结构随机延性需求谱的应用研究

结构的地震反应危险性曲线体现了结构的地震反应与地震动强度之间的关系,采用随机延性需求谱可以很方便地建立结构的地震反应危险性曲线。非线性结构在随机地震作用下的位移反应分析属于非线性随机振动问题,采用随机延性需求谱可以简单而有效的获得非弹性单自由度体系的随机位移反应的统计量,结合非线性静力分析,还可以进行多自由度结构的随机地震反应分析。此外,随机延性需求谱还可以用于结构的抗震可靠度分析。     

Diagnosis Modelling for Dependability Assessment of Fault‐Tolerant Systems Based on Stochastic Activity Networks

The growing demand for safety, reliability, availability and maintainability in modern technological systems has led these systems to become more and more complex. To improve their dependability, many features and subsystems are employed like the diagnosis system, control system, backup systems, and so on. These subsystems have all their own dynamic, reliability and performances and interact with each other in order to provide a dependable and fault‐tolerant system. This makes the dependability analysis and assessment very difficult. This paper proposes a method to completely model the diagnosis procedure in fault‐tolerant systems using stochastic activity networks. Combined with Monte Carlo simulation, this will allow the dependability assessment by including the diagnosis parameters and performances explicitly. Copyright © 2014 John Wiley & Sons, Ltd.     

How to Perform Continuous Sampling (CSP), Vol. 2: ASQC Basic Reference Series

Modeling recurrent event data is of current interest in statistics and engineering. This article proposes a framework for incorporating covariates in flowgraph models, with application to recurrent event data in systems reliability settings. A flowgraph is a generalized transition graph (GTG) originally developed to model total system waiting times for semi-Markov processes. The focus of flowgraph models is expanded by linking covariates into branch transition models, enriching the toolkit of available data analysis methods for complex stochastic systems. This article takes a Bayesian approach to the analysis of flowgraph models. Potential applications are not limited to engineering systems, but also extend to survival analysis.     

随机结构正交分解分析方法

现代复杂结构的建造促成了随机结构分析研究的发展。在这一领域中,随机结构分析的正交分解分析方法为随机结构分析与建模研究提供了新的工具。本文概括介绍了作者所发展的扩阶系统方法,列举了近年来扩阶系统方法在常见建筑工程结构分析中的应用案例。研究结果表明：采用随机结构分析的观点,结构发生各种程度破坏概率会发生大幅度变化。     

Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique

This paper discusses a type of redundancy that is typical in a multi-state system. It considers two interconnected multi-state systems where one multi-state system can satisfy its own stochastic demand and also can provide abundant resource (performance) to another system in order to improve the assisted system reliability. Traditional methods are usually not effective enough for reliability analysis for such multi-state systems because of the “dimensional curse” problem. This paper presents a new method for reliability evaluation for the repairable multi-state system considering such kind of redundancy. The proposed method is based on the combination of the universal generating function technique and random processes methods. The numerical example is presented to illustrate the proposed method.     

地震作用下大型升船机结构的响应特征分析

从振动力学的角度,以某大型升船机建筑结构为背景,对升船机结构的动力特性及在地震作用下升船机结构的确定性和随机反应特征进行了较系统的分析。首先建立了升船机建筑结构的三维分析模型,对升船机结构进行了动力特性及时程响应特征分析。然后,在总结与分析有关地震动随机模型研究成果的基础上,通过比较,选择了具有较全面描述输入地震动随机特性的数学模型,并对升船机结构的功率谱响应特征进行了分析。最后,基于上述结构反应特征分析,给出了升船机建筑结构抗震可靠度计算模型的适用性建议。     

二自由度碰撞振动系统的随机响应

用拟不可积哈密顿系统随机平均法研究了二自由度磁撞振动系统的随机响应，先将二自由度随机激励的碰撞振动系统表示成随机激励的耗散的哈密顿系统形式，然后用拟不可积哈密顿系统的随机平均法得到了以系统哈密顿函数为基本变量的一维It^↑o随机微分方程，最后用数值方法求解与该方程相应的稳态FPK方程，得到系统响应的平稳概率密度。两个算例的结果与数字模拟结果的比较表明了随机平均法在二自由度磁撞振动系统的随机响应分析中的有效性。     

Nonzero repair times dependent on the failure hazard

It is common in the literature on the reliability and maintenance of repairable systems to model the repair times as instantaneous. However, this is an unreasonable assumption for some complex systems, especially those requiring a high level of reliability, and such systems may spend a significant proportion of their lifetimes under maintenance and repair. We model the ageing of such a system with alternating stochastic processes. Operational times are generated at random and may have an increasing failure rate. Repair times are generated from a random process where the repair time is related to the hazard rate at failure. This yields lengthened repair times at late stages in a system subject to an increasing failure hazard rate but also accommodates long repair times at young ages in systems with a bathtub-shaped hazard rate function. We derive analytic results for a set of special cases of the model, show how simulation and inference can be carried out, and apply our method to real data from a large car manufacturer.     

Stochastic amplification in epidemics

The role of stochasticity and its interplay with nonlinearity are central current issues in studies of the complex population patterns observed in nature, including the pronounced oscillations of wildlife and infectious diseases. The dynamics of childhood diseases have provided influential case studies to develop and test mathematical models with practical application to epidemiology, but are also of general relevance to the central question of whether simple nonlinear systems can explain and predict the complex temporal and spatial patterns observed in nature outside laboratory conditions. Here, we present a stochastic theory for the major dynamical transitions in epidemics from regular to irregular cycles, which relies on the discrete nature of disease transmission and low spatial coupling. The full spectrum of stochastic fluctuations is derived analytically to show how the amplification of noise varies across these transitions. The changes in noise amplification and coherence appear robust to seasonal forcing, questioning the role of seasonality and its interplay with deterministic components of epidemiological models. Childhood diseases are shown to fall into regions of parameter space of high noise amplification. This type of "endogenous" stochastic resonance may be relevant to population oscillations in nonlinear ecological systems in general.     

Predicting laser weld reliability with stochastic reduced‐order models

Laser welds are prevalent in complex engineering systems and they frequently govern failure. The weld process often results in partial penetration of the base metals, leaving sharp crack‐like features with a high degree of variability in the geometry and material properties of the welded structure. Accurate finite element predictions of the structural reliability of components containing laser welds requires the analysis of a large number of finite element meshes with very fine spatial resolution, where each mesh has different geometry and/or material properties in the welded region to address variability. Traditional modeling approaches cannot be efficiently employed. To this end, a method is presented for constructing a surrogate model, based on stochastic reduced‐order models, and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry is captured by calibrating plasticity parameters to experimental observations of necking as, because of the ductility of the welds, necking – and thus peak load – plays the pivotal role in structural failure. The proposed method is exercised for a simplified verification problem and compared with the traditional Monte Carlo simulation with rather remarkable results. Copyright © 2015 John Wiley & Sons, Ltd.     

An optimized technique for reliability analysis of safety‐critical systems: A case study of nuclear power plant

Stochastic models are extensively used in quantifying the reliability of safety critical systems. These models use the state‐space model for reliability quantification. Markov chain is comprehensively used in describing a sequence of possible events of any system in which the probability of each event depends only on the state attained in the previous event. Markov chains are convenient to model the software system of the SCS with the help of Petri Nets, a directed bipartite graph widely used for the verification and validation of real‐time systems. However, the stochastic model suffers from the state‐space explosion problem. In this paper, we proposed a technique for reliability analysis of safety critical systems, excavating into the coherent optimization of Markov chain. The approach has been validated on 17 safety critical systems of nuclear power plants.     

随机结构动力分析的扩阶系统方法

本文发展了一类用于随机结构系统动力分析的扩阶系统方法。基于随机空间的正交展开理论,文中推导给出了扩阶系统动力方程的一般公式。这组公式可以适用于同时具有随机质量、随机阻尼、随机刚度参数的多自由度动力系统。通过引入虚拟结构的概念,文中建议了形成扩阶系统动力矩阵的有限元方法。通过对比算例分析,证实了扩阶系统方法的可行性与可靠性。最后,讨论了一个很重要现象：随机系统均值反应与相应均值参数系统反应之间的差异并指出了此差异的意义。     

Predictive maintenance of complex system with multi-level reliability structure

Onboard sensors, which constantly monitor the states of a system and its components, have made the predictive maintenance (PdM) of a complex system possible. To date, system reliability has been extensively studied with the assumption that systems are either single-component systems or they have a deterministic reliability structure. However, in many realistic problems, there are complex multi-component systems with uncertainties in the system reliability structure. This paper presents a PdM scheme for complex systems by employing discrete time Markov chain models for modelling multiple degradation processes of components and a Bayesian network (BN) model for predicting system reliability. The proposed method can be considered as a special type of dynamic Bayesian network because the same BN is repeatedly used over time for evaluating system reliability and the inter-time–slice connection of the same node is monitored by a sensor. This PdM scheme is able to make probabilistic inference at any system level, so PdM can be scheduled accordingly.     

基于随机无网格伽辽金法和蚂蚁算法的结构可靠性分析

 用摄动随机无网格伽辽金法(PSEFGM)求解随机结构的响应,然后采用蚂蚁算法对结构可靠性进行了分析。摄动随机无网格伽辽金法具有不需要划分单元和精度高等特点。蚂蚁算法是一种智能型随机搜素优化算法,对目标函数没有任何可微甚至连续的要求,可有效克服经典算法易于陷入局部最优解的常见弊病。数值实例表明,在随机结构可靠性分析方面,随机无网格迦辽金法与蚂蚁算法比经典算法具有明显的优势。     

动力可靠度约束下基于概率测度变换-全局收敛移动渐近线法的结构优化设计EI北大核心CSCD

基于动力可靠度的结构优化是实现随机动力系统优化设计的重要途径。针对设计变量为系统中部分随机变量分布均值的情形,提出了一种基于动力可靠度的结构优化设计方法。在该方法中,通过概率密度演化理论实现了结构动力可靠度的高效分析。在此基础上,结合概率测度变换,可以在不增加任何确定性结构分析的前提下,实现动力可靠度对设计变量的灵敏度分析。进而,通过将上述概率密度演化-测度变换方法嵌入全局收敛移动渐近线法,实现了基于动力可靠度的结构优化设计问题的高效求解。数值算例的结果表明,所提方法可以显著降低结构分析次数,具有较高的效率与稳健性。     

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito–Taylor’s discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations.     

Optimum design of stochastically excited non‐linear dynamic systems without geometric constraints

This paper presents an efficient procedure for min–max dynamic response optimization of stochastically excited non‐linear systems with multiple time‐delayed inputs. This procedure employs a stochastic linearization technique to overcome system non‐linearity and an auto‐covariance analysis technique to represent the original stochastic mechanical model in a suitable form for optimization. Special attention is given to the sensitivity analysis, due to the complex nature of the problem. Therefore, exact expressions are obtained in a simple form for the evaluation of the required gradients, which greatly improve the stability and efficiency of the optimization algorithm. The numerical results and performance are presented by means of solving two min–max dynamic response optimization problems. Copyright © 2002 John Wiley & Sons, Ltd.     

Metrology of Virtual Systems

An analysis is made of the system principles of the metrological assurance of the design of virtual systems, namely systems with artificial intelligence elements. A structural stochastic approximation principle enables the considerable a priori uncertainty to be overcome and provides high metrological indicators for the rate of adaptation, reliability, and stability of the results.     

A Stochastic EM Algorithm for Progressively Censored Data Analysis

Progressive censoring technique is useful in lifetime data analysis. Simple approaches to progressive data analysis are crucial for its widespread adoption by reliability engineers. This study develops an efficient yet easy‐to‐implement framework for analyzing progressively censored data by making use of the stochastic EM algorithm. On the basis of this framework, we develop specific stochastic EM procedures for several popular lifetime models. These procedures are shown to be very simple. We then demonstrate the applicability and efficiency of the stochastic EM algorithm by a fatigue life data set with proper modification and by a progressively censored data set from a life test on hard disk drives. Copyright © 2013 John Wiley & Sons, Ltd.     

System reliability analysis of spatial variance frames based on random field and stochastic elastic modulus reduction method

This paper presents the stochastic elastic modulus reduction method for system reliability analysis of spatial variance frames based on the perturbation stochastic finite element method (PSFEM) and the local average of a random field. The stochastic responses and reliability index of each element of a structural frame are characterized by the PSFEM and the first-order second-moment method, to properly handle the correlation structures and scale of fluctuation of random fields. A strategy of elastic modulus adjustment for the estimation of system reliability is developed to determine the range and magnitude of elastic modulus reduction, by taking the element reliability index as a governing parameter. The collapse mechanism and system reliability index of a stochastic framed structure are determined through iterative computations of the PSFEM. Compared with the failure mode approaches in traditional system reliability analysis, the proposed method avoids two major difficulties, namely the identification of significant failure modes and estimation of the joint probability of failure modes. The influences of the correlation structure and scale of fluctuation of the random field upon system reliability are investigated to demonstrate the accuracy and computational efficiency of the proposed methodology in system reliability analysis of spatial variance frames.