Effective bearing fault diagnosis is vital for the safe and reliable operation of rotating machinery. In practical applications, bearings often work at various rotational speeds as well as load conditions. Yet, the bearing fault diagnosis under multiple conditions is a new subject, which needs to be further explored. Therefore, a multi-scale deep belief network (DBN) method integrated with attention mechanism is proposed for the purpose of extracting the multi-scale core features from vibration signals, containing four primary steps: preprocessing of multi-scale data, feature extraction, feature fusion, and fault classification. The key novelties include multi-scale feature extraction using multi-scale DBN algorithm, and feature fusion using attention mechanism. The benchmark dataset from University of Ottawa is applied to validate the effectiveness as well as advantages of this method. Furthermore, the aforementioned method is compared with four classical fault diagnosis methods reported in the literature, and the comparison results show that our proposed method has higher diagnostic accuracy and better robustness.
The dynamic wireless communication network is a complex network that needs to consider various influence factors including communication devices, radio propagation, network topology, and dynamic behaviors. Existing works focus on suggesting simplified reliability analysis methods for these dynamic networks. As one of the most popular modeling methodologies, the dynamic Bayesian network (DBN) is proposed. However, it is insufficient for the wireless communication network which contains temporal and non-temporal events. To this end, we present a modeling methodology for a generalized continuous time Bayesian network (CTBN) with a 2-state conditional probability table (CPT). Moreover, a comprehensive reliability analysis method for communication devices and radio propagation is suggested. The proposed methodology is verified by a reliability analysis of a real wireless communication network.
Degradation and overstress failures occur in many electronic systems in which the operation load and environmental conditions are complex. The dependency of them called dependent competing failure process (DCFP), has been widely studied. Electronic system may experience mutual effects of degradation and shocks, they are considered to be interdependent. Both the degradation and the shock processes will decrease the limit of system and cause cumulative effect. Finally, the competition of hard and soft failure will cause the system failure. Based on the failure mechanism accumulation theory, this paper constructs the shock-degradation acceleration and the threshold descent model, and a system reliability model established by using these two models. The mutually DCFP effect of electronic system interaction has been decomposed into physical correlation of failure, including acceleration, accumulation and competition. As a case, a reliability of electronic system in aeronautical system has been analyzed with the proposed method. The method proposed is based on failure physical evaluation, and could provide important reference for quantitative evaluation and design improvement of the newly designed system in case of data deficiency.
Convolutional neural networks (CNNs) are well suited to bearing fault classification due to their ability to learn discriminative spectro-temporal patterns. However, gathering sufficient cases of faulty conditions in real-world engineering scenarios to train an intelligent diagnosis system is challenging. This paper proposes a fault diagnosis method combining several augmentation schemes to alleviate the problem of limited fault data. We begin by identifying relevant parameters that influence the construction of a spectrogram. We leverage the uncertainty principle in processing time-frequency domain signals, making it impossible to simultaneously achieve good time and frequency resolutions. A key determinant of this phenomenon is the window function’s choice and length used in implementing the short-time Fourier transform. The Gaussian, Kaiser, and rectangular windows are selected in the experimentation due to their diverse characteristics. The overlap parameter ’s size also influences the outcome and resolution of the spectrogram. A 50% overlap is used in the original data transformation, and ±25% is used in implementing an effective augmentation policy to which two-stage regular CNN can be applied to achieve improved performance. The best model reaches an accuracy of 99.98% and a cross-domain accuracy of 92.54%. When combined with data augmentation, the proposed model yields cutting-edge results.
A fractional-order cumulative optimization GM(1,2) model based on grey theory is proposed to study the relationship between torpedo loading and working reliabilities. In this model, the average relative error function related to order and background value is established. Taking the average relative error function as the objective function, the optimal value of the two parameters is obtained through the optimization method, and the minimum value of the average relative error is determined. The calculation example shows that this method can greatly improve the accuracy of the model and more accurately reflect the relationship between torpedo loading and working reliabilities compared with the traditional GM(1,2) model.
The reliability-based selective maintenance (RSM) decision problem of systems with components that have multiple dependent performance characteristics (PCs) reflecting degradation states is addressed in this paper. A vine-Copula-based reliability evaluation method is proposed to estimate the reliability of system components with multiple PCs. Specifically, the marginal degradation reliability of each PC is built by using the Wiener stochastic process based on the PC’s degradation mechanism. The joint degradation reliability of the component with multiple PCs is established by connecting the marginal reliability of PCs using D-vine. In addition, two RSM decision models are developed to ensure the system accomplishes the next mission. The genetic algorithm (GA) is used to solve the constraint optimization problem of the models. A numerical example illustrates the application of the proposed RSM method.
Solar arrays are important and indispensable parts of spacecraft and provide energy support for spacecraft to operate in orbit and complete on-orbit missions. When a spacecraft is in orbit, because the solar array is exposed to the harsh space environment, with increasing working time, the performance of its internal electronic components gradually degrade until abnormal damage occurs. This damage makes solar array power generation unable to fully meet the energy demand of a spacecraft. Therefore, timely and accurate detection of solar array anomalies is of great significance for the on-orbit operation and maintenance management of spacecraft. In this paper, we propose an anomaly detection method for spacecraft solar arrays based on the integrated least squares support vector machine (ILS-SVM) model: it selects correlated telemetry data from spacecraft solar arrays to form a training set and extracts n groups of training subsets from this set, then gets n corresponding least squares support vector machine (LS-SVM) submodels by training on these training subsets, respectively; after that, the ILS-SVM model is obtained by integrating these submodels through a weighting operation to increase the prediction accuracy and so on; finally, based on the obtained ILS-SVM model, a parameter-free and unsupervised anomaly determination method is proposed to detect the health status of solar arrays. We use the telemetry data set from a satellite in orbit to carry out experimental verification and find that the proposed method can diagnose solar array anomalies in time and can capture the signs before a solar array anomaly occurs, which reflects the applicability of the method.
Remaining useful life (RUL) prediction is one of the most crucial components in prognostics and health management (PHM) of aero-engines. This paper proposes an RUL prediction method of aero-engines considering the randomness of failure threshold. Firstly, a random-coefficient regression (RCR) model is used to model the degradation process of aero-engines. Then, the RUL distribution based on fixed failure threshold is derived. The prior parameters of the degradation model are calculated by a two-step maximum likelihood estimation (MLE) method and the random coefficient is updated in real time under the Bayesian framework. The failure threshold in this paper is defined by the actual degradation process of aero-engines. After that, a expectation maximization (EM) algorithm is proposed to estimate the underlying failure threshold of aero-engines. In addition, the conditional probability is used to satisfy the limitation of failure threshold. Then, based on above results, an analytical expression of RUL distribution of aero-engines based on the RCR model considering random failure threshold (RFT) is derived in a closed-form. Finally, a case study of turbofan engine is used to demonstrate the effectiveness and superiority of the RUL prediction method and the parameters estimation method of failure threshold proposed.
The existing software bug localization models treat the source file as natural language, which leads to the loss of syntactical and structure information of the source file. A bug localization model based on syntactical and semantic information of source code is proposed. Firstly, abstract syntax tree (AST) is divided based on node category to obtain statement sequence. The statement tree is encoded into vectors to capture lexical and syntactical knowledge at the statement level. Secondly, the source code is transformed into vector representation by the sequence naturalness of the statement. Therefore, the problem of gradient vanishing and explosion caused by a large AST size is obviated when using AST to the represent source code. Finally, the correlation between bug reports and source files are comprehensively analyzed from three aspects of syntax, semantics and text to locate the buggy code. Experiments show that compared with other standard models, the proposed model improves the performance of bug localization, and it has good advantages in mean reciprocal rank (MRR), mean average precision (MAP) and Top N Rank.
Remaining useful life (RUL) prediction is one of the most crucial elements in prognostics and health management (PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression (RCR) model with fusing failure time data. Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures, the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function (PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.
The reliability evaluation of a multistate network is primarily based on d-minimal paths/cuts (d-MPs/d-MCs). However, being a nondeterminism polynomial hard (NP-hard) problem, searching for all d-MPs is a rather challenging task. In existing implicit enumeration algorithms based on minimal paths (MPs), duplicate d-MP candidates may be generated. An extra step is needed to locate and remove these duplicate d-MP candidates, which costs significant computational effort. This paper proposes an efficient method to prevent the generation of duplicate d-MP candidates for implicit enumeration algorithms for d-MPs. First, the mechanism of generating duplicate d-MP candidates in the implicit enumeration algorithms is discussed. Second, a direct and efficient avoiding-duplicates method is proposed. Third, an improved algorithm is developed, followed by complexity analysis and illustrative examples. Based on the computational experiments comparing with two existing algorithms, it is found that the proposed method can significantly improve the efficiency of generating d-MPs for a particular demand level d.
Component reallocation (CR) is receiving increasing attention in many engineering systems with functionally interchangeable and unbalanced degradation components. This paper studies a CR and system replacement maintenance policy of series repairable systems, which undergoes minimal repairs for each emergency failure of components, and considers constant downtime and cost of minimal repair, CR and system replacement. Two binary mixed integer nonlinear programming models are respectively established to determine the assignment of CR, and the uptime right before CR and system replacement with the objective of minimizing the system average maintenance cost and maximizing the system availability. Further, we derive the optimal uptime right before system replacement with maximization of the system availability, and then give the relationship between the system availability and the component failure rate. Finally, numerical examples show that the CR and system replacement maintenance policy can effectively reduce the system average maintenance cost and improve the system availability, and further give the sensitivity analysis and insights of the CR and system replacement maintenance policy.
According to the requirements of the live-virtual-constructive (LVC) tactical confrontation (TC) on the virtual entity (VE) decision model of graded combat capability, diversified actions, real-time decision-making, and generalization for the enemy, the confrontation process is modeled as a zero-sum stochastic game (ZSG). By introducing the theory of dynamic relative power potential field, the problem of reward sparsity in the model can be solved. By reward shaping, the problem of credit assignment between agents can be solved. Based on the idea of meta-learning, an extensible multi-agent deep reinforcement learning (EMADRL) framework and solving method is proposed to improve the effectiveness and efficiency of model solving. Experiments show that the model meets the requirements well and the algorithm learning efficiency is high.
This paper presents a joint optimization policy of preventive maintenance (PM) and spare ordering for single-unit systems, which deteriorate subject to the delay-time concept with three deterioration stages. PM activities that combine a non-periodic inspection scheme with age-replacement are implemented. When the system is detected to be in the minor defective stage by an inspection for the first time, place an order and shorten the inspection interval. If the system has deteriorated to a severe defective stage, it is either repaired imperfectly or replaced by a new spare. However, an immediate replacement is required once the system fails, the maximal number of imperfect maintenance (IPM) is satisfied or its age reaches to a pre-specified threshold. In consideration of the spare ’s availability as needed, there are three types of decisions, i.e., an immediate or a delayed replacement by a regular ordered spare, an immediate replacement by an expedited ordered spare with a relative higher cost. Then, some mutually independent and exclusive renewal events at the end of a renewal cycle are discussed, and the optimization model of such a joint policy is further developed by minimizing the long-run expected cost rate to find the optimal inspection and age-replacement intervals, and the maximum number of IPM. A Monte-Carlo based integration method is also designed to solve the proposed model. Finally, a numerical example is given to illustrate the proposed joint optimization policy and the performance of the Monte-Carlo based integration method.
Aiming to evaluate the reliability of phase-transition degrading systems, a generalized stochastic degradation model with phase transition is constructed, and the corresponding analytical reliability function is formulated under the concept of the first hitting time. The phase-varying stochastic property and the phase-varying nonlinearity are considered simultaneously in the proposed model. To capture the phase-varying stochastic property, a Wiener process is adopted to model the non-monotonous degradation phase, while a Gamma process is utilized to model the monotonous one. In addition, the phase-varying nonlinearity is captured by different transformed time scale functions. To facilitate the practical application of the proposed model, identification of phase model type and estimation of model parameters are discussed, and the initial guesses for parameters optimization are also given. Based on the constructed model, two simulation studies are carried out to verify the analytical reliability function and analyze the influence of model misspecification. Finally, a practical case study is conducted for illustration.
In this paper, we focus on the failure analysis of unmanned autonomous swarm (UAS) considering cascading effects. A framework of failure analysis for UAS is proposed. Guided by the framework, the failure analysis of UAS with crash fault agents is performed. Resilience is used to analyze the processes of cascading failure and self-repair of UAS. Through simu-lation studies, we reveal the pivotal relationship between resilience, the swarm size, and the percentage of failed agents. The simulation results show that the swarm size does not affect the cascading failure process but has much influence on the process of self-repair and the final performance of the swarm. The results also reveal a tipping point exists in the swarm. Meanwhile, we get a counter-intuitive result that larger-scale UAS loses more resilience in the case of a small percentage of failed individuals, suggesting that the increasing swarm size does not necessarily lead to high resilience. It is also found that the temporal degree failure strategy performs much more harmfully to the resilience of swarm systems than the random failure. Our work can provide new insights into the mechanisms of swarm collapse, help build more robust UAS, and develop more efficient failure or protection strategies.
An effective maintenance policy optimization model can reduce maintenance cost and system operation risk. For mission-oriented systems, the degradation process changes dynamically and is monotonous and irreversible. Meanwhile, the risk of early failure is high. Therefore, this paper proposes a dynamic condition-based maintenance (CBM) optimization model for mission-oriented system based on inverse Gaussian (IG) degradation process. Firstly, the IG process with random drift coefficient is used to describe the degradation process and the relevant probability distributions are obtained. Secondly, the dynamic preventive maintenance threshold (DPMT) function is used to control the early failure risk of the mission-oriented system, and the influence of imperfect preventive maintenance (PM) on the degradation amount and degradation rate is analysed comprehensively. Thirdly, according to the mission availability requirement, the probability formulas of different types of renewal policies are obtained, and the CBM optimization model is constructed. Finally, a numerical example is presented to verify the proposed model. The comparison with the fixed PM threshold model and the sensitivity analysis show the effectiveness and application value of the optimization model.
Electric power is widely used as the main energy source of ship integrated power system (SIPS), which contains power network and electric power network. SIPS network reconfiguration is a non-linear large-scale problem. The reconfiguration solution influences the safety and stable operation of the power system. According to the operational characteristics of SIPS, a simplified model of power network and a mathematical model for network reconfiguration are established. Based on these models, a multi-agent and ant colony optimization (MAACO) is proposed to solve the problem of network reconfiguration. The simulations are carried out to demonstrate that the optimization method can reconstruct the integrated power system network accurately and efficiently.
Rolling element bearings are machine components used to allow circular movement and hence deliver forces between components of machines used in diverse areas of industry. The likelihood of failure has the propensity of increasing under prolonged operation and varying working conditions. Hence, the accurate fault severity categorization of bearings is vital in diagnosing faults that arise in rotating machinery. The variability and complexity of the recorded vibration signals pose a great hurdle to distinguishing unique characteristic fault features. In this paper, the efficacy and the leverage of a pre-trained convolutional neural network (CNN) is harnessed in the implementation of a robust fault classification model. In the absence of sufficient data, this method has a high-performance rate. Initially, a modified VGG16 architecture is used to extract discriminating features from new samples and serves as input to a classifier. The raw vibration data are strategically segmented and transformed into two representations which are trained separately and jointly. The proposed approach is carried out on bearing vibration data and shows high-performance results. In addition to successfully implementing a robust fault classification model, a prognostic framework is developed by constructing a health indicator (HI) under varying operating conditions for a given fault condition.
Recently, the physics-of-failure (PoF) method has been more and more popular in engineering to understand the failure mechanisms (FMs) of products. However, due to the lack of system modeling methods and problem-solving algorithms, the information of FMs cannot be used to evaluate system reliability. This paper presents a system reliability evaluation method with failure mechanism tree (FMT) considering physical dependency (PDEP) such as competition, trigger, acceleration, inhibition, damage accumulation, and parameter combination. And the binary decision diagram (BDD) analytical algorithm is developed to establish a system reliability model. The operation rules of ite operators for generating BDD are discussed. The flow chart of system reliability evaluation method based on FMT and BDD is proposed. The proposed method is applied in the case of an electronic controller drive unit. Results show that the method is effective to evaluate system reliability from the perspective of FM.
The planetary reducer is a common type of transmission mechanism, which can provide high transmission accuracy and has been widely used, and it is usually required with high reliability of transmission characteristics in practice. During the manufacturing and usage stages of planetary reducers, uncertainties are ubiquitous and wear is inevitable, which affect the transmission characteristics and the reliability of planetary reducers. In this paper, belief reliability modeling and analysis considering multi-uncertainties and wear are proposed for planetary reducers. Firstly, based on the functional principle and the influence of wear, the performance margin degradation model is established using the hysteresis error as the key performance parameter, where the degradation is mainly caused by the accumulated wear. After that, multi-source uncertainties are analyzed and quantified separately, including manufacturing errors, uncertainties in operational and environmental conditions, and uncertainties in performance thresholds. Finally, the belief reliability model is established based on the performance margin degradation model. A case study of a planetary reducer is applied and the reliability sensitivity analysis is implemented to show the practicability of the proposed method. The results show that the proposed method can provide some suggestions to the design and manufacturing phases of the planetary reducer.
Navigation via signals of opportunity (NAVSOP) is able to realize positioning by making use of hundreds of different signals that are all around us. A method to realize NAVSOP for low earth orbit (LEO) satellites is proposed in this paper, in which the global navigation satellite system (GNSS) authorized signals are utilized as the signal of opportunity (SOP). At first, the carrier recovery technique is studied under the premise that the pseudo-code is unknown. Secondly, a method based on characteristics of Doppler frequency shift is proposed to recognize the navigation satellites. Thirdly, the extended Kalman filter (EKF) is utilized to estimate the orbital parameters by using carrier phase measurements. Finally, the proposed method is evaluated by using signals generated by a satellite navigation data simulator. The simulation results show that the proposed method can successfully realize navigation via GNSS authorized signals.
In complex systems, functional dependency and physical dependency may have a coupling effect. In this paper, the reliability of a k-out-of-n system is analyzed considering load-sharing effect and failure mechanism (FM) propagation. Three types of FMs are considered and an accumulative damage model is proposed to illustrate the system behavior of the k-out-of-n system and the coupling effect between load-sharing effect and FM propagation effect. A combinational algorithm based on Binary decision diagram (BDD) and Monte-Carlo simulation is presented to evaluate the complex system behavior and reliability of the k-out-of-n system. A current stabilizing system that consists of a 3-out-of-6 subsystem with FM propagation effect is presented as a case to illustrate the complex behavior and to verify the applicability of the proposed method. Due to the coupling effect change, the main mechanism and failure mode will be changed, and the system lifetime is shortened. Reasons are analyzed and results show that different sensitivity factors of three different FMs lead to the change of the development rate, thus changing the failure scenario. Neglecting the coupling effect may lead to an incomplete and ineffective measuring and monitoring plan. Design strategies must be adopted to make the FM propagation insensitive to load-sharing effect.
Fiber optical gyroscope (FOG) is a highly reliable navigation element, and the degradation trajectories of its two accuracy indexes are monotonic and non-monotonic respectively. In this paper, a flexible accelerated degradation testing (ADT) model is used for analyzing the bivariate dependent degradation process of FOG. The time-varying copulas are employed to consider the dynamic dependency structure between two marginal degradation processes as the Wiener process and the inverse Gaussian process. The statistical inference is implemented by utilizing an inference function for the margins (IFM) approach. It is demonstrated that the proposed method is powerful in modeling the joint distribution with various margins.
Test selection is to select the test set with the least total cost or the least total number from the alternative test set on the premise of meeting the required testability indicators. The existing models and methods are not suitable for system level test selection. The first problem is the lack of detailed data of the units’ fault set and the test set, which makes it impossible to establish a traditional dependency matrix for the system level. The second problem is that the system level fault detection rate and the fault isolation rate (referred to as "two rates") are not enough to describe the fault diagnostic ability of the system level tests. An innovative dependency matrix (called combinatorial dependency matrix) composed of three submatrices is presented. The first problem is solved by simplifying the submatrix between the units’ fault and the test, and the second problem is solved by establishing the system level fault detection rate, the fault isolation rate and the integrated fault detection rate (referred to as "three rates") based on the new matrix. The mathematical model of the system level test selection problem is constructed, and the binary genetic algorithm is applied to solve the problem, which achieves the goal of system level test selection.
This paper proposes reliability and maintenance models for systems suffering random shocks arriving according to a non-homogeneous Poisson process. The system degradation process include two stages: from the installation of a new system to an initial point of a defect (normal stage), and then from that point to failure (defective stage), following the delay time concept. By employing the virtual age method, the impact of external shocks on the system degradation process is characterized by random virtual age increment in the two stages, resulting in the corresponding two-stage virtual age process. When operating in the defective state, the system becomes more susceptible to fatigue and suffers from a greater aging rate. Replacement is carried out either on failure or on the detection of a defective state at periodic or opportunistic inspections. This paper evaluates system reliability performance and investigates the optimal opportunistic maintenance policy. A case study on a cooling system is given to verify the obtained results.
The availability of a periodic inspection system under mixed maintenance policies is studied in this paper. To accommodate the characteristic of multiple failure modes for complex systems, the system failures can be divided into two failure modes: hard failure and soft failure. When hard failure occurs, the corresponding corrective maintenance will be performed, taking a random time under the perfect maintenance policy; in contrast, if the soft failure is found, the corresponding preventive maintenance will be performed, taking a random time under the imperfect maintenance policy. The dynamic age setback model is adopted for imperfect maintenance, which can accurately reflect the fault characteristics of the degraded system. Then an analytical model for system steady state availability and instantaneous availability are derived. Moreover, the optimal method to maximize the system steady-state availability through adjusting the inspection interval is researched. According to the above research, the optimization of system unit time cost, preventive maintenance intervals and availability is researched. Finally, the developed approach is demonstrated by a numerical example.
Due to the simplicity and flexibility of the power law process, it is widely used to model the failures of repairable systems. Although statistical inference on the parameters of the power law process has been well developed, numerous studies largely depend on complete failure data. A few methods on incomplete data are reported to process such data, but they are limited to their specific cases, especially to that where missing data occur at the early stage of the failures. No framework to handle generic scenarios is available. To overcome this problem, from the point of view of order statistics, the statistical inference of the power law process with incomplete data is established in this paper. The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method. Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework. The results show that the proposed method has more flexibility and more applicability.
The optimization of inspection intervals for composite structures has been proposed, but only one damage type, dent damage, has been addressed so far. The present study focuses on the two main damage types of dent and delamination, and a model for optimizing the inspection interval of composite structures is proposed to minimize the total maintenance cost on the premise that the probability of structure failure will not exceed the acceptable level. In order to analyze the damage characteristics and the residual strength of the composite structure, the frequency, energy, size, and depth of the damage are studied, and the situation of missing detection during the inspection is considered. The structural residual strength and total maintenance cost are quantified corresponding to different inspection intervals. The proposed optimization method relieves the constraints in previous simulation methods, and is more consistent with the actual situation. Finally, the outer wing of aircraft is taken as an example, and with the historical cases and experimental data, the optimization method is verified. The optimal inspection interval is shorter than the actually implemented inspection interval, and the corresponding maintenance cost is reduced by 23.3%. The result shows the feasibility and effectiveness of the proposed optimization method.
Condition-based maintenance (CBM) is receiving increasing attention in various engineering systems because of its effectiveness. This paper formulates a new CBM optimization problem for continuously monitored degrading systems considering imperfect maintenance actions. In terms of maintenance actions, in practice, they scarcely restore the system to an as-good-as new state due to residual damage. According to up-to-data researches, imperfect maintenance actions are likely to speed up the degradation process. Regarding the developed CBM optimization strategy, it can balance the maintenance cost and the availability by the searching the optimal preventive maintenance threshold. The maximum number of maintenance is also considered, which is regarded as an availability constraint in the CBM optimization problem. A numerical example is introduced, and experimental results can demonstrate the novelty, feasibility and flexibility of the proposed CBM optimization strategy.
