Reliability Analysis Of Complex Systems Research Articles

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.

Selective transmit modeling framework of complex system reliability analysis considering failure correlation

To improve the efficiency and accuracy of complex system reliability analysis considering failure correlation, a selective transmit modeling framework (STMF) is proposed by integrating multi-stage selective modeling (MSM) strategy with multi-failure transmit modeling (MTM) architecture. In MSM, the modeling quality of multi-learner is discussed to establish the optimal functional relationship between multi-variable and multi-response by considering the suitability of modeling samples, and the fitting performance of copula functions is quantified to construct the optimal correlation model between multi-failure through distance measure. For MTM, the correlation sequence measurement structure of multiple modes is established to construct the joint reliability analysis model of complex structure by updating iteratively the margin distribution functions with the strongest correlation. Taking the turbine bladed disk as study object, the validation of the proposed STMF is verified by comparing with other methods. The analytical results of study case can be expressed as that (i) STMF holds the superior performance in modeling accuracy and time-consuming, at 2.6308 × 10-2 and 0.4638 s respectively; (ii) STMF also has the best property in simulation, separately at 2.2123 s in simulation efficiency and at 99.9899 % in simulation precision; (iii) the reliability 0.9876 of study case obtained by STMF is higher than the reliability 0.9855 that depends on the mutual independence assumption. The effort of this work is prominent to promote effectively the quantification of multi-failure correlation and the improvement of reliability analysis performance for complex systems.

Decomposed-coordinated framework with intelligent extremum network for operational reliability analysis of complex system

The analysis of operational reliability in complex systems, which involve numerous subsystems and multiple disciplines, presents significant computational challenges due to their highly nonlinear, transient nature and the presence of many hyperparameters. Although reliability analysis models have made progress, they are still inadequate for accurately modeling composite functions with multiple sublayers and sub-functions. To improve the performance of modeling composite functions, the decomposed-coordinated intelligent extremum network model (DC-IENM) is proposed in this paper. The present study employs the decomposed-coordinated (DC) strategy as a means to effectively address the coordination relationship among multiple analysis objectives. To assess the efficacy of the proposed approach, two illustrative examples are considered: (1) the approximate and probabilistic analysis of a nonlinear function with multiple responses, and (2) the reliability analysis of civil aircraft brake system temperature. These examples serve to demonstrate the effectiveness of the developed DC-IENM. Furthermore, the modeling and simulation properties are rigorously examined by means of a comparative analysis involving various methodologies. The obtained results unequivocally indicate that the proposed DC-IENM exhibits distinct advantages in terms of both computational efficiency and precision.

Unsupervised and supervised learning for the reliability analysis of complex systems

AbstractIn this paper, a strategy to deal with high‐dimensional reliability systems with multiple correlated components is proposed. The goal is to construct a state function that enables the classification of the states of components in one of two categories, that is, failure and operative, in case of dealing with a large number of units in the system. To this end, it is proposed a new algorithm that combines a factor analysis algorithm (unsupervised learning) with local‐logistic and isotonic regression (supervised learning). The reliability function is estimated and system failures are predicted in terms of the variables in the original state space. The dimensions in the latent state space are defined by blocks of units with a certain dependence structure. The flexibility of the model allows quantifying locally the effect that a particular unit has on the system performance and a ranking of components can be obtained under the philosophy of the Birnbaum importance measure. The good performance of the proposal is assessed by means of a simulation study. Also a real data case is considered to illustrate the method.

An integrated modelling framework for complex systems safety analysis

AbstractThe ever‐increasing complexity of engineering systems has fuelled the need for novel and efficient computational tools able to enhance the accuracy of current modelling strategies for industrial systems. Indeed, traditional Fault and Event Tree techniques still monopolize the reliability analysis of complex systems despite their limitations, such as the inability to capture underlying dependencies between components or to include degradation processes and complex maintenance strategies into the analysis. However, the lack of alternative solutions able to tackle large‐scale modelling efficiently has contributed to the continued use of such methodologies, together with their robustness and familiarity well rooted in engineering practice. The current paper defines a novel modelling framework for safety system performance which retains the capabilities of both fault and event tree methods, but also overcomes their limitations. The ambition is to provide a technique for application to real‐world systems preserving a familiar user–model interface and grounding the novel approach in well‐known and established reliability techniques. In order to describe the methodology developed and demonstrate its validity, five case‐studies referring to a simplified industrial plant cooling system are analysed and discussed. Further discussion regarding the scalability of the proposed approach is provided, outlining the advantages of the current implementation and its computational cost.

An evidential network-based hierarchical method for system reliability analysis with common cause failures and mixed uncertainties

Redundant design has been widely used in aerospace systems, nuclear systems, etc. which calls for particular attention to common cause failure problems in such systems with various kinds of redundant mechanisms. Besides, imprecision and epistemic uncertainties also need to be taken into account for system reliability modeling and assessment. In this paper, a comprehensive study based on the evidential network is performed for the reliability analysis of complex systems with common cause failures and mixed uncertainties. The decomposed partial α-factor is used to separate the contribution of independent parts and common cause parts of basic failure events. Mixed uncertainties are quantified and expressed by the D-S evidence theory, and the system reliability with uncertainties is modeled by evidential network. Furthermore, two layers, i.e. a decomposed event layer and coupling layer, are embedded into the evidential network of the system, and, as a result, the hierarchical structure of system reliability is constructed. The importance and sensitivities of various component types and their impact on system reliability are detected. The presented evidential network-based hierarchical method is applied to analyze the reliability of an auxiliary power supply system of a train and the results demonstrate the effectiveness of this method.

Reliability analysis for complex system with multi-source data integration and multi-level data transmission

The Bayesian theory is appealing for reliability analysis of complex system using the data incorporation. However, there are still gaps among existing methods, such as that the common method is applicable to two-level system, multi-source data for components are not considered, k-out-of-n and standby structures are not studied with series and parallel simultaneously, the reliability is usually estimated as discrete variable, etc. For these problems, a Bayesian-based method is proposed on system under multiple levels. First, multi-source data for each target are integrated in lower level by Bayesian theory to derive the posterior distribution for reliability. Next, they are transmitted to higher level through the deterministic function concerning reliability depending on system structure. Further, the transmitted data from lower level are transformed to induced prior distribution for parameters in distribution of lifetime and integrated with native data in higher level to obtain the posterior for reliability. Finally, the reliability and remaining useful lifetime with respect to times in system-level are presented after the successive information propagation. An illustrative example is given to show the application of proposed method. Together with the sensitivity analysis, it proves that this method is feasible, practical and robust.

Efficient reliability analysis of complex systems in consideration of imprecision

In this work, the reliability of complex systems under consideration of imprecision is addressed. By joining two methods coming from different fields, namely, structural reliability and system reliability, a novel methodology is derived. The concepts of survival signature, fuzzy probability theory and the two versions of non-intrusive stochastic simulation (NISS) methods are adapted and merged, providing an efficient approach to quantify the reliability of complex systems taking into account the whole uncertainty spectrum. The new approach combines both of the advantageous characteristics of its two original components: 1. a significant reduction of the computational effort due to the separation property of the survival signature, i.e., once the system structure has been computed, any possible characterization of the probabilistic part can be tested with no need to recompute the structure and 2. a dramatically reduced sample size due to the adapted NISS methods, for which only a single stochastic simulation is required, avoiding the double loop simulations traditionally employed.Beyond the merging of the theoretical aspects, the approach is employed to analyze a functional model of an axial compressor and an arbitrary complex system, providing accurate results and demonstrating efficiency and broad applicability.

Adoption of a Bayesian Network for the Operational Reliability Analysis of Aircraft Systems

To assess and analyze the operational reliability of aircraft systems, an aircraft system Bayesian network (ASBN) method is proposed with the functional and logical coupling relationship of aircraft components, which integrates the characteristics of components related to aircraft operation, is built for analyzing the operational reliability under considering the effect of stochastic features. The aircraft system operating reliability is first assessed by forward inference of ASBN. And the most likely failure component or subsystem under the appearance of different failure condition severity categories are identified. The results show that the aircraft system operating reliability is not as high as the reliability of its components; the most likely failure component or subsystem are those tightly connected to other components or subsystems. The efforts of this paper provide a useful way for deriving operational reliability analysis of complex systems.

A method for transformation from dynamic fault tree to binary decision diagram

Dynamic fault tree (DFT) is a powerful modeling approach for reliability analysis of complex system with dynamic failure behaviors. In reality, the tree structure may be highly coupled either by shared basic events or by the high-level dynamic gates. Currently, the application of sequential binary decision diagram (SBDD)-based method for quantitative analysis of such highly coupled DFTs is mainly limited to DFTs whose dynamic gates locate in the bottom of the tree. Moreover, there is no efficient way dealing with the dependencies among different nodes of a SBDD 1-path. This paper makes an improvement to the SBDD-based approach. A generation procedure is proposed to directly construct the binary decision diagram (BDD) model for a DFT with arbitrary tree structure. During the construction, the sequential-dependent information of the tree is derived as several BDD nodes, each indicates a binary-sequential event representing the sequence of two occurred basic events. A topological sorting is applied on each 1-path of the resultant BDD to obtain its contained disjoint cut sequences. Based on this, both qualitative and quantitative analysis can be performed on the DFT with no limitations on tree structure, and its minimal cut sequence set (CSS) is obtained as disjoint. Examples are provided for verification and comparison, and the results illustrate the merits of the proposed approach.

A new reliability method for small failure probability problems by combining the adaptive importance sampling and surrogate models

Reliability analysis for structural systems with multiple failure modes and expensive-to-evaluate simulations is challenging. In this paper, a new and efficient system reliability method is proposed based on the adaptive importance sampling and kriging models. The Metropolis–Hastings (M–H) algorithm is used to construct several Markov chains to fully explore complex failure regions. A number of Markov chain states are selected as the center of the component importance sampling functions to generate samples for reliability analysis. Based on the component importance sampling function of each selected chain state, the system importance sampling function is constructed with the weighting index. The system importance sampling function can be constructed effectively because it does not involve time-consuming simulations and the most probable point (MPP) search. The new learning function, which is directly linked to the system failure probability, is developed to adaptively select the best added samples for refining the kriging models at each iteration. The adaptive importance sampling method and kriging models are well-combined for system reliability analysis in the proposed method. Compared with existing methods, the proposed method, generally, offers the following advantages: (1) The learning function and stopping criterion are directly linked to system failure probability; (2)the adaptive importance sampling and kriging models are well-combined to yield accurate results based on a small sample size for small failure probability problems; (3) the weights of sampling centers are considered, and the MPP search is not required at each iteration; (4) it is applicable for complex systems regardless of the structure and system failure probability level. Three numerical examples are analyzed, which demonstrate that the proposed method is effective for complex system reliability analysis.

Physics-based probabilistic models: Integrating differential equations and observational data

This paper proposes a general formulation for physics-based probabilistic models that are computationally convenient for uncertainty quantification and reliability analysis of complex systems while integrating the governing physical laws. The proposed formulation starts with the prediction of the quantities of interest using differential equations that represent the governing physical laws. For computational efficiency, the solution of the governing differential equations might be approximated. The predictions from the differential equations are then improved by introducing analytical correction terms that capture those physical characteristics of the phenomenon not fully captured by the differential equations. The paper also presents nested probabilistic models for uncertain physical characteristics that are difficult to measure. Observational data are required to calibrate the nested probabilistic models and correction terms. To provide context, the paper discusses physics-based probabilistic models for a class of boundary value problems that includes as a special case, the steady advection–diffusion–reaction equation, governing a diverse range of physical, chemical, and biological phenomena. Using the Bayesian approach, the differential equations are combined with observational data and any prior information to estimate the unknown model parameters and uncertain system characteristics. The paper then formulates the reliability problem for the computation of failure probability of physical and engineering systems using the proposed physics-based probabilistic models. To illustrate, the paper considers the reliability analysis of axially loaded rock socketed drilled shafts.

A real time methodology of cluster-system theory-based reliability estimation using k-means clustering

With rapidly increase in the design and application of complex system engineering, life and reliability analysis methods for these engineering have received much attention. A novel real time reliability analysis methodology is proposed based on the cluster-system theory and k-means clustering. Firstly, the system consisting of three or more identical or similar sub-systems facing the same load or task is defined as cluster-system. By analyzing the key performance parameters, sub-systems with similar performance are divided into a family-system, so that each sub-system can be used as reference sample for other sub-systems in the identical family-system. The cubic spline interpolation method under first-order boundary conditions is used to fit the average variation of key performance parameters of family-systems. The residual life of family-system can be obtained by determining the threshold of key performance parameters of sub-system through experiments or experience. Then reliability of the whole system is estimated by the contribution of each sub-system in cluster-system to solve the problem that there is no fault data and reference samples in the reliability analysis of complex system. Application in the Five-hundred-meter Aperture Spherical Telescope (FAST) demonstrates the effectiveness of the proposed method, compared to traditional reliability analysis methods based on experimental statistics.

Monte Carlo Simulation Approach to Reliability Analysis of Complex Systems

Abstract The article presents new results concerned with general procedures and algorithms to assess the reliability of complex systems with various reliability structures. The analytical method and based on it the simulation method were used to estimate the reliability characteristics of the port grain transportation system. Finally, the general simulation algorithm was developed to evaluate the reliability characteristics of ageing complex systems. In this case, the systems operating processes were described by any distributions of sojourn times in operation states and the reliability functions of their components were modified in such a way that these components are not characterized by a “lack of memory”. The application of this algorithm has been illustrated by the results for exemplary complex two-state systems.

Application of GO methodology in reliability analysis of aircraft flap hydraulic system

ABSTRACTThe Goal-Oriented methodology (GO methodology) is an effective method for the reliability analysis of complex systems. It is especially suitable for the reliability analysis of multi-state complex systems containing the actual logistics, such as current, airflow and liquid flow. In order to solve the limitation that the GO methodology is not suitable for the reliability analysis of the system with feedback loop, the Boolean algebra idea is introduced to construct the Boolean operation formula of the feedback loop. In this paper, a certain type of civil aircraft flap hydraulic system with feedback loop is taken as the research object. According to the structural schematic diagram of the flap hydraulic system, the GO model of the flap hydraulic system is established. Next, the GO calculation is carried out to obtain the reliability of the flap hydraulic system. The comparison between the system reliability without feedback loop and that with feedback loop proves that the GO methodology with feedback loop is more accurate. The reliability of the system is analyzed by using the fault tree analysis (FTA) method, and the GO methodology with feedback loop is compared with the FTA method to verify the availability and correctness of the GO methodology in the reliability analysis and safety evaluation of aircraft flap hydraulic system.

System Reliability Assessment with Imprecise Probabilities

The exact statistical characteristics of some components may be unavailable because of the limited sample information in practical engineering. One challenge that system reliability analysis faces is dealing with limited sample sizes, which introduces the potential for a high level of uncertainty in the analysis results. In this paper, we propose a procedure for the reliability analysis of complex systems with a limited number of samples. Bayesian inference is used to estimate the parameter intervals of the life distributions of the components with a limited number of samples. Then, probability boxes (p-box) are constructed from the parameter intervals to represent the life distributions of the components with a limited number of samples. In addition, the theory of survival signature is applied to calculate the reliability of the system with a mixture of precise and imprecise knowledge of the life distributions of the components. Finally, two numerical examples are given to illustrate the validity of the methods.

Reliability Analysis of Complex Systems with Failure Propagation

Failure propagation is a critical factor for the reliability and safety of complex systems. To recognise and identify failure propagation of systems, a deep fusion model based on deep belief network (DBN) and Bayesian structural equation model (BSEM) is proposed. The deep belief network is applied to extract features between status monitoring data and the performance degradation in different failure components. To calculate the path weight of failure propagation, the Bayesian structural equation model is proposed to study the relationship among different fault modes. After getting the performance degradation of each fault through DBN and calculating the path weight of fault propagation by BSEM, it is available to get the overall reliability of the system. The aircraft landing gear system with 19 fault patterns is selected to evaluate the feasibility of the proposed deep fusion model. The results demonstrate that the overall reliability of the system can be obtained by analysing the fault propagation of multiple fault patterns, and the proposed model has a lower deviation than traditional back propagation neural network.

Multi-level approach for important component identification and reliability evaluation for complex system by survival signature

PurposeThe purpose of this paper is to identify the critical components of a complex system by using survival signature. First, a complex system is abstracted with varying scales and generates a multi-levels model. Then reliability evaluations can be conducted by survival signature from rough to fine for tracing and identifying them. Finally, the feasibility of the proposed approach is demonstrated by an actual production system.Design/methodology/approachThe paper mainly applies a multi-level evaluating strategy for the reliability analysis of complex systems with components of multiple types. In addition, a multi-levels model of a complex system is constructed and survival signature also used for evaluation.FindingsThe proposed approach was demonstrated to be the feasibility by an actual production system that is used in the case study.Research limitations/implicationsThe case study was performed on a system with simple network structure, but the proposed approach could be applied to systems with complex ones. However, the approach to generate the digraphs of abstraction levels for complex system has to be developed.Practical implicationsSo far the approach has been used for the reliability analysis of a machining system. The approach that is proposed for the identification of critical components also can be applied to make maintenance decision.Originality/valueThe multi-level evaluating strategy that was proposed for reliability analysis and the identification of critical components of complex systems was a novel method, and it also can be applied as index to make maintenance planning.

A Double Hybrid State-Space Model for Real-Time Sensor-Driven Monitoring of Deteriorating Systems

With the rising complexity of deteriorating systems and availability of advanced sensors, the need for more robust and reliable methods for condition monitoring and dynamic maintenance decision-making has significantly increased. To generate more reliable results for reliability analysis of complex systems, we propose a new generative framework for failure prognosis utilizing a hybrid state-space model (SSM) that represents the evolution of the system’s operating condition and its degradation over time. The proposed model can employ a set of real-time sensor measurements to: 1) diagnose the hidden degradation level of the system and 2) predict the likelihood and the uncertainty of failure without imposing unrealistic heavy distributional assumptions. We provide analytical results for the prediction and update steps of the associated particle filter, as well as for the estimation of model parameters. A single-layer feed-forward neural network (Extreme Learning Machine) was used to model the nonparametric relationship between the multi-dimensional observation process and the rest of system’s dynamics. We demonstrate the application of our framework through numerical experiments on a set of simulated data and a turbofan engine degradation data set. Note to Practitioners —The prognosis of the future health status in degrading systems using sensor data generally requires many distributional assumptions, such as a parametric relationship between the hidden degradation level and sensor measurements, and a predefined degradation threshold. This paper proposes a new model that formulates the relationship between degradation level, sensor measurements, and operating conditions in a multi-layer generative manner that helps accommodate interpretability and uncertainty. Results obtained utilizing simulated and real-life data prove that the developed method can yield reasonable prognostic estimates for important measures, such as the remaining useful life of the system.

Application of dynamic evidential networks in reliability analysis of complex systems with epistemic uncertainty and multiple life distributions

With the modernization and intelligent of industrial equipment and systems, the challenges of dynamic characteristics, failure dependency and uncertainties have aroused by the increasing of system complexity. Besides, various types of components may follow different life distributions which bring the multiple life distributions problem in systems. In order to model the impact of time dependency and epistemic uncertainty on the failure behavior of system, this paper combines the flexible dynamic modeling with the uncertainty expression. Its advantages are intuitively graphical representation and reasoning that brought by evidential network (EN). After that, the discrete time dynamic evidential network (DT-DEN) is introduced to analyze the reliability of complex systems, and the network inference mechanism is clearly defined. The evidence theory and original definition and inference mechanism of conventional EN is firstly recommended, and the DT-DEN is further presented. Furthermore, the multiple life distributions are synthesized into the DT-DEN to tackle the epistemic uncertainty and mixed life distribution challenges. Specifically, the dynamic logic gates are converted into equivalent DENs with distinguished conditional mass tables, and then the belief interval of system reliability can be calculated by network forward reasoning. Finally, the availability and efficiency of the proposed method is verified by some numerical examples.