Reliability Analysis Of Systems Research Articles

Application of picture fuzzy set theory to reliability and risk analysis of complex industrial systems

Application of picture fuzzy set theory to reliability and risk analysis of complex industrial systems

System reliability analysis of geogrid reinforced retaining wall using random finite element method

Stabilizing earthwalls is extremely important in geotechnical engineering projects and has become an integral part of transportation infrastructures. Meanwhile, geogrid reinforced retaining walls have been the attention of designers due to their advantages. On the other hand, the soil heterogeneity and the requirement of investigating the internal (geogrid rupture and geogrid pullout) and external (global and lateral displacement) stability modes of these structures have necessitated performing system reliability analysis. In this study, finite element in conjunction with random fields is used to evaluate the reliability of these walls. For this purpose, a finite element program is coded in MATLAB to obtain internal and external safety factors considering staged construction. The deterministic program is extended to a stochastic framework to account for spatial variability of soil parameters in retained backfill, foundation soil, and reinforced fill. In the last part of this study, reliability indices of stability modes are calculated to obtain the series system reliability index, utilizing the Sequential Compounding Method (SCM). The results indicated that the effect of soil heterogeneity is more significant on internal stability modes compared to external stability modes especially geogrid pullout. The results of the system reliability analysis demonstrated more critical conditions thus the reliability index of the system was less than the reliability index of individual components.

A Curved Surface Integral Method for Reliability Analysis of Multiple Failure Modes System with Non-Overlapping Failure Domains

Abstract In the study of reliability of systems with multiple failure modes, approximations can be obtained by calculating the probability of failure for each state function. The first-order reliability method and the second-order reliability method are effective, but they may introduce significant errors when dealing with certain nonlinear situations. Simulation methods such as line sampling method and response surface method can solve implicit function problems, but the large amount of calculation results in low efficiency. The curved surface integral method (CSI) has good accuracy in dealing with nonlinear problems. Therefore, a system reliability analysis method (CSIMMS) is proposed on the basis of CSI for solving multiple failure modes system reliability problems with non-overlapping failure domains. The order of magnitude of the failure probability is evaluated based on the reliability index and the degree of nonlinearity, ignoring the influence of low order of magnitude failure modes, and reducing the calculation of the system failure probability. Finally, CSIMMS and other methods are compared by three numerical examples, and the results show the stability and accuracy of the proposed method.

Multi-fidelity wavelet neural operator surrogate model for time-independent and time-dependent reliability analysis

Operator learning frameworks have recently emerged as an effective scientific machine learning tool for learning complex nonlinear operators of differential equations. Since neural operators learn an infinite-dimensional functional mapping, it is useful in applications requiring rapid prediction of solutions for a wide range of input functions. A task of a similar nature arises in many applications of uncertainty quantification, including reliability estimation and design under uncertainty, each of which demands thousands of samples subjected to a wide range of possible input conditions, an aspect to which neural operators are specialized. Although the neural operators are capable of learning complex nonlinear solution operators, they require an extensive amount of data for successful training. Unlike the applications in computer vision, the computational complexity of the numerical simulations and the cost of physical experiments contributing to the synthetic and real training data compromise the performance of the trained neural operator model, thereby directly impacting the accuracy of uncertainty quantification results. We aim to alleviate the data bottleneck by using multi-fidelity learning in neural operators, where a neural operator is trained by using a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. We propose the multi-fidelity wavelet neural operator, capable of learning solution operators from a multi-fidelity dataset, for efficient and effective data-driven reliability analysis of dynamical systems. We illustrate the performance of the proposed framework on bi-fidelity data simulated on coarse and refined grids for spatial and spatiotemporal systems.

A novel LSTM-integrated non-intrusive ROM for reliability analysis of hysteretic systems with large stochastic dimension

Failure probability estimation of hysteretic systems subjected to random process excitation appears in many practical engineering applications, such as structures subjected to earthquake and vibration control. This task is computationally challenging due to the need for repeated solutions of a high-resolution model. This cost grows significantly with the stochastic dimension — characterized by the number of random variables, in this case, arising from the discretization of the random excitation. To address this issue, a novel non-intrusive reduced order model (ROM) is proposed in this paper. Accordingly, the complexity due to spatial discretization is first reduced using proper orthogonal decomposition. However, interpolation among response time histories in the resulting reduced solution space is computationally infeasible due to large stochastic dimensionality. An existing ROM developed by the authors is now improved by adopting a long short-term memory (LSTM) network for this interpolation. Furthermore, this adoption required two additional modifications in the mathematical structure of the ROM related to data compression and nonlinear coupling. The proposed methodology can be seamlessly integrated with black-box nonlinear solvers. Through detailed numerical studies on a beam on Winkler foundation and a multi-storied building frame subjected to stationary and non-stationary excitations, the proposed ROM is found to be accurate, efficient, and robust with respect to the frequency band of interest. The ROM has shown reduction of two orders of magnitude in the computational time. Furthermore, the proposed ROM is inherently parallelizable and holds promise to be scaled to other types of nonlinear systems with large stochastic dimensionality.

Reliability analysis of multiple repairable systems under imperfect repair and unobserved heterogeneity

AbstractImperfect repairs (IRs) are widely applicable in reliability engineering since most equipment is not completely replaced after failure. In this sense, it is necessary to develop methodologies that can describe failure processes and predict the reliability of systems under this type of repair. One of the challenges in this context is to establish reliability models for multiple repairable systems considering unobserved heterogeneity associated with systems failure times and their failure intensity after performing IRs. Thus, in this work, frailty models are proposed to identify unobserved heterogeneity in these failure processes. In this context, we consider the arithmetic reduction of age (ARA) and arithmetic reduction of intensity (ARI) classes of IR models, with constant repair efficiency and a power‐law process distribution to model failure times and a univariate Gamma distributed frailty by all systems failure times. Classical inferential methods are used to estimate the parameters and reliability predictors of systems under IRs. An extensive simulation study is carried out under different scenarios to investigate the suitability of the models and the asymptotic consistency and efficiency properties of the maximum likelihood estimators. Finally, we illustrate the practical relevance of the proposed models on two real data sets.

The Reliability and Availability Analysis of a Single-Unit System under the Influence of Random Shocks and the Variation in Demand from Production with Erlang Distribution

This study evaluates the reliability measures for a system consisting of a single unit that is subject to random shocks at random times with mismatches between demand and production. The system may sometimes be subject to random shocks leading to a system failure with probability p. The system may also fail completely for various reasons other than shocks. The unit is serviced by a technician if it is affected by a shock. However, the system may fail during operation for various other reasons, such as a programming error, human error, operational continuity and stress, and weather conditions. A single technician immediately repairs or maintains the failed unit. The system is in an operational state when there is demand or in an idle state when there is no demand. The distributions of all times in this system follow a negative exponential, while the time to repair follows a two-stage Erlang distribution. The expressions for the reliability metrics are obtained as functions of time using the Laplace transform and the supplementary variables technique. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, the efficiency of the system is illustrated using numerical examples.

Precise Modeling and Analysis of Aviation Power System Reliability via the Aviation Power System Reliability Probability Network Model

This study addresses the challenges of accurately analyzing the reliability of aviation power systems (APS) using traditional models by introducing the Aviation Power System Reliability Probability Network Model (APS-RPNM). The model directly transforms the system architecture into an equivalent probability network, aiming to develop a precise reliability model that captures system functions and fault logic. By classifying APS components into five distinct structural patterns and mapping them to corresponding nodes in the APS-RPNM, the model is successfully constructed. Specifically, None-Input-to-Multiple-Output components are transformed into two-state nodes, while Multiple-Input-to-None-Output, Single-Input-to-Multiple-Output, and Multiple-Input-to-Single-Output components are mapped to three-state nodes. For Multiple-Input-to-Multiple-Output components, a novel approach employing multiple two-state sub-nodes is adopted to capture their complex functional logic. A case study comparing the performance of the APS-RPNM with the traditional minimal path set method in reliability analysis was conducted. The results demonstrate that the APS-RPNM not only simplifies the model construction process and eliminates errors stemming from subjective engineering judgments but also enables the efficient computation of power supply reliability for all load points in a single inference by integrating all of the components. This significantly improves computational efficiency and system dependency analysis capabilities, highlighting the APS-RPNM’s tremendous potential in optimizing the reliability design of APS.

Unsaturated soil nailing wall system reliability analysis using random finite element

This study focuses on the evaluation of stability for a typical unsaturated Soil Nailing Wall System (SNWS), considering variations in soil shear strength, suction, and elasticity modulus. The Random Finite Element Method (RFEM) is employed to derive the reliability indices for stability modes, including Global Stability (GS), Lateral Displacement Stability (LDS), Tensile Strength Stability (TSS), and Pullout Resistance Stability (PRS), which serve as essential components of the SNWS. Finally, the Sequential Compounding Method (SCM) is utilized to combine these modes of stability and their direct influence on the system reliability index. The results show although the maximum Coefficient of Variation (COV) of the soil parameters was 11%, the COV of lateral displacements at the top of the wall was obtained as 19%, which shows the significant influence of considering the soil heterogeneity. Furthermore, uncertainties of elasticity modulus and matric suction lead to an increase in GS, LDS, and PRS. The calculated system reliability index was found to be lower than the lowest reliability index of the individual components. The findings indicate that while the inclusion of matric suction and elasticity modulus may enhance the mean values of stability modes, there is a possibility that the system reliability index could decrease.

The system reliability of steel trusses with correlated variables

The paper focuses on the system reliability of steel trusses with correlated variables. The correlation between bearing capacities of bars was considered. Two static truss schemes were considered. Nodal forces were the only load. The Finite Element Method analysis was conducted in Robot Structural Analysis program. To conduct system reliability analysis it is essential to find cut-sets, it was realized by stiffness matrix spectral analysis. Then reliability analysis was performed in Sysrel module of Strurel computing environment. First Order Reliability Method was used as the base, Subset Simulation method was used to check the correctness of the results. The sensitivity analysis of reliability index enabled the authors to draw conclusions, which variables have the greatest influence on the reliability of the structure. The effects of actions and bearing capacities were assumed to be the only random variables and that the excessing the bearing capacities of bars is the only way the structure can get into failure area.

Investigating the Reliability of an Existing Top Angle and Seat Pad Semi-Rigid Connection System Using Advanced Modelling Techniques

The investigation introduces an advanced model procedure for evaluating the structural reliability of semi-rigid frame connections in existing aged buildings. Specifically, the focus is on the top angle and seat pad (TA–SP) semi-rigid connection, which was not initially considered in the current design standards. The approach employs a plastic hinge model to predict the ultimate strength of the connection and its beam-to-column behaviour. In order to increase computational efficiency, the investigation leverages the nonlinear behaviour of the finite element (FE) model to validate critical parameters. The statistical properties of the existing connection were obtained based on past experimental data, highlighting the weakest elements in the system. The first-order and second-order reliability methods and Monte Carlo simulations were employed to estimate the reliability index. Percentile errors were assessed to understand their impact on higher-order interactions. This new technique of identification quantifies the probability of the system failure interactions. Notably, a 45% lesser error aligns with the target reliability index, while a 114.5% larger error indicates a significant deviation from actual failure probability values. Each methodology introduced adheres to the current standard, and the system reliability analysis provides a vigorous conclusions scheme framework for assessing the existing TA–SP semi-rigid connection.

Reliability‐based resilience assessment method for mooring systems under mooring failure

AbstractOffshore floating structures rely heavily on their mooring systems, which can be disrupted by various events during long‐term operation. These could lead to a mooring failure, affecting the usual operations of the structure or even causing more severe hazards. Resilience provides a comprehensive evaluation of how the mooring system performs after a disaster, which is key to optimizing the structural design and operational safety. In this paper, we develop a general and user‐friendly method to quantitatively assess the resilience of mooring systems under mooring failure. We use the reliability index to represent the performance of the mooring system. We then derive its RV, ACI, and RCI, which are based on a system performance curve and reliability analysis. We also consider the effects of climate change and the corrosion of the mooring chain. These factors can significantly affect environmental loads, structural performance, and the recovery process. Moreover, an illustrative example is provided that guides us through the methodology. The proposed method is applied to assess the resilience of a certain mooring system in the South China Sea over a 30‐year service life under different failure scenarios. Our results indicate that overlooking climate change in the design and operation of the mooring system can lead to a significant overestimation of its reliability index and resilience value.

Statistical reliability analysis of marine systems with varied levels of redundancy

In designing autonomous vessels for long-duration independent operation, maintaining the performance of machinery systems without human intervention is a key challenge. Designers are faced with a range of potential system architecture choices but have little guidance on which will be optimal. Working only with high-reliability components can increase the probability of completing a voyage successfully, though the availability of such components may be limited. Alternatively, designers can select a redundant architecture to provide options for reconfiguration if a component fails during a voyage, such architectures typically have weight, space, and cost implications. This work presents a parametric exploration of the probability of system failures over time under different architectures. The reliability of individual components is expressed through exponential probability distributions and the weight of each component is approximated. Two systems are presented and the effectiveness of various architectures for both systems is compared. A simple design penalty function is also tracked to capture the different architectures’ weight and implication number of components. From this study optimal architectures for long-term autonomous missions are proposed.

Cost optimization and reliability analysis of fault tolerant system with service interruption and reboot

Due to widespread usage in many real time systems, reliability modeling and cost optimization of fault tolerance system have drawn attention of the practitioners. The fault tolerance in these systems can be provided by the support of maintenance and redundant components that help in smooth operation of the system in spite of failure of some active components. This investigation deals with the performance modeling of a fault-tolerant system consisting of a finite number of active (online) and standby components. During the switching from active to standby, the recovery procedure is performed, which may be imperfect. In case of imperfect recovery, the system reboot takes place. The maintenance of all the components is managed by a repairman (server) which is subject to failure. When the server is interrupted for rendering the service, functioning does not get stopped due to the system switch-over from perfect working to working breakdown mode. The system works even when the server is on working vacation and performs repair jobs of the failed components. The machine repair model based on Markovian process is developed to derive the transient probabilities and other performance indices of the fault tolerant system using Laplace transforms and matrix analytical method. Using the direct search strategy and particle swarm optimization, the cost-benefit analysis is done. The optimal design of the control parameters for the fault-tolerant system are presented by framing a cost-effective ratio function. The model is examined computationally by performing the numerical simulation and cost optimization.

A reliability analysis method for fuzzy multi-state system with common cause failure based on improved the weakest T-norm

Recently, the reliability analysis of complex engineering systems has been confronted with a range of challenges, including fuzziness, multiple states, and common cause failures. In particular, factors such as changes in the working environment and human error contribute to the fuzzy probability value for each state in the system, which brings great challenges to its reliability analysis. In this paper, a new reliability analysis method for fuzzy multi-state system with common cause failure is proposed, which developed the fault tree analysis method and fuzzy set theory. First, a model integrating common cause failure with fuzzy T-S fault tree analysis model has been illustrated, and the equivalent model is given. Meanwhile, a novel fuzzy arithmetic method based on the weakest n-dimension T-norm is designed to solve the proposed model. Finally, the aircraft power system is analyzed as an example to verify the effectiveness of the proposed method. The result shows that the proposed method effectively enhances the capacity of failure tree analysis in assessing the reliability of complex systems characterized by multiple states, fuzziness, and common cause failures.

Composite reliability analysis of electric power systems considering climatic and spatial conditions using self-organizing map

This article presents an innovative approach by integrating different models that represent the failure rates of components related to weather events, considering the geographic location and its variation over time, to a customized Monte Carlo simulation model to ensure the draw synchronized with the load and generation curves, and then quantify the impact of these events through the power flow. The study focuses on using a neural network is trained to classify/filter system states in order to reduce the need for electrical studies and speed up the reliability assessment process. The approach is demonstrated with reference to the IEEE-RTS network test case. The results obtained indicate that the inclusion of renewable sources and climatic conditions have a significant impact on reliability indicators, as failure rates subject to these meteorological conditions tend to increase, providing a greater risk of simultaneous shutdowns, and contributing to the worsening of the system severity index. Therefore, the proposed model allows for a faster and more realistic reliability assessment, directing the planning of expansions and reinforcements and allowing risk monitoring during system operation.

System reliability analysis of Cable-stayed bridge using pair Copula and ICLHS with unequal weights under seismic loading

Considering the correlation between different components, quantifying the failure probability of a high-level hyper-static structure under non-stationary seismic loading is of great significance in guiding earthquake-resistant design and fortification of bridges. In this study, a high-pier and large-span railway cable-stayed bridge in the mountainous region were employed to evaluate the seismic performance. First, the basic theoretical methods of the non-stationary random seismic motion simulation, equivalent extreme value theory based on extreme value distribution (EVD), improved Latin hypercube sampling (ICLHS) with unequal weighted fractional moment estimation and Pair Copula technique are presented. Second, the finite element analysis model of the cable-stayed bridge was established based on the OpenSees platform, the seismic response samples of the bridge were calculated under three levels of seismic ground motion to determine the first passage failure probability of the main components of the bridge under the design failure modes. Finally, the Pair Copula function was introduced to estimate the seismic system reliability of the cable-stayed bridge. The optimal Copula type that can describe the correlation between the bridge components was selected through goodness-of-fit tests such as AIC, BIC, and the minimum distance method. The failure probability of the entire system was obtained by calculating the selected Copula function type under seismic loading.

Editor's Note for article entitled “Reliability analysis of battery energy storage system for various stationary applications”

Editor's Note for article entitled “Reliability analysis of battery energy storage system for various stationary applications”

Response and reliability analysis of a nonlinear VEH systems with FOPID controller by improved stochastic averaging method and LBFNN algorithm

In engineering, it is an important issue to guarantee the normal working of a vibration energy harvesting (VEH) device to harvest electricity. However, the determination of the system dynamics is a huge challenge due to random excitation, nonlinear structure, and control force. This paper aims to study the response and reliability of a kind of nonlinear and coupled VEH system with an FOPID controller. The stationary response is analyzed by an improved stochastic averaging method, in which an amplitude-dependent frequency is taken into account during the averaging procedure in the case of the strongly nonlinear system. Time-varying reliability in the VEH system is analyzed by using a new LBFNN algorithm, and weight coefficients at each time in this algorithm is obtained through an iteration procedure. Numerical results show that there are essential differences between the weakly nonlinear system and the strongly nonlinear one in terms of averaging procedure and response probability. The fractional orders in the FOPID controller are critical parameters to bring stochastic bifurcations. In addition, strongly nonlinear structure together with lower-order fractional derivative and higher-order fractional integration in FOPID controller are helpful to enhance the reliability performance of the VEH system.

System reliability modeling and analysis for a marine power equipment operating in a discrete‐time dynamic environment

AbstractExploring on reliability modeling and analysis on a marine equipment in a dynamic environment is a meaningful and challenging issue, because the system commonly carries out the task at sea away from land and suffers a distinct influence of environment. Thus, a reliability model of a multi‐state repairable system operating in dynamic environment is developed by introducing the background of the marine power system in this paper. The novelty of the research lies in the modeling and computing methods are relatively innovative by employing the aggregated stochastic processes, Hadamard production and matrix‐analytic method. First, the working modes of the marine power system under several different kinds of conditions are introduced. Then, the evolution of both the system states and environment are described as discrete‐time Markov chains with multiple and different transition probability matrices. The failure probability and repair probability of components are also distinct in different environments. Furthermore, some performance indexes, especially the index relevant to the environment, are derived, respectively. Finally, the conclusion is obtained by a numerical example of the marine power system, which also illustrates the validity and applicability of the proposed model.