AK-SYSi: an improved adaptive Kriging model for system reliability analysis with multiple failure modes by a refined U learning function

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.

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.

PLIC-FSR-SYS: System reliability analysis based on parallel learning of influential components with filtered sample region

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.

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.

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

Despite the substantive literature on remaining useful life (RUL) prediction, less attention is paid to the influence of epistemic uncertainty and aleatory uncertainty in multiple failure behaviors in the accuracy of RUL. The research question in this study was: can uncertainties be quantified in predicting the RUL of systems with multiple failure modes? The first objective was to quantify the uncertainties in the prediction of RUL, considering known multiple failure modes. This objective used vibration data from accelerated degradation experiments of rolling element bearings. The second objective was to calculate the uncertainties in the prediction of RUL, considering the multiple failure modes as unknown. The experimental data used in this objective were from run-to-failure tests of Li-ion batteries. An analysis was performed on how the uncertainties affect the RUL prediction in systems with known multiple failure modes and systems where the multiple failure modes were unknown. A Bayesian neural network (BNN) was used to quantify epistemic and aleatory uncertainty while predicting RUL. The results of the qualitative uncertainties on RUL in systems with multiple failure modes were presented and discussed. Also, the study yielded an RUL uncertainty quantification model for multiple failure modes. The proposed framework's performance in the RUL prediction was demonstrated. Finally, the epistemic and aleatory uncertainties were quantified in the system's RUL. It was shown that systems that fail due to the same failure mode tend to have similar uncertainty values over time. The results in this paper may lead to the design of more reliable systems that exhibit multiple failure modes.

Multiple failure modes analysis and weighted risk priority number evaluation in FMEA

Taking the main shaft system of hydraulic turbine-generator unit as an object,the nonlinear dynamic equation is established by the finite element method.Based on the equation,the nonlinear vibration characteristics of the system are analyzed and the excitation frequencies of the system are obtained.Considering the randomness of the structure parameters,material parameters,hydraulic parameters and electromagnetic parameters of system,the gradients of natural frequencies to the random parameters are obtained.According to the criterion that the absolute values of difference between the natural frequencies and excitation frequencies of system should be less than specific values,the failure probability with one single failure mode and the combined failure probability with two failure modes are calculated by dividing the variable space into several simple areas.The nonlinear vibration reliability model of the main shaft system of hydraulic turbine-generator units with correlated failure modes is constructed and the method by which the nonlinear vibration reliability of system with multiple failure modes can be analyzed is proposed.An example is presented and the nonlinear vibration reliability model is proved by the Monte Carlo method.

5 - Potential loss from failure for non-repairable components and systems with multiple failure modes

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

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.

In many cases a two-state approach for reliability analysis of systems composed of multiple components is not appropriate. This is so especially when redundancy is applied or when some components have multiple failure modes having non-identical impacts on system performance. For example, consider a redundant rectifier system consisting of two diodes connected in series (Fig. 5.1(a)) and without repair. The diodes might suffer two distinct failure modes: a short-circuit failure D2allowing current to pass in both directions and an open failure D3. Figure 5.1(b) shows the states and the corresponding transitions for a diode. It will be obvious that the system is only redundant to short-circuit failures and that the redundancy is not active for open failures. Even worse, the probability of an open system failure has almost been doubled. This means that the two different failure modes of the diodes have different impacts on system performance and, therefore, cannot be treated as one single failure mode. For this simple system a combinatorial solution is still possible as:R = P r{Da1Db1∪ Da1Db2∪ Da2Db1}, however, the logic expression for system success contains dependent events since the diode states D1and D2are mutually exclusive. In Chapter 7 it is shown how to deal with systems of multistate items more generally while Chapter 8 explains how to perform probability calculations on large logical expressions with dependent events.

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.

This paper proposes a reliability analysis framework for glass fiber-reinforced polymer- (GFRP-) reinforced concrete systems with uncertain capacities and demands over time. Unfortunately, there has been limited discussion or research done related to the potential change of failure modes over time. Therefore, a rational approach is needed to integrate multiple failure modes in a single analysis framework, considering uncertainties of time-variant demands and capacities. To account for multiple failure modes, this study proposes the limit state function to estimate the safety margin, based on strain values of GFRP-reinforcing bars. A proposed limit state function can capture the likelihood of both shear and flexural failure modes, simultaneously. In this study, seven typical bridge deck configurations (e.g., varied deck thickness, girder spacing, and bar size) were exposed to various ambient temperatures. Simulation results show that reliability indices of 100-year exposure exhibit significant variance, ranging from 2.35 to 0.93, with exposure temperatures ranging from 13 to 33°C. Exposure temperature and time are the dominant factors influencing the reliability indices, so are the ones that need to be changed. As exposure time and/or exposure temperature increase, the flexural capacity model plays an important role to determine the reliability indices. When flexural and shear failure modes are equally dominant, reliability indices can capture risks of both failures, using the proposed strain-based approach.