Failure-mode importance measures in structural system with multiple failure modes and its estimation using copula

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.

Many modern structural systems usually consist of multiple failure modes. One failure mode may affect other failure modes due to the same working environment and random input variables, meaning that these failure modes are not independent. The assumption of independence among failure modes simplifies the calculation of reliability of structural systems, but it adds approximation error. Different from the dependence between two failure modes, the dependence of multiple failure modes is more complicated. In this paper, on the basis of vine copula function, which is a flexible tool to describe the multivariate dependence, the dependence of multiple failure modes of the structural systems is mainly studied and analyzed. Then Rosenblatt transformation and Monte Carlo simulation method are utilized to evaluate the reliability of structural systems. Furthermore, in order to research the importance of failure modes, two indices combined with empirical copula functions are extended, which can quantitatively measure the importance of failure modes. The multiple failure modes can be ranked based on proposed importance analysis, and the ones that have greater influence on the system can be found out, thus simplifying the system analysis. Finally, in order to confirm the applicability and rationality of the proposed method, an engineering case about a mechanism system with five failure modes is presented.

Studies on the theory of structural system reliability includes identifi- cation of main the failure modes and calculation of inclusive failure probabilities for the structural system. The efficient and accurate identification of failure modes in structural systems is difficult and represents a key focus for research in sys- tem reliability. The fundamental theory of the branch and bound algorithm for stage critical strength is reviewed in this paper. Some deficiencies in this method are highlighted. Corresponding approaches to overcome these deficiencies are pro- posed. Calculated system reliability solutions to the classical model, a truss with 10 elements, indicate that the improvement measures proposed in this paper increase the efficiency of recognising the main failure modes of the structural system, and are readily validated. The outcomes of this type of benchmark analysis suggest that the proposed methodology may be capable of representing a suitable basis for the structural system reliability analysis of complex truss-like structures, includ- ing transmission towers. Using the proposed approach, the principal failure modes and system reliability of a transmission tower are calculated. Based on practical engineering considerations, effective methods to improve this structural system re- liability are proposed.

Markov models are commonly used for unavailability analysis of redundant systems. However, due to the exploding states of Markov models for redundant systems, the states need to be merged to simplify the computation, which is called micro-Markov models. However, how to derive the failure rates and repair rates of the newly developed micro-Markov models has not been studied thoroughly. Therefore, this paper proposes detailed explanations and rules to derive the static unavailability by the micro-Markov models for thek-out-of-n:G systems with multiple failure modes. Firstly, two properties about applying the Markov models to the repairable system with independent multiple failure modes are presented. Based on these two properties, two rules are proposed for implementing the micro-Markov models. The micro-Markov models provide the exact same results for the repairablek-out-of-n:G system with multiple independent failure modes and repair mechanisms and approximate results for systems with multiple hybrid failure modes. A case study of safety integrity verification for safety instrumented systems is provided to illustrate the application of the proposed method. The conceptual comparison and numerical examples demonstrate the reasonability and usefulness of the proposed micro-Markov models.

Dominant mechanisms in stochastic plastic frames

Probabilistic Risk Assessment of RCC Dam Considering Grey-Stochastic-Fuzzy Uncertainty

An equivalent linear method for structural system reliability with nonlinear safety margins

The numerical determination of the multinormal integral is required in many problems of statistics and, recently, turned out to be a key problem in structural and operational system reliability [1,2]. For example, the analysis of multi-component systems with multiple failure modes (series — or weakest-link systems) requires the evaluation of the probability of a union of failure events. If equivalent hyperplanes [3] in the so-called standard normal space [4] which represent the modal and/or componental failure sets of the system can be produced, e.g. by FORM/SORM methods, the union probability can be computed as a multinormal integral. As another example the quantification of the redundancy in a system in a probabilistic sense requires the evaluation of intersection probabilities [5,6]. Again, this problem can be reduced to the computation of a multinormal integral if the boundaries of the failure sets can be linearised appropriately. Even if asymptotic second-order approximations of the failure surfaces are used, the evaluation of multinormal integrals is part of the solution to general intersection probabilities [2,7].

Portable electronic products subjected to transient shock may exhibit multiple failure modes in vicinity of the interconnects. Failure is often diagnosed by loss of functionality using techniques including the built-in self test, which provides limited insight into reliability and remaining useful life. In this paper prognostic framework for electronic systems has been developed with neural network based self organizing maps. The presented approach resides in the pre-failure space with a focus on electronic systems with multiple failure modes. Unsupervised learning of the neural net has been used to train the neural net for identification of individual failure modes. Feature vectors have been developed based on damage pre-cursors from time-spectral measurements. The clustered damage pre-cursors have been correlated with failure modes of the underlying damage. Several chip-scale packages have been studied, with leadfree second-level interconnects including SAC305, SAC405 alloys. Transient strain has been measured during the drop-event using digital image correlation and high-speed cameras operating at 100,000 fps. Continuity has been monitored simultaneously for failure identification. In addition, explicit finite element models have been developed and various kinds of failure modes have been simulated such as solder ball cracking, trace fracture, package falloff and solder ball failure. Fault modes predicted by simulation based pre-cursors have been correlated with those from experimental data. Activation of different neurons in the lattice for various failure modes and combinations of failure modes has been demonstrated. Previously the authors have developed techniques based on statistical pattern recognition for leading indication of impending failure and detection of damage initiation and progression [Lall 2006 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> , 2007 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> , 2008]. Early classification of multiple failure modes in the pre-failure space is new.

The present paper studies the reliability-based structural optimization of the civil engineering in the seismic zone. The objective is to minimize the sum of construction material cost and the expected failure loss under severe earthquake, which is obtained by the sum of the products of the failure probability and its failure losses for the important failure modes. The set of constraints includes the deterministic constraints, and the constraints based on structural reliability—the reliability index constraints of structural element failure for the serviceability state under minor earthquake and the failure probability of the structural system for the ultimate limit state under severe earthquake. By introducing the load roughness index, the structural system reliability computation under hazard load can be greatly simplified, which is approximately determined by its weakest failure mode. Finally, the numerical example of high rising shear RC frame is calculated.

Over the last four decades, structural system reliability (SSR) has been an active research topic as engineering systems including structures and infrastructure networks become more complex, and the computational power has been remarkably advanced. Among many efforts to advance SSR technologies, the research by Prof. Armen Der Kiureghian in the early 2000s is considered to have built critical pathways to the development of next-generation SSR methods by revisiting the topic of SSR. As demonstrated in Der Kiureghian (Structural system reliability, revisited. Proceedings, 3rd ASRANet International Colloquium, Glasgow, UK, July 10-12, 2006), his research efforts led to new insights and perspectives on critical topics of structural system reliability. This has encouraged researchers to perform a variety of research activities to develop new SSR technologies that can address challenges and needs in risk management of real-world systems. This chapter provides a review on such efforts to reload the research community with SSR technologies, which were made possible by the revisit. The chapter reviews the following SSR methods: linear programming bounds, matrix-based system reliability method, sequential compounding method, cross-entropy-based adaptive importance sampling, selective recursive decomposition algorithm, branch-and-bound employing system reliability bounds, and genetic-algorithm-based selective search for dominant system failure modes. For each of the reviewed methods, their main concepts, applications and follow-up research activities are presented along with discussions on merits, remaining challenges, and future research needs.

Preventive maintenance for heterogeneous parallel systems with two failure modes

Offshore system safety and reliability considering microbial influenced multiple failure modes and their interdependencies

A new method for analyzing the reliability of mechanism is proposed. The proposed method suggests the use of two response surface functions to evaluate the reliability probability. Structural reliability can be calculated through the analysis of the maximum stress and the maximum deformation of crank-rocker mechanism to establish its limit states equations respectively and then ganged sample these response surfaces that is double response surface, structural reliability can be calculated. Aiming at analyzing reliability of mechanical system with multiple components which have multiple failure modes, this method can realize the whole reliability analysis under the consideration of the correlation of these failure modes. The example result indicates that calculation velocity of this method is high; precision of this method is exact. It can be used in other researches and projects.

An anomaly detection and failure mode classification method has been developed for electronic assemblies with multiple failure modes. The presented prognostic health management method targets the pre-failure space of the electronic assembly life to trigger repair or replacement of impending failures. Presently, health monitoring systems focus on reactive diagnostic detection of failure modes. Examples of diagnostic detection include the built in self test and on-board diagnostics. In this paper, damage pre-cursors from time-spectral measurements of the electronic assemblies has been measured under applied vibration and shock stimulus. The time-evolution of spectral content of the damage pre-cursors has been studied using joint time frequency analysis in a full-field manner on the printed circuit assembly. Frequency moments have been used to build a feature vector. Evolution of the feature vector with damage initiation and progression has been studied under shock and vibration. The feature vector from multiple locations in the board assemblies has been mapped into a de-correlated feature space using Sammon’s mapping. Several chip-scale packages have been studied, with SAC305 and SAC405 leadfree second-level interconnects. Transient strain has been measured during the drop-event using digital image correlation and high-speed cameras operating at 100,000 fps. Continuity has been monitored simultaneously for failure identification. In addition, explicit finite element models have been developed and various kinds of failure modes have been simulated such as solder ball cracking, trace fracture, package falloff and solder ball failure. The neural net has been trained using simulated data-sets created from error-seeded models with specific failure modes. The neural net has then been used to identify and classify the failure modes in board assemblies experimentally. Supervised learning of multilayer neural net in conjunction with parity has been used to identify the hard-separation boundaries between failure mode clusters in the de-correlated feature space. The assemblies have been cross-sectioned to verify the identified failure modes. Cross-sections indicate that the experimentally measured failures modes correlate well with the position of the cluster in the de-correlated feature space.