Complex Multi-state System Research Articles

Biobjective Maintenance Strategy Optimization for Complex Multistate Systems Based on PH Distribution

Biobjective Maintenance Strategy Optimization for Complex Multistate Systems Based on PH Distribution

Component uncertainty importance measure in complex multi-state system considering epistemic uncertainties

Importance measures can be used to identify the vulnerable components in an aviation system at the early design stage. However, due to lack of knowledge or less available information on the component or system, the epistemic uncertainties may be one of the challenging issues in importance evaluation. In addition, the properties of the aircraft system, which are the fundamentals of the component importance measure, including the hierarchy, dependency, randomness, and uncertainty, should be taken into consideration. To solve these problems, this paper proposes the component Uncertainty Integrated Importance Measure (component UIIM) which considers multiple epistemic uncertainties in the complex multi-state systems. The degradation process for the components is described by a Markov model, and the system reliability model is developed using the Markov hierarchal evidential network. The concept of integrated importance measure is then extended into component UIIM to evaluate the component criticality rather than the component state change criticality, from the perspective of system performance. A case study on displacement compensation hydraulic system is presented to show the effectiveness of the proposed uncertainty importance measure. The results show that the component UIIM can be an effective method for evaluating the component criticality from system performance perspective at the system early design.

Reliability analysis of multi-state series systems with k-out-of-n: G subsystems considering performance sharing

Motivated by real-world engineering systems, this paper presents an in-depth exploration of a novel reliability model for a complex multi-state series system (MSSS) that incorporates a performance sharing mechanism. Specifically, the MSSS is composed of m distinct subsystems featuring a k-out-of-n: G structure. The ith subsystem consists of ni elements, such that a minimum of ki functioning elements is required for normal operation. Transmission devices (TDs) are present between adjacent subsystems to share surplus performance. Both element performance and subsystem demand are treated as random variables, and the performance of all elements in each subsystem is cumulated to meet its individual random demand. Subsystem failure can result from either an inability to meet performance demands or an insufficient number of functioning elements. The surplus performance of a subsystem can only be transferred to its adjacent subsystem via the TD. The entire MSSS will fail if at least one subsystem does not work properly by using performance sharing mechanism. To analyze the reliability indexes of the MSSS, a new algorithm based on the generalized universal generating function (GUGF) has been developed. Numerical examples are provided to illustrate the accuracy and effectiveness of the proposed model and method.

Algorithms for Bayesian network modeling and reliability inference of complex multistate systems with common cause failure

Algorithms for Bayesian network modeling and reliability inference of complex multistate systems with common cause failure

Random sparse generators of Markovian evolution and their spectral properties.

The evolution of a complex multistate system is often interpreted as a continuous-time Markovian process. To model the relaxation dynamics of such systems, we introduce an ensemble of random sparse matrices which can be used as generators of Markovian evolution. The sparsity is controlled by a parameter φ, which is the number of nonzero elements per row and column in the generator matrix. Thus, a member of the ensemble is characterized by the Laplacian of a directed regular graph with D vertices (number of system states) and 2φD edges with randomly distributed weights. We study the effects of sparsity on the spectrum of the generator. Sparsity is shown to close the large spectral gap that is characteristic of nonsparse random generators. We show that the first moment of the eigenvalue distribution scales as ∼φ, while its variance is ∼sqrt[φ]. By using extreme value theory, we demonstrate how the shape of the spectral edges is determined by the tails of the corresponding weight distributions and clarify the behavior of the spectral gap as a function of D. Finally, we analyze complex spacing ratio statistics of ultrasparse generators, φ=const, and find that starting already at φ⩾2, spectra of the generators exhibit universal properties typical of Ginibre's orthogonal ensemble.

Asymmetric Switching of Edge Modes by Dynamically Encircling Multiple Exceptional Points

Dynamically encircling exceptional points (EPs) in the parameter space of a non-Hermitian system has drawn widespread attention for realizing asymmetric mode switching and related applications. While previous works have been restricted to two-level systems, the switching between edge states in a multistate system that contains more complex dynamics remains to be explored. Herein, asymmetric switching of edge modes in multistate systems is demonstrated by encircling multiple EPs. A multistate non-Hermitian system containing multiple EPs is constructed based on a one-dimensional lattice, which can support four edge-localized modes. Dynamically encircling the EPs in parameter space leads to a specific edge mode surviving to the end, determined by the encircling direction. Correspondingly, optical waveguide arrays are designed to investigate mode evolution through refractive index modulation. Simulated results show that clockwise (counterclockwise) encirclement leads to an output mode localized at the left (right) side of the waveguide array with a phase difference of 0 (\ensuremath{\pi}), regardless of the input modes; this excellently illustrates the asymmetric switching of edge modes in a multistate system. Moreover, such an effect can be extended to the multistate system with an arbitrary number of EPs. This work enables investigation of interesting effects in non-Hermitian physics by engineering the EPs and topological properties, especially for complex multistate systems, which will be useful for developing functional nanophotonic devices.

Reliability analysis of complex multi-state system based on universal generating function and Bayesian Network

In the complex multi-state system (MSS), reliability analysis is an important research content, both for equipment design, manufacturing, operation and maintenance. Universal Generating Function (UGF) is an essential method in reliability analysis, which efficiently obtains system reliability by a fast algebraic procedure. However, when structural relationships between subsystems or components are unclear or without explicit expressions, the UGF method is difficult to use or not applicable at all. Bayesian Network (BN) has a natural advantage in terms of reliability inference for the relationship without explicit expressions. When the number of components is extremely large, though, it has the defects of low efficiency. To overcome the respective shortcomings of UGF and BN, a novel reliability analysis method called UGF-BN is proposed for the complex MSS. In the UGF-BN framework, the UGF method is first used to analyze the bottom components with a large number. Then probability distributions obtained are taken as the input of BN. Finally, the reliability of the complex MSS is modeled by the BN method. This proposed method improves the computational efficiency, especially for the MSS with a large number of bottom components. Besides, the aircraft reliability-based design optimization based on the UGF-BN method is further studied with budget constraints on mass, power, and cost. Finally, two cases are used to demonstrate and verify the proposed method.

MMAPs to Model Complex Multi-State Systems with Vacation Policies in the Repair Facility

Two complex multi-state systems subject to multiple events are built in an algorithmic and computational way by considering phase-type distributions and Markovian arrival processes with marked arrivals. The internal performance of the system is composed of different degradation levels and internal repairable and non-repairable failures can occur. Also, the system is subject to external shocks that may provoke repairable or non-repairable failure. A multiple vacation policy is introduced in the system for the repairperson. Preventive maintenance is included in the system to improve the behaviour. Two types of task may be performed by the repairperson; corrective repair and preventive maintenance. The systems are modelled, the transient and stationary distributions are built and different performance measures are calculated in a matrix-algorithmic form. Cost and rewards are included in the model in a vector matrix way. Several economic measures are worked out and the net reward per unit of time is used to optimize the system. A numerical example shows that the system can be optimized according to the existence of preventive maintenance and the distribution of vacation time. The results have been implemented computationally with Matlab and R (packages: expm, optim).

Multistate Reliability Analysis of Recessive Fault of Mechanical Meta-Action Unit Based on Markov Process

In order to clearly express the reliability dynamic change process of mechanical meta-action units with recessive fault on continuous time series, this paper proposes a reliability analysis method for multistate systems with recessive failures of mechanical meta-action units based on the fusion of vibration signal analysis and Markov process. By analyzing the vibration signal, five major recessive fault types of mechanical meta-action units are determined. By analyzing the experimental data and based on the average time of the first occurrence of five major recessive faults, a performance level state representation model of mechanical meta-action unit based on fault importance weight is established. Then, based on the repairable characteristics of the mechanical element action unit, the two-way state transition model and state probability differential equation of mechanical meta-action units are established, and the state probability of each state is obtained. Next, under the condition of determining the initial state, the change process curves of the instantaneous availability, instantaneous average performance, and instantaneous average performance deficit of the mechanical meta-action unit are obtained by solving the reliability index calculation formula. Finally, this paper takes the worm rotation meta-action unit as an example to verify the law and probability of the state transition of the mechanical meta-action unit, and the performance level change accompanying the state transition process, by analyzing the failure modes and causes of recessive faults, the corresponding reliability control measures are formulated, and the control effects before and after reliability control are analyzed. The research results show that this method can effectively improve the accuracy of the state probability when calculating the state probability of each state, and compared with the discrete Markov model, when studying the reliability of complex multistate systems, this method can dynamically describe the change process of state probability, instantaneous availability, instantaneous average performance, and instantaneous average performance deficit in real time under the condition of continuous time-dependent variables. It has certain guiding significance for the reliability analysis of mechanical element action units in the long-term range.

Accelerated Sampling Research Under Task Optimized Strategy for Multistate Systems

The complex multi-state systems joint operation simulation and two task strategies are explored. For Monte Carlo sampling, based on the indirect sampling method, the principle of accelerated sampling methods, including forced transition FT and fault biasing FB, is studied. It is found that the direct adoption of the current FT and FB will result in systematic bias for the calculation of task success metrics. For the bias, state-transition chain truncation is studied, and its definition and truncation rules are proposed. In case study, after the simulation of various parameter combinations, it is found that when the sailing time is relatively smaller than the equipment reliability, which means a small probability event for the sampling of equipment faults, the ASM based on indirect sampling is applicable. Otherwise, the conventional sampling method should be used. The proposed state-transition chain truncation rule is also verified in case study.

Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model.

Reliability Analysis of a Complex Multistate System Based on a Cloud Bayesian Network

This study focused on mixed uncertainty of the state information in each unit caused by a lack of data, complex structures, and insufficient understanding in a complex multistate system as well as common-cause failure between units. This study combined a cloud model, Bayesian network, and common-cause failure theory to expand a Bayesian network by incorporating cloud model theory. The cloud model and Bayesian network were combined to form a reliable cloud Bayesian network analysis method. First, the qualitative language for each unit state performance level in the multistate system was converted into quantitative values through the cloud, and cloud theory was then used to express the uncertainty of the probability of each state of the root node. Then, the β-factor method was used to analyze reliability digital characteristic values when there was common-cause failure between the system units and when each unit failed independently. The accuracy and feasibility of the method are demonstrated using an example of the steering hydraulic system of a pipelayer. This study solves the reliability analysis problem of mixed uncertainty in the state probability information of each unit in a multistate system under the condition of common-cause failure. The multistate system, mixed uncertainty of the state probability information of each unit, and common-cause failure between the units were integrated to provide new ideas and methods for reliability analysis to avoid large errors in engineering and provide guidance for actual engineering projects.

Reliability Modeling and Evaluation of Complex Multi-State System Based on Bayesian Networks Considering Fuzzy Dynamic of Faults

Reliability Modeling and Evaluation of Complex Multi-State System Based on Bayesian Networks Considering Fuzzy Dynamic of Faults

Algorithms for Bayesian network modeling and reliability inference of complex multistate systems: Part I – Independent systems

As the number of complex multistate systems’ components increases, one major challenge to analyze the reliabilities of complex multistate systems by Bayesian network (BN) is that the memory storage requirements (MSRs) of conditional probability table (CPT) increase exponentially. When the components reach a certain amount, the MSRs of CPT will exceed the computer's random access memory (RAM). To solve this problem, this two-part paper proposes a novel multistate compression algorithm to compress the CPT so that the MSRs of CPT can be reduced apparently. In this Part I, an independent multistate inference algorithm is proposed to perform the inference of BN based on the compressed CPT for the complex multistate independent systems. Given the evidence of system, the backward inference algorithm is proposed to update the probability distributions of compoents. The above proposed algorithms can be generally applied to any complex multistate independent system without constraints on system structure and state configurations. In addition, the Part II studies the application of compression idea in the complex multistate dependent systems. Finally, two case studies are used to validate the performance of the proposed algorithms.

Reliability evaluation of a k-out-of-n(G)-subsystem based multi-state system with common bus performance sharing

In this paper, a new reliability model for a complex multi-state system (MSS) with performance sharing is proposed. The MSS consists of m different k-out-of-n(G) subsystems which are connected by a transmission system. Subsystem i is composed of ni non-identical components, in which at least ki working components are demanded for the operating of the subsystem. The performances of the components in subsystem i are accumulated to meet its demand. Subsystem i fails if its performance demand is not satisfied or the number of working components is insufficient. The surplus performance of any subsystem can be shared by other subsystems experiencing performance deficiency via the transmission system. The entire system fails if at least one subsystem fails after performance sharing. An algorithm based on the universal generating function (UGF) is developed to evaluate the reliability of the entire system. Analytical and numerical examples are provided to show the effectiveness of the proposed method. Finally, a structure optimization problem of the performance sharing system with given transmission capacity C is discussed.

Dynamically encircling exceptional points in a three-mode waveguide system

Dynamically encircling exceptional points (EPs) in non-Hermitian systems has attracted considerable attention recently, but all previous studies focused on two-state systems, and the dynamics in more complex multi-state systems is yet to be investigated. Here we consider a three-mode non-Hermitian waveguide system possessing two EPs, and study the dynamical encircling of each single EP and both EPs, the latter of which is equivalent to the dynamical encircling of a third-order EP that has a cube-root behavior of eigenvalue perturbations. We find that the dynamics depends on the location of the starting point of the loop, instead of the order of the EP encircled. Compared with two-state systems, the dynamical processes in multi-state systems exhibit more non-adiabatic transitions owing to the more complex topological structures of energy surfaces. Our findings enrich the understanding of the physics of multi-state non-Hermitian systems and may lead to the design of new wave manipulation schemes.

Zastosowanie sieci bayesowskiej do analizy niezawodności złożonych systemów wielostanowych w warunkach niepewności

Reliability analysis of complex multi-state system has uncertainty, which is caused by complex structures, limited test samples, and insufficient reliability data. By introducing fuzzy mathematics and grey system theory into the Bayesian network, the model of the grey fuzzy Bayesian network is built, and the reliability analysis method of complex uncertainty multi-state system with the non-deterministic membership function and the interval characteristic quantity is proposed in this paper. Using the trapezoidal membership function with fuzzy support radius variable to describe the fault state of the component, it can effectively avoid the influence of human subjective factors on the selection of the membership function and solve the problem that the fault states of the system and its components are difficult to define accurately. And the conditional probability table containing interval grey numbers is constructed to effectively express the uncertain fault logic relationship between the system and its components. Moreover, a parameter planning model of the system reliability characteristic quantities is constructed, and the system reliability characteristic quantities are expressed as the form of interval values. Finally, two sets of numerical experiments are conducted and discussed, and the results show that the proposed method is an effective and a promising approach to reliability analysis for complex uncertainty multi-state systems.

Improved compression inference algorithm for reliability analysis of complex multistate satellite system based on multilevel Bayesian network

Bayesian Network (BN) is a powerful tool for analyzing system reliability. However, for the complex multistate satellite system, the state combination explosion makes the reliability analysis based on BN computationally unaffordable. To solve this problem, compression algorithm and inference algorithm have been proposed. The original compression algorithm classifies all the phrases with same composition into the same type. The original compression algorithm classifies all the phrases with same composition into the same type. However, cases tested in this paper show that the results of inference can be incorrect when some node probability tables have special formulations. To solve the above defects, the compression algorithm and sequential inference algorithm are improved in this paper. Based on improved compression algorithm and improved inference algorithm, the improved compression inference algorithm (ICIA) is formed and extended to the application of multistate nodes with independent binary parent nodes. Besides, the multilevel BN (MBN) models are used to construct the BN models of complex multistate satellite systems so as to further improve inference efficiency. Cases tested in this paper show that the proposed algorithms are more efficient than the Bayes Net Toolbox and the AgenaRisk software for the reliability analysis of complex multistate satellite systems.

A Complex Multi-State System with Vacations in the Repair

A complex multi-state system subject to wear failure and given preventive maintenance is considered. Various internal levels of degradation are assumed. The repair facility is composed of a repairperson, who may take one or more vacations during the period considered. A policy is established for the repairperson’s vacation time. Two types of task may be performed by the repairperson: corrective repair and preventive maintenance. All embedded times in the system are phase type distributed. The transient and stationary distributions are determined and several reliability measures are developed in a matrix-algorithmic form. Costs and rewards are included in the model. The results are implemented computationally with Matlab. A numerical example shows that the distribution of vacation time can be optimised according to the net reward established.

Reliability Modeling and Analysis of Complex Multi-State Systems based on Weighted Triangular Fuzzy Numbers T-S Fault Tree

Reliability Modeling and Analysis of Complex Multi-State Systems based on Weighted Triangular Fuzzy Numbers T-S Fault Tree