标加速验证方法,该方法利用退化数据进行分析,在试验风险可接受的条件下提前截止试验,得出验证结果。同时,利用高环境应力可以加速退化过程,进一步减少试验时间。本文具体给出了分析和计算提前截止试验和利用高应力进行试验产生的额外风险的方法,保证了验证结果的真实可靠。最后利用案例证实了该方法在减少验证试验时间上的有效性。     

基于结构动力学方法的气动弹性分析

摘 要：对于气动与弹性的耦合模型,给出气动力的频域公式,并表示成有理多项式,通过等价的变换,能够推导出与结构动力学方程完全相似的、关于求解变量的二阶常微分方程组。于是,可以在计算结构动力学框架下实现气动弹性问题的分析和计算。此方法将通用计算结构动力学程序的功能与试验或数值分析得到的气动力模型相结合,简化了气动弹性的耦合分析、提高计算效率。