Reliability evaluation and importance analysis of structural systems considering dependence of multiple failure modes

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

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

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.

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.

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.

Various random factors in the bridge construction process directly affect the safety of the bridge life cycle. The existing theories on the reliability of bridge structure mainly focus on the reliability of components and the reliability of the bridge structure system in the completion and operation stages, while the research on the reliability of the structure system in the construction stage is relatively lacking. Therefore, this paper proposed using the Copula function to calculate the reliability index of the bridge structure construction process system. The basic theory of the Copula function was introduced in detail, and the formula was improved according to the actual situation of bridge construction. Finally, the sensitivity analysis of bridge system reliability was carried out. The research results showed that the method proposed in this paper based on Copula theory to calculate the reliability index of the bridge structure construction process system has strong applicability, simple calculation, and can be used in conjunction with the “interval estimation method”, which is suitable for large and complex bridge structural engineering. At the same time, the conclusion that the influence of failure mode correlation on structural reliability should not be ignored in the actual engineering construction process is confirmed.

Complex slopes are characterized by large numbers of failure modes, cut sets or link sets, or by statistical dependence between the failure modes. For such slopes, a systematic quantitative method, or matrix-based system reliability method, was described and improved for their reliability analysis. A construction formula of event vector cE was suggested to solve the difficulty of identifying any component E in sample space, and event vector c of system events can be calculated based on it, then the bounds of system failure probability can be obtained with the given probability information. The improved method was illustrated for four copper mine slopes with multiple failure modes, and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB. Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system. Otherwise, the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.

The concept of system reliability will be described in this chapter. A moment-based method for assessing the system reliability of series and non-series structures is investigated, with emphasis on series systems. The reliability index is directly calculated based on the first few moments of the system performance function of a structure. It requires neither the reliability analysis of the individual failure modes nor the iterative computation of derivatives, the computation of the mutual correlations among the failure modes, and any design points. As a practical topic, the evaluation of system reliability for ductile frame structures using methods of moment is introduced in the final part of this chapter. The difficulty in both failure mode identification and failure probability computation is still hard to overcome when using the traditional method for the system reliability assessment of ductile frame structures. To avoid the difficulties, a failure mode independent performance function with weak non-normality is introduced. The method of moments is then utilized to estimate the failure probability of ductile frame structures corresponding to the general performance function. From the numerical examples, it can be concluded that the introduced methodology successfully overcomes the two difficulties including the identification of significant failure modes and the computation of overall failure probabilities contributed from these significant modes in system reliability evaluation of ductile frame structures.

Many large complex equipment, such as spacecraft and satellite, are typical Phased Mission Systems (PMSs). Due to sophisticated structure and complex missions, the components and systems of PMS have multiple failure modes which are correlated. On the one hand, taking multiple correlated failure modes in to consideration can describe the multistate characteristics of the system more accurately and decouple the correlation between different phases of the system more clearly. On the other hand, its complexity makes the reliability evaluation of PMS more difficult. To solve this problem, this paper discusses the modeling method of multiple failure modes and their correlation, proposes an improved combination method of Multiple Failure Mode Tree (MFMT) and Multistate and Multivalued Decision Diagram (MMDD) model, and realizes the reliability evaluation of PMS in cross‐level (failure mode‐component‐system) and cross‐scale (single phase‐multiple phases). Finally, the proposed method is applied to evaluate the reliability of the satellite attitude orbit control system (AOCS) in order to verify its feasibility.

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.

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.

Electro-Mechanical Actuator (EMA) is a key component in the flight control actuation of the more electric aircraft. The degradation of EMA has a significant influence on its performance. Hence, the degradation estimation of EMA needs to be studied, which is an important part of the health monitoring of EMA. However, the multiple failure modes of EMA bring much difficulty for implementing degradation estimation. To solve this problem, a fusion degradation estimation method based on Continuous Hidden Markov Model (CHMM) and Generalized Linear Model (GLM) (i.e., Multiple CHMM-GLM) is proposed for EMA with multiple failure modes. Firstly, Health Indicator (HI) extraction models are formulated based on CHMM for multiple failure modes to extract HIs, which can be used to indicate the degradation degree of EMA. Secondly, the fusion degradation model for EMA with multiple failure modes is formulated based on the extracted HIs and GLM, in which the nonlinearity of a single HI and the coupling among multiple HIs are both considered. Finally, the output of the fusion degradation model is regarded as a HI to indicate the degradation degree of EMA. This study provides a new way for the degradation estimation of EMA with multiple failure modes, which can contribute to the Prognostics and Health Management (PHM) development of EMA. To evaluate the effectiveness of the proposed method, experiments are conducted utilizing EMA simulation and practical data. Experimental results show that the proposed method has a good performance in the degradation estimation for EMA with multiple failure modes.

Due to multiple implicit limit state functions needed to be surrogated, adaptive Kriging model for system reliability analysis with multiple failure modes meets a big challenge in accuracy and efficiency. In order to improve the accuracy of adaptive Kriging meta-model in system reliability analysis, this paper mainly proposes an improved AK-SYS by using a refined U learning function. The improved AK-SYS updates the Kriging meta-model from the most easily identifiable failure mode among the multiple failure modes, and this strategy can avoid identifying the minimum mode or the maximum mode by the initial and the in-process Kriging meta-models and eliminate the corresponding inaccuracy propagating to the final result. By analyzing three case studies, the effectiveness and the accuracy of the proposed refined U learning function are verified.

In an aircraft, the lock mechanism is one of the important components of the landing gear door lock system, whose working performance affects the aircraft flight performance directly. This research focuses on reliability assessment and reliability improvement of the locking process of an aircraft lock mechanism. First, according to the motion principle of the aircraft lock mechanism, a simulation model of the locking process is built by LMS Virtual.Lab simulation platform. Then, two performance functions of the two critical failure modes of the locking process about maximum locking resistance and required time are established, respectively. Subsequently, Kriging model and importance sampling method are combined to evaluate the reliability of the locking process. Finally, the reliability sensitivity is analyzed to identify critical variables which influence the reliability. Three cases are analyzed by adjusting the parameters of the two most critical variables, and the results show that the system reliability and the reliability of each failure mode are improved during the locking process of the aircraft lock mechanism.

With the incomplete probability information, the joint probability distribution modelling and system reliability-based optimization design of structural systems with failure interactions are challenging problems in the domain of reliability. This article is designed to propose a system reliability-based optimization design method for optimizing the scraper chain with multiple failure modes. Firstly, the common failure modes of the scraper chain are analysed. For each failure mode, a reliability model for the failure of scraper chains is obtained. Secondly, aiming at the joint failure probability modelling problem, a method for estimating the failure probability of the scraper chain based on system reliability is proposed. The reliability of scraper chains is calculated by the stochastic perturbation technique and the four-moment method. And then, the optimization design problem is discussed based on system reliability. And the optimal model is established. Finally, the effectiveness of the method is verified by the illustrative example of scraper chains. The proposed joint failure probability estimation method and design optimization are shown in the example. The results obtained can provide a reference for the optimal design of the scraper chain.