Reliability Analysis Of Systems Research Articles

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.

Simulating non-stationary and non-Gaussian cross-correlated fields using multivariate Karhunen–Loève expansion and L-moments-based Hermite polynomial model

In practical engineering, cross-correlated random fields are often used to model structural materials or random loads containing multiple correlations. Effective and accurate simulation of these cross-correlation fields is an important prerequisite for subsequent reliability analysis and uncertainty quantification of complex systems. Therefore, this paper proposes a new simulation method for non-stationary non-Gaussian cross-correlated random fields to satisfy realistic engineering requirements. In this new method, L-moments-based Hermite polynomials model (LHPM) is extended to non-stationary non-Gaussian cross-correlated fields. Then, a transformation model from non-stationary non-Gaussian correlation matrix function (CMF) to the underlying Gaussian CMF is explicitly given. Multivariate K-L expansion is further used to approximate the underlying Gaussian cross-correlated fields, where the eigenvalue and eigenfunctions are estimated via the Nyström method with uniform weights. The approximation permits the application of few random variables to characterize the entire Gaussian cross-correlated fields. Ultimately, the simulated underlying Gaussian cross-correlated fields are mapped back to the target non-stationary non-Gaussian cross-correlated fields based on LHPM. Three typical examples, including exponential kernel, Wiener process kernel and spatially varying non-Gaussian and nonstationary seismic ground motions, are used to validate the effectiveness of the proposed method. The source code is readily available at: https://github.com/zhaozhao23/Simulation-of-non-stationary-and-non-Gaussian-cross-correlated-fields.

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.

Reliability analysis of diesel engine cooling system based on improved Bayesian network

For the benefit of solving the problem of absoluteness of conditional probability distribution and difficulty in obtaining basic event probability in Bayesian networks, this paper studies the reliability of diesel engine cooling systems through leakage noise or gate intuitionistic fuzzy Bayesian network. Firstly, the leakage noise or gate is introduced into the intuitionistic fuzzy Bayesian network, which makes the results more realistic. Secondly, prior probability in the Bayesian network is obtained based on the similarity aggregation method of triangular intuitionistic fuzzy numbers. The results show that the introduction of leakage noise or gate, intuitionistic fuzzy set, and Bayesian network can solve the problem that the probability of basic events in a Bayesian network is difficult to obtain. The conditional probability table corrected by leakage noise or gate is more realistic and greatly reduces the workload. It is determined that the two weakest components of the cooling system are the thermostat and the water pump. The results show that the way in this paper can provide support for the reliability analysis of the complex system.

Reliability analysis of arbitrary systems based on active learning and global sensitivity analysis

System reliability analysis aims at computing the probability of failure of an engineering system given a set of uncertain inputs and limit state functions. Active-learning solution schemes have been shown to be a viable tool but as of yet they are not as efficient as in the context of component reliability analysis. This is due to some peculiarities of system problems, such as the presence of multiple failure modes and their uneven contribution to failure, or the dependence on the system configuration (e.g., series or parallel). In this work, we propose a novel active learning strategy designed for solving general system reliability problems. This algorithm combines subset simulation and Kriging/PC-Kriging, and relies on an enrichment scheme tailored to specifically address the weaknesses of this class of methods. More specifically, it relies on three components: (i) a new learning function that does not require the specification of the system configuration, (ii) a density-based clustering technique that allows one to automatically detect the different failure modes, and (iii) sensitivity analysis to estimate the contribution of each limit state to system failure so as to select only the most relevant ones for enrichment. The proposed method is validated on two analytical examples and compared against results gathered in the literature. Finally, a complex engineering problem related to power transmission is solved, thereby showcasing the efficiency of the proposed method in a real-case scenario.

A Bayesian network development methodology for fault analysis; case study of the automotive aftertreatment system

This paper proposes a structured methodology for generating a Bayesian network (BN) structure for an engineered system and investigates the impact of integrating engineering analysis with a data-driven methodology for fault analysis. The approach differs from the state of the art by using different initial information to build the BN structure. This method identifies the cause-and-effect relationships in a system by Causal Loop Diagram (CLD) and based on that, builds the Bayesian Network structure for the system. One of the challenges in identifying the root cause for a fault is to determine the way in which the related variable causes the fault. To deal with this challenge, the proposed methodology exploits Dynamic Fault Tree Analysis (DFTA), CLD and the correlation between variables. To demonstrate and evaluate the effectiveness of the presented method, it is implemented on the data-driven methodology applied to the automotive Selective Catalytic Reduction (SCR) system and the obtained results have been compared and discussed. The proposed methodology offers a comprehensive approach to build a BN structure for an engineered system, which can enhance the system's reliability analysis.

An efficient analysis method for system reliability of semi-rigid base asphalt pavement structure based on direct probability integral method

The structural design parameters of asphalt pavement inherently possess randomness. Reliability theory aids in considering the stochastic nature of these parameters in asphalt pavement design. However, as the number of considered random factors increases, the complexity of reliability calculation models and the consumption of computational resources also significantly escalate. To analyze the structural reliability of semi-rigid base asphalt pavements more efficiently and accurately, a method combining Weighted Kernel Density Estimation (Weighted-KDE) with Direct Probability Integration Method (DPIM) using sampling strategies was employed. Furthermore, integrating the equivalent extreme value principle, an asphalt pavement structural system reliability analysis method was proposed, considering multiple failure mode correlations. The numerical solution steps of this method are also outlined. Based on the typical semi-rigid asphalt pavement structure in China, this study utilized the elastic layer system method (the program Apbi) and a computational program developed in MATLAB to compare the efficiency and accuracy of calculating reliability between DPIM and the Monte Carlo Simulations (MCS). The computational outcomes indicate that, under the premise of selecting 18 random parameters, DPIM can achieve the required accuracy in assessing the reliability of asphalt pavement structure and system reliability. Analyzing how the number of samples affects the computational results reveals that using weighted-KDE and DPIM only needs a few hundred sample points to limit the relative error within 4 %, compared to the results obtained from 105 samples in MCS. The research findings demonstrate that DPIM incorporating the principle of equivalent extreme value events can serve as an efficient analytical approach for assessing the system reliability of asphalt pavement structures characterized by more complex failure modes.

Reliability analysis of complex systems using subset simulations with Hamiltonian Neural Networks

We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with computationally efficient gradient evaluations using Hamiltonian neural networks. This combination is especially advantageous because the neural network architecture conserves the Hamiltonian, which defines the acceptance criteria of the Hamiltonian Monte Carlo sampler. Hence, this strategy achieves high acceptance rates at low computational cost. Our approach estimates small failure probabilities using Subset Simulations. However, in low-probability sample regions, the gradient evaluation is particularly challenging. The remarkable accuracy of the proposed strategy is demonstrated on different reliability problems, and its efficiency is compared to the traditional Hamiltonian Monte Carlo method. We note that this approach can reach its limitations for gradient estimations in low-probability regions of complex and high-dimensional distributions. Thus, we propose techniques to improve gradient prediction in these particular situations and enable accurate estimations of the probability of failure. The highlight of this study is the reliability analysis of a system whose parameter distributions must be inferred with Bayesian inference problems. In such a case, the Hamiltonian Monte Carlo method requires a full model evaluation for each gradient evaluation and, therefore, comes at a very high cost. However, using Hamiltonian neural networks in this framework replaces the expensive model evaluation, resulting in tremendous improvements in computational efficiency.

Causal chain event graphs for remedial maintenance.

The analysis of system reliability has often benefited from graphical tools such as fault trees and Bayesian networks. In this article, instead of conventional graphical tools, we apply a probabilistic graphical model called the chain event graph (CEG) to represent the failures and processes of deterioration of a system. The CEG is derived from an event tree and can flexibly represent the unfolding of asymmetric processes. For this application, we need to define a new class of formal intervention we call remedial to model the causal effects of remedial maintenance. This fixes the root causes of a failure and returns the status of the system to as good as new. We demonstrate that the semantics of the CEG are rich enough to express this novel type of intervention. Furthermore, through the bespoke causal algebras, the CEG provides a transparent framework with which to guide and express the rationale behind predictive inferences about the effects of various types of remedial intervention. A backdoor theorem is adapted to apply to these interventions to help discover when a system is only partiallyobserved.

Reliability analysis of intelligent manufacturing systems based on improved FMEA combined with machine learning

Along with the booming of intelligent manufacturing, the reliability management of intelligent manufacturing systems appears to be becoming more significant. Failure mode and effects analysis (FMEA) is a prospective reliability management instrument extensively utilized to manage failure modes of systems, products, processes, and services in various industries. However, the conventional FMEA method has been criticized for its inherent limitations. Machine learning can handle large amounts of data and has merits in reliability analysis and prediction, which can help in failure mode classification and risk management under limited resources. Therefore, this paper devises a method for complex systems based on an improved FMEA model combined with machine learning and applies it to the reliability management of intelligent manufacturing systems. First, the structured network of failure modes is constructed based on the knowledge graph for intelligent manufacturing systems. Then, the grey relation analysis (GRA) is applied to determine the risk prioritization of failure modes. Hereafter, the k-means algorithm in unsupervised machine learning is employed to cluster failure modes into priority classes. Finally, a case study and further comparative analysis are implemented. The results demonstrate that failure modes in system security, production quality, and information integration are high-risk and require more resources for prevention. In addition, recommendations for risk prevention and monitoring of intelligent manufacturing systems were given based on the clustering results. In comparison to the conventional FMEA method, the proposed method can more precisely capture the coupling relationship between the failure modes compared with. This research provides significant support for the reliability and risk management of complex systems such as intelligent manufacturing systems.

Reliability analysis of systems with n-stage shock process and m-stage degradation

As two major types of damage, natural degradation and random shocks usually emerge in a system simultaneously and may exhibit some complex dependencies. An interesting and not negligible phenomenon is that systems at different health levels have differing resistance to these two damage processes. This study presents a multistate model to capture the main characteristics of a system with dependencies of both damage processes on the current damage level. In the case of multistage damage-level dependencies, the proposed model can be seen as an extension of existing multistage models, i.e., a composite model of n-stage shock process and m-stage degradation. The reliability and probability of system states at time t are derived under the framework of the Markov renewal process. We also use a Monte Carlo simulation to mimic the system lifespan and improve the multistate model. Finally, a study case of microelectromechanical systems is provided to demonstrate the application of the proposed methodology.

The effects of gradient index, aspect ratio, porosity, and boundary conditions on the buckling behavior of functionally graded porous beams: A k-out-of-n system reliability analysis

Functionally graded materials are a class of multifunctional materials that exhibit spatial variation in composition and microstructure. This deliberate variation is designed to effectively manage and manipulate changes in thermal, structural, or functional qualities within the material. The current study explores the system reliability of functionally graded porous beams (FGPB) subjected to buckling, focusing on the interplay of gradient index (0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10), aspect ratio (5, 10, 15, 20, 25, 30 and 35), porosity index (0, 0.1 and 0.2) and boundary conditions (simply supported, clamped–clamped and clamped-free), with a particular emphasis on the k-out-of-n system reliability assessment, employing three distinct methods such as Evolutionary, GRG Non-linear, and Lagrangian. The results show the system's sensitivity to changes in distribution parameters, with the Lagrangian method being the most robust and stable. The 10-out-of-12 system reliability analysis demonstrates that aspect ratio and even porosity distribution are reliable, while uneven porosity is not. This study enhances structural reliability analysis in FGPBs, enhancing system reliability considerations and paving the way for further advancements in structural reliability analysis.

System reliability analysis with small failure probability based on relevant vector machine and Meta-IS idea

Structural failure is a complex system problem and traditional methods face difficulties in solving system reliability problems with small failure probability. This paper proposes an efficient sampling simulation method termed SDMI, which integrates metamodel-based importance sampling (Meta-IS) with spherical decomposition (SD). SDMI transforms the failure probability into a product of spherical augmented failure probability and a correction factor. The implementation of SDMI for each component further facilitates the proposition of a system probability classification function. The integration of the relevant vector machine (RVM) leads to the proposal of a more efficient methodology, termed RVM-SDMI. The efficacy and precision of the proposed methods have been validated through four numerical examples and two engineering examples. The results demonstrate that SDMI successfully addresses the convergence challenges inherent in Meta-IS. Moreover, RVM-SDMI exhibits remarkable accuracy and computational efficiency in the system reliability analysis with small failure probabilities.

A novel probabilistic modeling for multilateral random attacks in cyber‐physical system reliability analysis

AbstractCyber‐Physical Systems (CPS) are at the forefront of the intersection between information technology and physical operations, revolutionizing industries such as communication, automation, control, and intelligent transportation. However, evaluating the reliability of CPS, especially in the presence of multilateral random attacks, poses a complex challenge. This paper introduces an inventive probabilistic modeling approach to enhance the analysis of CPS reliability under the influence of multilateral random attacks. We provide an overview of fundamental CPS concepts and their significant role in modern society, followed by a comprehensive exploration of multilateral random attacks. Our novel probabilistic modeling approach is presented as a means to improve the accuracy and robustness of CPS reliability assessments when faced with multilateral random attacks. Numerical experiments and simulations validate the effectiveness of our innovative approach, emphasizing its potential to fortify the reliability of Cyber‐Physical Systems.

Tests for homogeneity of distributions of component lifetimes from Type‐II censored system lifetime data with known system structures

AbstractIn system reliability analysis, researchers are interested in evaluating the characteristics of the lifetime distribution of components in a system based on system lifetime data. In collecting system lifetime data, a censoring scheme is often adopted due to time and budget constraints. In this article, we consider the situation where the system lifetime data from two different coherent systems are subjected to Type‐II right‐censoring, and we are interested in testing the homogeneity of component lifetime distributions based on Type‐II censored system lifetime data with known system structures. Based on the Mann‐Whitney test and empirical likelihood ratio tests developed for testing the homogeneity of component lifetime distributions with complete system lifetime data, we propose different non‐parametric test procedures using the permutation of the unobserved censored system lifetimes. We consider a restricted assumption on the censored lifetimes to reduce the permutations required in the computation. The computational approaches to obtain the critical values of the proposed test procedures are provided using the Monte Carlo method. A practical example is used to illustrate the proposed test procedures. Then, the power performance of the proposed test procedures is evaluated and compared through a Monte Carlo simulation study. The simulation results show that the proposed test procedures provide comparable power performance for Type‐II censored system lifetime data in contrast to the complete sample case under different scenarios. Finally, recommendations based on the simulation results and concluding remarks are provided.

Technological limitations of the Markov method for dependability analysis

Aim. To identify and classify the technical limitations of the Markov method of system dependability analysis, to define their boundaries taking into account the actual feasibility of the method, to show the opportunities of expanding the applicability of the Markov method. The paper examined the limitations associated with the automation of state graph construction and the mathematical solution of the corresponding systems of algebraic and differential equations using software. Methods. An approach is proposed to automatically constructing state graphs of technical systems defined by a structural diagram of dependability, as well as communication networks defined by a structural diagram. The paper examines approaches to reducing the dimension of a state graph that do not reduce the accuracy of dependability indicator calculation. The author also considers ways of reducing the dimensionality of a state graph by means of truncation or merging inoperative states that cause biased calculated dependability values. Results. The actual limits of applicability of the Markov method are shown along with their relevance in the context of modern information technologies. Approaches are shown that expand the applicability of the Markov method for analysing the dependability of large systems. The existing approach to state graph truncation were examined. Approaches to merging inoperative graph states were proposed and investigated (for bias). Conclusion. The approaches discussed in the paper allow extending the applicability of the Markov method of system dependability analysis to systems with a larger number of subsystems.

The probabilistic model for system reliability analysis of a steel plane and spatial trusses

The probabilistic model for system reliability analysis of a steel plane and spatial trusses

Friction-induced vibration reliability and sensitivity analysis of a braking system

In this study, reliability and sensitivity analyses are performed for the behavior of friction-induced vibration based on automotive braking systems. In this paper, a friction-induced vibration model of the braking system is developed using Newton’s second law. The accuracy of the vibration model is verified through experiments. The displacement response of the braking system is theoretically derived by convolution integration. The function of maximum displacement is obtained by solving the stationary point of displacement response. Based on this function, the limit state function of the maximum limit of friction-induced vibration displacement is established, and the reliability and sensitivity of the friction-induced vibration of the braking system are evaluated by using the Mean Value First Order Second Moment (MVFOSM) method. The results show that the reliability of the braking system increases with the increase of the mathematical expectation of the equivalent stiffness and decreases with the increase of the mathematical expectation of the system friction coefficient, normal force, and damping ratio. In addition, the sensitivity of the reliability varies significantly with the mathematical expectation of the system friction coefficient and damping ratio. Therefore, the system friction coefficient and damping ratio are the key parameters for the reliability design of the braking system.

A new method for analysis of marine sustainable energy systems

This paper proposes to utilise a new adaptive kernel density estimation (KDE) methodology based on linear diffusion processes for predicting the probability distribution tails of sea-state parameters. A key conclusion was reached that the proposed new methodology can lead to more accurate prediction results than traditional methods based on fittings to a measured significant wave height data set at National Data Buoy Center station 46014. This proposed methodology was subsequently utilised for deriving an accurate 50-year environmental contour line that was used in the dynamic analysis of a two-body point absorber wave energy converter. After systematically analysing the calculation results, another key conclusion was drawn that it is advantageous to use a more reliable contour line derived using the proposed new methodology for long-term dynamic analysis of wave energy converters. In summary, the proposed new adaptive KDE methodology is recommended to be utilised and to be refined continuously in future research work in the field of long-term reliability analysis of marine sustainable energy systems.

Hybrid response surface method for system reliability analysis of pile-reinforced slopes

To consider the complex soil-structure interaction in a pile-slope system, it is necessary to analyze the performance of pile-slope systems based on a three-dimensional (3D) numerical model. Reliability analysis of a pile-slope system based on 3D numerical modeling is very challenging because it is computationally expensive and the performance function of the pile failure mode is only defined in the safe domain of soil stability. In this paper, an efficient hybrid response surface method is suggested to study the system reliability of pile-reinforced slopes, where the support vector machine and the Kriging model are used to approximate performance functions of soil failure and pile failure, respectively. The versatility of the suggested method is illustrated in detail with an example. For the example examined in this paper, it is found that the pile failure can significantly contribute to system failure, and the reinforcement ratio can effectively reduce the probability of pile failure. There exists a critical reinforcement ratio beyond which the system failure probability is not sensitive to the reinforcement ratio. The pile spacing affects both the probabilities of soil failure and pile failure of the pile-reinforced slope. There exists an optimal location and an optimal length for the stabilizing piles.