Cross-machine remaining useful life (RUL) prediction via transfer learning often deteriorates in few-shot scenarios due to insufficient source data and severe distribution divergence. These challenges amplify degradation uncertainty and significantly reduce prognostic reliability. This fundamentally raises an open problem: what information is critical in few-shot transfer learning, and how can the information be exploited? To address this, we propose a deep wavelet scattering regression adaptation method that exploits stage-specific frequency information. A novel multi-stage time-frequency attention (MSTFA) mechanism is designed within a domain-adversarial network to extract physically-aware feature representations. Specifically, MSTFA utilizes a wavelet scattering network to identify the most critical frequency bands corresponding to distinct degradation stages. Domain-invariant representations are then obtained via adversarial training, while a Bayesian regressor is incorporated to quantify uncertainty and provide confidence intervals. The generalization error upper bound of the proposed method is also derived, which theoretically reveals the reason why the MSTFA mechanism works. Experiments are conducted on two bearing datasets and a real-world width-sizing machine bearing dataset from a large steel factory in China. The results reveal the quantitative importance of frequency information across different degradation stages, and prove that leveraging such information effectively improves the prognostic accuracy and reliability in few-shot scenarios, thus offering a feasible solution for industrial applications.

Machinery fault diagnosis plays an important role in machine Prognostic and Health Management (PHM). Leveraging the abundant data obtained from the Industrial Internet of Things (IIoT), the health states of machines can be effectively recognized, thereby ensuring the safety of the mechanical system. However, the lack of noise robustness and insufficient frequency domain perception make traditional methods to extract weak fault-related signals difficult under highly noisy conditions in practical industrial scenarios. Therefore, a method with abundant frequency domain learning ability is urgently needed. To this end, this paper proposes a PHM framework, a soft thresholding Fourier feature refiner network (Soft-FFRNet), for highly noisy bearing vibration signal diagnosis. Specifically, this framework includes a Fourier feature refiner which selectively extracts and refines the feature in the frequency domain from the perspectives of amplitude and phase. It achieves the extension from the time domain to the frequency domain. In addition, the proposed framework utilizes several residual blocks with soft thresholding to effectively improve the noise robustness. Their thresholds can adaptively change during the training process. The high-speed aeronautical (HSA) bearing and the motor bearing datasets with different noise levels are used to evaluate this framework. The results show that the proposed framework can effectively diagnose the faults under highly noisy conditions.

Vibration data compression is crucial for addressing the considerable data volume challenge in prognostics and health management (PHM). This challenge can be mitigated by compressing both the number of sample points and the size of individual sample points. However, achieving high-compression ratios (CRs) encounters two primary challenges. First, current optimal solutions for compressing sample point sizes, data binarization, suffer from low-compression efficiency. Second, in hybrid compression, the compression effects of individual sample point sizes are prone to being lost during the reduction of sample points, thus limiting the improvement of CRs. To address these challenges, a novel hybrid compression framework is introduced for vibration condition monitoring. Building upon this framework, an efficient compression method with encryption features is proposed. The main contributions of the proposed method are twofold. First, by introducing the concept of clustering-based binarization, compression of sample point sizes with high CRs is achieved while improving compression efficiency. Second, by designing compression sampling methods that preserve the original data properties, the failure of individual sample point size compression is prevented, and compression space is further expanded while enhancing data security. Experimental results demonstrate the overall superiority of the proposed method. Compared to existing approaches, it achieves significant improvements in CR while retaining key spectral information, enhancing compression efficiency, and ensuring better data security. Thus, it alleviates the challenges of the significant data volume posed to data storage, transmission, and processing in PHM.

In this article, we propose an active kriging-based learning method for hybrid reliability analysis (HRA) with random and interval variables. An improved sampling strategy is proposed to target the sampling areas. Samples with maximum responses greater than 0 and minimum responses less than 0 are selected and regarded as the candidate samples; then, aU-based learning function is developed in which multiple samples of the interval are considered instead of one particular sample. To terminate the proposed method, a hybrid convergence criterion is proposed. Finally, an improved optimization strategy based on the DIRECT algorithm is developed for the Monte Carlo simulation conducted for the HRA. The performance of the proposed method is demonstrated by four numerical cases. The results illustrate that the proposed method is accurate and efficient for HRA.

As an extension of binary system model, multistate systems (MSSs) are more flexible for modeling reliabilities of real-life engineering systems. In the conventional MSS theory, it is usually assumed that the performance of the system and components can be characterized by one measure. However, the assumption is difficult to be satisfied for some complex engineering systems that have different forms of performances at the same time. For example, the integrated energy system can supply various forms of energy simultaneously, including electrical power, natural gas, and heat. Therefore, the conventional MSS is difficult to model the system with multiple performances. In this article, a general multiperformance measure MSS model is proposed. The fundamental assumptions and key definitions are provided for such systems. The ordering methods to compare performance measure vectors are introduced. The concepts of separability, monotonicity, relevancy, coherency, and equivalency of the component and the system are developed to characterize the system properties. Examples are given to illustrate these definitions.

A module of a fault tree is an independent subtree that has no input from the rest of the tree and no output to the rest, except the top events. Modularization is an important technique to reduce the computation cost for large, complex fault tree analysis. This article presents a new linear-time algorithm that is more efficient and easier to code for finding modules existing in fault trees. Two main stages are included in the proposed algorithm: branching and transforming. To demonstrate the efficiency and applicability of the proposed algorithm, comparisons are performed between the proposed algorithm and other linear-time algorithms for finding modules in fault trees. Results have shown the superiority and effectiveness of the proposed algorithm.

The critical issue for fault diagnosis of wheel-set bearings in high-speed trains is to extract fault features from vibration signals. To handle high complexity, strong coupling, and low signal-to-noise ratio of the vibration signals, this article proposes a novel multibranch and multiscale convolutional neural network that can automatically learn and fuse abundant and complementary fault information from the multiple signal components and time scales of the vibration signals. The proposed method combines the conventional filtering methods and the idea of the multiscale learning, which can extend the breadth and depth of the feature learning process. Consequently, the proposed network can perform better. The experimental results on the wheelset bearing dataset demonstrate that the proposed method has better antinoise ability and load domain adaptability and can diagnose 12 fault types more accurately when compared with the five state-of-the-art networks.

Induction motor-planetary gearbox drivetrains are widely used for industrial productions, including machine tools in manufacturing systems. For fault diagnosis of planetary gearboxes in such electromechanical systems, motor current signal analysis provides an effective alternative approach, because motor current signals have easier accessibility and are free from time-varying transfer path effects. Planetary gearbox faults generate load torque oscillations, leading to both amplitude modulation and frequency modulation (AM-FM) effects on induction motor current signals. To thoroughly understand gear fault features in current signals, an AM-FM current signal model is derived through mechanical-magnetic-electric interaction analysis, explicit equation of Fourier spectrum is derived, and sidebands characteristics are summarized. To avoid an intricate sideband analysis, amplitude and frequency demodulation analyses are proposed, explicit equations of corresponding demodulated spectra are derived, and gear fault features are summarized. The theoretical derivations are validated through lab experiments. Localized fault on the sun, planet, and ring gears are all successfully diagnosed using the proposed method.

Multistate series-parallel system (MSSPS) is a widely used model for representing engineering systems, whose reliability has been extensively analyzed. Universal generating function (UGF) is an efficient method for evaluating the reliability of MSSPS. However, when facing the large-scale MSSPS, where the number of system components and possible states are enormous, calclating the exact system reliability can be rather time-consuming. To evaluate the reliability of large-scale MSSPS more efficiently, this paper proposes an approximation method, named continuization discretization approximation (CDA) method. The CDA approach consists of continuization and discretization processes. The continuization process applies Gaussian approximation method based on the central limit theory and the UGF technique to evaluate parallel subsystems. While the discretization process discretizes the continuous distribution to a discrete one, and proposes an algorithm to evaluate the series subsystems efficiently. The efficiency and accuracy performance of the CDA method can be adjusted by parameters according to the computational resource and the system scale. The newly proposed method is compared to the existing methods in evaluating the large-scale MSSPS. Numerical examples show that the CDA method has evident advantage in computational efficiency with satisfactory accuracy performance.

The d-MP is a special state vector such that the maximal flow is d in the related network and any state vector less than d-MP is not a d-MP. The d-MP is one of the major tools in evaluating the reliability of a multistate flow network. The d-MPs for all d problem is to search for all d-MPs for all possible d. Decision-makers may use them to choose the best d under given scenarios. Current algorithms for addressing this problem are all based on the addition of 1-MPs and (d - 1)-MPs to generate d-MP combinations, and then detect and remove d-MP combinations with infeasible states, redundant states, and/or duplications. A new algorithm based on the subtraction of (d + 1)-MPs and 1-MPs to obtain d-MP combinations is proposed in this paper to overcome the above three obstacles in current algorithms. The time complexity and demonstration of the proposed algorithm are also analyzed and provided using examples. An experiment is conducted to compare the performance of the proposed subtraction-based algorithm with that of the best known addition-based algorithm.

Rotating machines are widely used in industry and often work under harsh and varying speed conditions. Fault diagnosis under varying speed conditions is needed to prevent major shutdowns. This paper aims to develop an intelligent rotating machinery fault diagnosis strategy based on deep neural networks (DNNs) and order tracking (OT). The developed strategy can automatically conduct rotating machinery fault diagnosis under both constant and varying speed conditions. Case studies on a rolling element bearing dataset and a fixed-shaft gearbox dataset show the superiority in diagnosis accuracy of the proposed strategy over reported approaches.

In this paper, a nonlinear dynamic model is developed considering backlash, time-varying mesh stiffness (TVMS), and sliding friction. Friction is firstly introduced to a spur gear pair nonlinear dynamic model under random load. Transient characteristics of the spur gear transmission system are studied. The results show that random load causes longer duration of transient state and stronger vibration in steady state than deterministic load. In addition, friction plays dual roles in the gear random dynamics. Friction causes higher dispersion of the gear pair's relative angular displacement in the transient state while lower dispersion in the steady state.

Safety instrumented system (SIS) is widely applied to reduce or prevent risk in industry. Practical SIS commonly meets with epistemic uncertainty arising from incompleteness of knowledge on various input parameters due to lack of data. Epistemic uncertainty can be reduced by collecting more knowledge or data. Epistemic uncertainty in input parameters can lead to variation in probability of failure to perform its intended functions on demand (PFD) for an SIS. This paper employs the complementary cumulative distribution function of PFD to define exceedance probability (EP) that the PFD exceeds a prescribed value. Sensitivity analysis is further investigated, analyzing the effect of an epistemically uncertain input parameter with truncated distribution on EP of an SIS. We have derived the analytic expression for evaluating the effect, and only an evaluation is needed to estimate the effects of all the parameters. Two examples are employed to demonstrate the applicability of the proposed method. We further compare the effects for the truncated and nontruncated parameter situations. Their results converge to the same ones as the truncated region of an input parameter decreases to zero. When the truncated region of an input parameter is less than 10-3, the corresponding results can be approximated by the ones of the nontruncated case with lower computational cost.

In this paper, we will consider the selective maintenance problem for multistate series systems with stochastic dependent components. In multistate systems, the health state of a component may vary from perfect functioning to complete failure. The stochastic dependence (S-dependence) between components is discussed and categorized into two types in multistate context. First, the failure of a component can immediately cause complete failures of some other components in the system. Second, as components deteriorate, the reduced working performance rate of a multistate component affects the state as well as the degradation rate of its subsequent components in series structure. The system reliability is evaluated using an approach based on stochastic process. A cost-based selective maintenance model is developed for the multistate system with S-dependent components to maximize the total system profit, which includes the production gain and loss in the next mission as well as possible maintenance costs for the system. Analyses of systems with independent and dependent components are provided. It is observed that ignoring S-dependence in the system may lead to alternative maintenance decision making and an optimistic estimation of the system performance.

This paper develops ordering heuristics to improve the efficiency of reliability evaluation for multistate two-terminal networks given all minimal path vectors ( d-MPs for short). In the existing methods, all d-MPs are treated equally. However, we find that the importance of each d-MP is different, and different orderings affect the efficiency of reliability evaluation. Based on the above observations, we introduce the length definitions for d-MPs in a multistate two-terminal network, and develop four ordering heuristics, called O1, O2, O3, and O4, to improve the efficiency of the Recursive Sum of Disjoint Products (RSDP) method for evaluating network reliability. The results show that the proposed ordering heuristics can significantly improve the reliability evaluation efficiency, and O1 performs the best among the four methods. In addition, an ordering heuristic is developed for the reliability evaluation of multistate two-terminal networks given all minimal cut vectors ( d-MCs).

Importance measures in reliability engineering are used to identify weak components of a system and signify the roles of components in contributing to proper functioning of the system. Recently, an integrated importance measure (IIM) has been proposed to evaluate how the transition of component states affects the system performance based on the probability distributions and transition rates of component states. In the system operation phase, the bathtub curve presents the change of the transition rate of component states with time, which can be described by three different Weibull distributions. The behavior of a system under such distributions can be modeled by the semi-Markov process. So, based on the reported IIM equations of component states, this paper studies how the transition of component states affects system performance under the semi-Markov process. This measure can provide useful information for preventive actions (such as monitoring enhancement, construction improvement, etc.), and provide support to improve system performance. Finally, a simple numerical example is presented to illustrate the utilization of the proposed method.

Traditional time-based reliability assessment methods evaluate the reliability of a multi-state system (MSS) from a population or a statistical perspective that the reliability of a system is computed purely based upon historical time-to-failure data collected from a large population of identical components or systems. These methods, however, fail to characterize the stochastic behaviors of a specific individual system. In this paper, by utilizing system-level observation history, a dynamic reliability assessment method for MSSs is put forth. The proposed recursive Bayesian formula is able to dynamically update the reliability function of a specific MSS over time by incorporating system-level inspection data. The dynamic reliability function, state probabilities, and remaining useful life distribution of an MSS in residual lifetime are derived for two common cases: the degradation of components follows a homogeneous continuous time Markov process, and a non-homogeneous continuous time Markov process. The effectiveness and accuracy of the proposed method are demonstrated via two numerical examples.

The aero-engine is the heart of an airplane. Operational reliability assessment that aims to identify the reliability level of the aero-engine in the service phase is of great significance for improving flight safety. Traditionally, reliability assessment is carried out by statistical analysis on large failure samples. Because the operational reliability of a specific aero-engine is an individual problem lacking statistical sample data, traditional reliability assessment methods may be insufficient to assess the operational reliability of an individual aero-engine. The operational states of the aero-engine can be identified by its condition information. Changes in the condition information reflect the performance degradation of the aero-engine. Aiming at the assessment of the operational reliability of individual aero-engines, a novel similarity index (SI) is proposed by analyzing the condition information from the fault-free state, and the current state. A condition subspace is first obtained by kernel principal component analysis (KPCA). Subspace similarity is then represented by subspace angles, i.e., kernel principal angles (KPAs). The cosine function is finally utilized as a mapping function to transform the subspace angles into a similarity index. The index can be used as a non-probabilistic metric for operational reliability assessment. Only the condition information is needed for computation of the similarity index, thus it can be performed conveniently for online assessment. The effectiveness of the proposed method is validated by three case studies regarding the health assessment of aero-engines subjected to system-level and component-level degradation. The positive results demonstrate that the proposed SI is an effective metric for operational reliability assessment of individual aero-engines.

This paper proposes age and periodic replacement last models with continuous, and discrete policies. That is, an operating unit is replaced preventively at time T of operation as a strategic policy, or at a number N of working cycles to satisfy successive job completion, whichever occurs last. Such policies are named as replacement last, and their expected cost rates and optimal policies are obtained. However, the focus of this paper is to compare replacement last with replacement first policies, which are formulated under the classical assumption of whichever occurs first. From the points of cost and performability, different comparative methods for continuous and discrete optimizations are demonstrated to determine in what cases we should adopt replacement last rather than replacement first. All theoretical discussions in this paper are made analytically, and are computed numerically.

Dynamic fault tree (DFT) analysis has been used to account for dynamic behaviors such as the sequence-dependent, functional-dependent, and priority relationships among the failures of basic events. Various methodologies have been developed to analyze a DFT; however, most methods require a complex analytical procedure or a significant simulation time for an accurate analysis. In this paper, a stochastic computational approach is proposed for an efficient analysis of the top event's failure probability in a DFT with priority AND (PAND) gates. A stochastic model is initially proposed for a two-input PAND gate, and a successive cascading model is then presented for a general multiple-input PAND gate. A stochastic approach using the proposed models provides an efficient analysis of a DFT compared to an accurate analysis or algebraic approach. The accuracy of a stochastic analysis increases with the length of random binary bit streams in stochastic computation. The use of non-Bernoulli sequences of random permutations of fixed counts of 1s and 0s as initial input events' probabilities makes the stochastic approach more efficient, and more accurate than Monte Carlo simulation. Non-exponential failure distributions and repeated events are readily handled by the stochastic approach. The accuracy, efficiency, and scalability of the stochastic approach are shown by several case studies of DFT analysis.

With regard to the AMFM characteristics, and especially the cyclostationarity of gear vibrations, cyclic spectral analysis is used to extract the modulation features of gearbox vibration signals to detect and assess localized gear damage. The explicit equation for the cyclic spectral density in a closed form for AMFM signals is deduced, and its properties in the joint cyclic frequency-frequency domain are summarized. The ratio between the sum of the cyclic spectral density magnitude along the frequency axis at the cyclic frequencies of modulating frequency and 0 Hz varies monotonically with the amplitude modulation magnitude. Hence it is useful to track modulation magnitude. Localized gear damage generates periodic impulses, and its growth increases the magnitude of periodic impulses. Consequently, the amplitude modulation magnitude of gear AMFM vibration signals increases. Hence the ratio can be used as an indicator of the health condition of gearboxes. The analysis of both gear crack simulation vibration signals and gearbox lifetime experiments shows a globally monotonic increase as gear damage severity increases. The proposed approach has the potential to assess the health of gearboxes, and predict severe damage.

Thek-out-of-n:Gsystem is widely used in reliability and maintenance engineering. We consider a generalk-out-of-n:Gsystem which has identical components with identical repair time and lifetime distributions. There areRidentical repairmen in the system. The shut-off rules of suspended animation, continuous operation, and a mixture of these two are studied. Repair times and lifetimes are assumed to be statistically independent and exponentially distributed (within, and between). We derive new closed form solutions for important performance measures including steady state availability, mean time to system failure, and mean time to first system failure.

The multi-state$k$-out-of-$n$system model finds wide applications in industry, and has been extensively studied in recent years. This model has also been generalized to the multi-state weighted$k$-out-of-$n$system model. Recursive methods, and universal generating functions (UGF) are two primary algorithms for exact performance evaluation of multi-state$k$-out-of-$n$systems. However the computational burden becomes the crucial factor when there is a “dimension damnation” problem caused by the increase in the number of components in the system, and the number of possible states a component may be in. In situations wherein exact values of system reliability are not necessary, we may use more efficient algorithms to approximate system reliability. In this paper, we develop a comprehensive framework for reliability approximation of multi-state weighted$k$-out-of-$n$systems. Two fuzzy based multi-state weighted$k$-out-of-$n$system models are defined. Procedures for building these two models from the conventional models are also introduced. The fuzzy recursive methods, and fuzzy UGF techniques are developed to evaluate such systems. The clustering technique, and curve fitting method are used to determine the fuzzy weights, and probabilities of states in the models.

A multi-state system (MSS) model is a more flexible tool for representing engineering systems than the conventional binary system model, which has been widely studied in recent research. The multi-state weightedk-out-of-nsystem model is the generalization of the multi-statek-out-of-nsystem model, where the componentiin statejcarries a certain utility. In this paper, we propose a multi-state system structure called hierarchical weighted multi-statek-out-of-nsystems. In such a system, the structure of the system can be decomposed into different hierarchical levels, and a subsystem at each level can be represented using a multi-state weightedk-out-of-nstructure. The proposed system structure can find applications in many real life systems, and a municipal infrastructure is a typical example of such a structure. The definition of the hierarchical multi-state weightedk-out-of-nsystem model is proposed in this paper. Universal generating functions (UGF) are used to evaluate reliabilities of the defined systems. Moreover, to reduce computational complexity, recursive algorithms are developed to obtain lower, and upper bounds of the defined system reliabilities.

The signature of a system is a useful tool in a variety of applications including the evaluation of the reliability characteristics of systems, and the comparison of the performance of competing systems. We study the evaluation and application of signatures of systems involving two common failure criteria which are common in real life applications. The failure or survival of these systems generally depends on the number of consecutively failed or working components, or total number of failed or working components in the whole system. We provide a method for obtaining the signatures of such systems. Applications of the results are also presented.

The development of accurate health condition prediction approaches has been a key research topic in condition based maintenance (CBM) in recent years. However, current health condition prediction approaches are not accurate enough, which has become the bottleneck for achieving the full power of CBM. Neural network based methods have been considered to be a very promising category of methods for equipment health condition prediction. In this paper, we propose a neural network prediction model called extended recurrent neural network (ERNN). An ERNN based approach is developed for health condition prediction of gearboxes based on the vibration data collected from a gearbox experimental system. The results demonstrate the capability of the ERNN based approach for producing satisfactory health condition prediction results. A comparative study based on the gearbox experiment data further establishes ERNN as an effective recurrent neural network model for equipment health condition prediction.

Preventive maintenance (PM) is a maintenance program with activities initiated at predetermined intervals, or according to prescribed criteria, and intended to reduce the probability of failure, or the degradation of the functioning of an item. In the literature, a number of PM models have been introduced to depict the effectiveness of PM. Based on these models, approaches to scheduling PM policies have been considerably studied. This paper attempts to review existing PM models, and investigate their inter-relationships. We then categorize these models into three classes: linear, nonlinear, and a hybrid of both. These three PM model classes depict the relationships of the hazard functions before, and after a PM. Possible extensions to these three PM models are discussed. The statistical properties for models are derived, and approaches to optimizing the PM policy are given.

Compared with a binary system model, a multi-state system model provides a more flexible tool for representing engineering systems in real life. In conventional multi-state theory, it is assumed that the exact probability and performance level of each component state are given. However, it may be difficult to obtain sufficient data to estimate the precise values of these probabilities and performance levels in many highly reliable modern engineering systems. New techniques are needed to solve these fundamental problems. A general fuzzy multi-state system model is proposed in this article to overcome these deficiencies. The basic definitions and assumptions of such systems are introduced. The concepts of relevancy, coherency, and equivalence are used to characterize the properties of such systems. Future research directions include performance evaluation algorithms for the defined fuzzy multi-state systems.

Algorithms have been available for exact performance evaluation of multi-state k-out-of-n systems. However, especially for complex systems with a large number of components, and a large number of possible states, obtaining "reliability bounds" would be an interesting, significant issue. Reliability bounds will give us a range of the system reliability in a much shorter computation time, which allow us to make decisions more efficiently. The systems under consideration are multi-state k-out-of-n systems with i.i.d. components. We will focus on the probability of the system in states below a certain state d, denoted by Qsd. Based on the recursive algorithm proposed by Zuo & Tian [14] for performance evaluation of multi-state k-out-of-n systems with i.i.d. components, a reliability bounding approach is developed in this paper. The upper, and lower bounds of Qsdare calculated by reducing the length of the k vector when using the recursive algorithm. Using the bounding approach, we can obtain a good estimate of the exact Qsdvalue while significantly reducing the computation time. This approach is attractive, especially to complex systems with a large number of components, and a large number of possible states. A numerical example is used to illustrate the significance of the proposed bounding approach.

Current studies of the optimal design of multi-state series-parallel systems often focus on the problem of determining the optimal redundancy for each stage. However, this is only a partial optimization. There are two options to improve the system utility of a multi-state series-parallel system: 1) to provide redundancy at each stage, and 2) to improve the component state distribution, that is, make a component in states with respect to higher utilities with higher probabilities. This paper presents an optimization model for a multi-state series-parallel system to jointly determine the optimal component state distribution, and optimal redundancy for each stage. The relationship between component state distribution, and component cost is discussed based on an assumption on the treatment on the components. An example is used to illustrate the optimization model with its solution approach, and that the proposed reliability-redundancy allocation model is superior to the current redundancy allocation models.

Dual-failure scenarios are a real possibility in today's optical networks and it is becoming more and more important for carriers and network operators to consider them when designing their networks. In this paper, we develop and analyze a linear programming model to design ap-cycle network to meet a user-specified minimum dual failure restorability. Results show thatp-cycle networks designed for single-failure restorability only exhibit some inherent dual-failure restorability, and that explicitly providing dual-failure restorability is less costly in more richly connected networks.

Fault diagnosis plays an important role in ensuring system reliability. Accurate fault diagnosis relies on data, fault features, diagnostic knowledge, reasoning, and decision-making. The following issues such as certainty and sufficiency of collected data, importance of features in diagnosis, and accuracy of diagnostic knowledge affect the accuracy of fault diagnosis greatly. Dempster-Shafer (D-S) evidence theory based multi-information fusion can provide a mechanism for representation of uncertain and imprecise information. However, it cannot directly handle the issues of evidence sufficiency, evidence importance, or conflicting evidences. An improved D-S evidence theory through the introduction of a fuzzy membership function, importance indexes, and conflict factors is reported in this paper. Experiment analysis results indicate that the proposed method is effective for practical fault diagnosis

In this paper, we provide an algorithm for evaluating the system state distribution for any multi-state consecutive-k-out-of-n:G system including the decreasing multi-state G system, the increasing multi-state G system, and other G systems. We evaluated our proposed algorithms in terms of the orders of computation time, and memory requirement. Furthermore, we conducted a numerical experiment to determine the actual computation time. Our proposed algorithm is more effective for systems with a large n.

The generalized multi-state k-out-of-n:G system model defined by Huang provides more flexibilities for modeling of multi-state systems. However, the performance evaluation algorithm they proposed for such systems is not efficient, and it is applicable only when the k/sub i/ values follow a monotonic pattern. In this paper, we defined the concept of generalized multi-state k-out-of-n:F systems. There is an equivalent generalized multi-state k-out-of-n:G system with respect to each generalized multi-state k-out-of-n:F system, and vice versa. The form of minimal cut vector for generalized multi-state k-out-of-n:F systems is presented. An efficient recursive algorithm based on minimal cut vectors is developed to evaluate the state distributions of a generalized multi-state k-out-of-n:F system. Thus, a generalized multi-state k-out-of-n:G system can first be transformed to the equivalent generalized multi-state k-out-of-n:F system, and then be evaluated using the proposed recursive algorithm. Numerical examples are given to illustrate the effectiveness and efficiencies of the proposed recursive algorithms.

In this paper, we propose a definition of the dominant multi-state system. Under the proposed definition, multi-state systems are divided into two groups without reference to component relevancy conditions: dominant systems, and nondominant systems. Dominant systems can be further divided into two groups: with binary image, and without binary image. A multi-state system with binary image implies that its structure function can be expressed in terms of binary structure functions such that it can be treated as a binary system structure, and existing algorithms for reliability evaluation of binary systems can be applied for system performance evaluation. A technique is provided for establishing the bounds of performance distribution of dominant systems without binary image. The properties of dominant systems are studied. Examples are given to illustrate applications of the proposed definitions and methods.

We combine independent component analysis in the frequency domain (ICA-FD) and Morlet wavelet filtering for gearbox fault diagnosis. Collected vibration signals from a gearbox are separated into two components with ICA-FD. Morlet wavelet filtering is then applied to the separated components. The optimal shape parameter, /spl beta/, of the basic Morlet wavelet is obtained by minimizing the wavelet entropy. Better diagnosis results are obtained with this combination than using wavelet filtering alone.

In a binary k-out-of-n:G system, k is the minimum number of components that must work for the system to work. Let 1 represent the working state and 0 the failure state, k then indicates the minimum number of components that must be in state 1 for the system to be in state 1. This paper defines the multi-state k-out-of-n:G system: each component and the system can be in 1 of M+1 possible states: 0, 1, ..., M. In Case I, the system is in state /spl ges/j iff at least k/sub j/ components are in state /spl ges/j. The value of k/sub j/ I 1 can be different for different required minimum system-state level j. Examples illustrate applications of this definition. Algorithms for reliability evaluation of such systems are presented.

Based on a real industrial application, three new system reliability models are proposed: combined k-out-of-n:F and consecutive-k/sub c/-out-of-n:F system; combined k-out-of-m/spl middot/n:F and linear connected-(r,s)-out-of-(m,n):F system; and combined k-out-of-m/spl middot/n:F consecutive-k/sub c/-out-of-n:F and linear connected-(r,s)-out-of-(m,n):F system. Reliability evaluation algorithms are provided for these models. The computation times of the algorithms for these models are, respectively: O(n/spl middot/k), O(k/spl middot/n/spl middot/2/sup m//spl middot/s/sup m-r+2/), O(k/spl middot/n/spl middot/(2k/sub c/)/sup m/spl middot//s/sup m-r+1/). The algorithms are used for system reliability evaluation of furnace systems. The concept of the combined k-out-of-n:F and 1-dimensional and 2-dimensional consecutive-k-out-of-n:F systems can be extended to other variations of the consecutive-k-out-of-n:F systems, e.g., the consecutive-k-out-of-n:G system and 1-dimensional and 2-dimensional r-within-k-out-of-n:F systems. The concept of Markov chain imbeddable (MIS) systems is another excellent tool that can be used for analysis of such combined system structures.

Object-oriented Petri nets with changeable structure (OPNs-CS) is capable of modeling a system with uncertainty and subject to change. Prevention of occurrence of conflicts and deadlock in a system controlled based on an OPNs-CS model is essential to ensure that the system functions. Formal descriptions of three conflicts in OPNs-CS and the algorithms for identifying the changes to conflicts are presented, which is important for automatic OPNs-CS model building and conflict resolution. In addition, there is given an algorithm for deadlock detection that is based on O-graph of the equivalent OPNs-CS (EOPNs-CS) model rather than that of OPNs-CS model. The substitution of EOPNs-CS for OPNs-CS dramatically reduces the size and complexity of O-graph and makes the detection much simplified.