Artificial intelligence (AI)-enhanced automated fault diagnosis (AFD) has become increasingly popular for chiller fault diagnosis with promising classification performance. In practice, a sufficient number of fault samples are required by the AI methods in the training phase. However, faulty training samples are generally much more difficult to be collected than normal training samples. Data augmentation is introduced in these scenarios to enhance the training data set with synthetic data. In this study, a variational autoencoder-based conditional Wasserstein GAN with gradient penalty (CWGAN-GP-VAE) is proposed to diagnose various faults for chillers. A detailed comparative study has been conducted with real-world fault data samples to verify the effectiveness and robustness of the proposed methodology.Note to Practitioners—This work attacks the fact that faulty training samples are usually much harder to be collected than the normal training samples in the practice of chiller automated fault diagnosis (AFD). Modern supervised learning chiller AFD relies on a sufficient number of faulty training samples to train the classifier. When the number of faulty training samples is insufficient, the conventional AFD methods fail to work. This study proposed a variational autoencoder-based conditional Wasserstein GAN with gradient penalty (CWGAN-GP-VAE) framework for generating synthetic faulty training samples to enrich the training data set for machine learning-based AFD methods. The proposed algorithm has been carefully designed, implemented, and practically proved to be more effective than the existing methods in the literature.

Resource availability of cloud computing systems is vital for today's information infrastructures. However, the constituent computing nodes are not fault free. The availability requirements on the delivered computing resources should be defined clearly by using a formal, contractual agreement, known as the Service Level Agreement (SLA), between providers and customers. To reduce the risk of various SLA violations, an efficient analysis of resource availability is important. This paper proposes a new analytical approach based on multi-valued decision diagrams (MDD) for the efficient resource availability analysis of cloud computing systems with heterogeneous, multi-state computing nodes. Particularly, a novel and efficient MDD construction method is presented to generate compact MDD models encoding different amounts of cumulative computing resources. Two detailed case studies are performed to illustrate basics and application of the proposed approach to reduce SLA violations and guarantee the availability requirements on the delivered computing resources. Benchmark studies are further conducted to show efficiency of the proposed MDD-based approach as compared with the continuous-time Markov chains-based method and the universal generation function-based method.

To improve the success probability of a mission execution, scheduled checkpointing is often implemented to save completed portions of the mission task so that a system can resume the mission execution effectively after its restoration whenever the system failure occurs. This paper considers a repairable computing system subject to the scheduled checkpointing. The checkpointing intervals are deterministic, but can be even or uneven. The system repair time is fixed while the system time-to-failure can follow any arbitrary type of distributions. The maximum number of repairs is specified by a certain threshold value. A multi-valued decision diagram (MDD)-based analytical approach is proposed to evaluate the exact success probability of a mission execution for the considered repairable system. The proposed approach enables generating a compact mission MDD model where identical subMDD models can be merged to improve computational efficiency and reduce storage requirement. The MDD model, once being constructed, can be reused for system reliability evaluations using different input parameter values. A benchmark study is presented to show the efficiency of proposed MDD approach. A case study is performed to illustrate the application of the proposed MDD approach to facilitate decision making about proper system design and parameter selection.

Currently, mobile edge computing (MEC) is one of the most popular techniques used to respond to real-time services from a wide range of mobile terminals. Compared with single-phase systems, commercial services in MEC can be modeled as phased-mission systems (PMS) and are much more complex, because of the dependencies across the phases. Over the past decade, researchers have proposed a set of new algorithms based on BDD for fault tree analysis of a wide range of PMS with various mission requirements and failure behaviors. The analysis to be performed on a fault tree can be either qualitative or quantitative. For the quantitative fault tree analysis of PMS by means of BDD, much work has been conducted. However, for the qualitative fault tree analysis of PMS by means of BDD, no much related work can be found. In this paper, we have presented some efficient methods to calculate the MCS encoding by a PMS BDD. Firstly, three kinds of redundancy relations-inclusive relation, internal-implication relation, and external-implication relation-within the cut set are identified, which prevent the cut set from being minimal cut set. Then, three BDD operations, IncRed, InImpRed, and ExImpRed, are developed, respectively, for the elimination of these redundancy relations. Using some proper combinations of these operations, MCS can be calculated correctly. As an illustration, some experimental results on a benchmark MEC system are given.

Rapid advancement in micro-electromechanical techniques leads to the wide application of wireless sensor networks (WSNs). In a linear WSN (LWSN), all sensor nodes are arranged in a straight line to monitor health status of some linear infrastructure structure such as bridges, highways, pipelines, etc. To enhance reliability of the infrastructure monitoring services, LWSNs are often designed to incorporate a limited number of backbone nodes for transferring or relaying information, leading to a more complex hybrid structure. In this paper, a multivalued decision diagram (MDD)-based analytical approach is proposed to evaluate performance of an LWSN system with backbone nodes. Particularly, we model and analyze the probability that the hybrid LWSN performs at a particular performance level, which is characterized by the number of sensor nodes being able to reach the base station. A single compact MDD model is constructed by sharing all isomorphic submodel structures involved in different performance levels. The MDD model, once being constructed, can be reused for evaluation using different failure time distributions or mission time. A case study is presented to substantiate the application of the proposed MDD approach for developing the optimal backbone node allocation strategy to guarantee the reliability requirement on the infrastructure monitoring services.

Modern computing systems typically use a large number of independent, non-identical computing nodes to perform a set of coordinated computations in parallel. The computing system and its constituent computing nodes often exhibit more than two performance levels or states corresponding to different computing powers. This paper models and evaluates performability of largescale multi-state computing systems, which is the probability that a computing system performs at a particular performance level. The heterogeneity in the constituent components of different nodes (due to factors such as different model generations, model suppliers, and operating environments) makes performability analysis difficult and challenging. In this paper a specification method for system performance level (SPL) is first introduced. A multi-valued decision diagram (MDD) based approach is then proposed for performability analysis of multi-state computing systems consisting of nodes with different state occupation probabilities, which encompasses novel and efficient MDD model generation procedures. Example and benchmark studies are performed to show that the proposed approach can offer efficient performability analysis of large-scale computing systems.

Modern computing systems typically utilize a large number of computing nodes to perform coordinated computations in parallel or simultaneously. They can exhibit multiple performance states or levels due to statuses or failures of their consistent nodes. Performability analysis is concerned with assessing the probability that the computing system performs at a particular performance level. In the context of performability analysis, these computing systems can be modeled using k-to-l-out-of-n structures. This paper proposes new analytical methods based on binary decision diagrams (BDD) for the performability analysis of large computing systems with unrepairable computing nodes. A new and efficient BDD algorithm that makes full uses of the special k -to-l-out-of-n structure is first proposed for systems with computing node having identical computing powers. New simplification rules are further proposed to generate compact and canonical BDD models for systems with heterogeneous computing nodes characterized by different computing powers. Ordering heuristic is also explored to further reduce the size of BDD models. Examples are provided to illustrate the proposed BDD-based performability analysis methodology as well as its efficiency in analyzing large-scale computing systems.

In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone can be modeled as a k-connected m-fold dominating set ((k, m)-CDS for short). In this paper, we present a constant approximation algorithm for the minimum weight (k, m)-CDS problem in unit disk graphs under the assumption that k and m are two fixed constants with m ≥ k. Prior to this paper, constant approximation algorithms are known for k = 1 with weight and 2 ≤ k ≤ 3 without weight. Our result is the first constant approximation algorithm for the (k, m)-CDS problem with general k, m and with weight. The performance ratio is (α+5ρ) fork ≥ 3 and (α+2.5ρ) for k = 2, where α is the performance ratio for the minimum weight m-fold dominating set problem and ρ is the performance ratio for the subset k-connected subgraph problem (both problems are known to have constant performance ratios).

To save energy and alleviate interference, connected dominating set (CDS) was proposed to serve as a virtual backbone of wireless sensor networks (WSNs). Because sensor nodes may fail due to accidental damages or energy depletion, it is desirable to construct a fault tolerant virtual backbone with high redundancy in both coverage and connectivity. This can be modeled as a k-connected m-fold dominating set (abbreviated as (k, m)-CDS) problem. A node set C ⊆ V (G) is a (k, m)-CDS of graph G if every node in V(G)\C is adjacent with at least m nodes in C and the subgraph of G induced by C is k-connected. Constant approximation algorithm is known for (3, m)-CDS in unit disk graph, which models homogeneous WSNs. In this paper, we present the first performance guaranteed approximation algorithm for (3, m)-CDS in a heterogeneous WSN. In fact, our performance ratio is valid for any topology. The performance ratio is at most γ, where γ = α + 8 + 2 ln(2α - 6) for α ≥ 4 and γ = 3α +2 ln 2 for α <; 4, and α is the performance ratio for the minimum (2, m)-CDS problem. Using currently best known value of α, the performance ratio is ln δ +o(ln δ), where δ is the maximum degree of the graph, which is asymptotically best possible in view of the non-approximability of the problem. Applying our algorithm on a unit disk graph, the performance ratio is less than 27, improving previous ratio 62.3 by a large amount for the (3, m)-CDS problem on a unit disk graph.

Using a connected dominating set (CDS) to serve as a virtual backbone of a wireless sensor network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to accidental damage or energy depletion, it is desirable to construct a fault tolerant CDS, which can be modeled as a k-connected m-fold dominating set ((k, m)-CDS for short). A subset of nodes C ⊆ V(G) is a (k, m)-CDS of G if every node in V(G)\C is adjacent with at least m nodes in C and the subgraph of G induced by C is k-connected. In this paper, we present an approximation algorithm for the minimum (3, m)-CDS problem with m > 3, which has size at most γ times that of an optimal solution, where γ = α + 8 + 21n(2α - 6) for α > 4 and γ = 3α + 2 In 2 for α <; 4, and α is the approximation ratio for the minimum (2, m)-CDS problem. This is the first performance-guaranteed algorithm for the minimum (3, m)-CDS problem in a general wireless network, and improves previous performance ratio in a homogeneous wireless sensor network by a large amount.

In a network system, a propagated failure (PF) is a failure originating from a network component that can cause extensive damages to other network components or even the failure of the entire system. Existing works on PFs have mostly assumed the deterministic effect from a component PF, i.e., a fixed subset of system components is affected whenever the PF occurs. However, in many real-world systems, the components may have different levels of protection, and the effect of damage from a component PF can be dependent upon the status of other components within the same system or the occurrence order of component failures. This paper proposes a new analytical method based on multi-valued decision diagrams (MDDs) for the reliability analysis of network systems with dependent propagation effects. Particularly, new MDD modeling procedures are proposed for considering different types of dependent PF effects introduced by different protection levels. After the system MDD is generated using a new MDD combination algorithm to efficiently handle the dependent PF effects, methods for computing the network reliability and component importance measures are presented. The detailed analysis of an example network system subjected to dependent PFs is presented to illustrate the basics and application of the proposed method. It is shown that the proposed MDD-based method generates smaller model size and thus presents lower computational complexity in the model generation and evaluation than the existing Markov method and separable method.

Dynamic fault trees (DFTs) have been used for many years because they can easily provide a concise representation of the dynamic failure behaviors of general non-repairable fault tolerant systems. However, when repeated failure events appear in real-life DFT models, the traditional modularization-based DFT analysis process can still generate large dynamic subtrees, the modeling of which can lead to a state explosion problem. Examples of these kinds of large dynamic subtrees abound in models of real-world dynamic software and embedded computing systems integrating with various multi-function components. This paper proposes an efficient, multiple-valued decision-diagram (MDD)-based DFT analysis approach for computing the reliability of large dynamic subtrees. Unlike the traditional modularization methods where the whole dynamic subtree must be solved using state-space methods, the proposed approach restricts the state-space method only to components associated with dynamic failure behaviors within the dynamic subtree. By using multiple-valued variables to encode the dynamic gates, a single compact MDD can be generated to model the failure behavior of the overall system. The combination of MDD and state-space methods applied at the component or gate level helps relieve the state explosion problem of the traditional modularization method, for the problems we explore. Applications and advantages of the proposed approach are illustrated through detailed analyses of an example DFT, and through two case studies.

Many practical systems are phased-mission systems (PMSs), where the mission consists of multiple, consecutive, and non-overlapping phases of operation. An accurate reliability analysis of a PMS must consider statistical dependence of component states across phases, as well as dynamics in system configurations, success criteria, and component behavior. This paper proposes a new method based on multiple-valued decision diagrams (MDDs) for the reliability analysis of a non-repairable binary-state PMS. Due to its multi-valued logic nature, the MDD model has recently been applied to the reliability analysis of multistate systems. In this work, we present a novel way to adapt MDDs for the reliability analysis of systems with multiple phases. Examples show how the MDD models are generated and evaluated to obtain the mission reliability measures. Performance of the MDD-based method is compared with an existing binary decision diagram (BDD)-based method for PMS analysis. Empirical results show that the MDD-based method can offer lower computational complexity as well as a simpler model construction and improved evaluation algorithms over those used in the BDD-based method.

Many practical systems are phased-mission systems with multimode failures (MFPMSs) where the mission consists of multiple nonoverlapping phases of operation, and the system components may assume more than one failure mode. In MFPMSs, dependence arises among different phases and among different failure modes of the same component, which makes the reliability analysis of MFPMSs difficult. This paper proposes a new analytical method based on multivalued decision diagrams (MDDs) for the reliability analysis of nonrepairable MFPMSs. MDDs have recently been applied to the reliability analysis of single-phase systems with multiple component states. In this paper, we make the new contribution by proposing a novel way to adapt MDDs for the reliability analysis of systems with multiple phases and multimode failures. Examples show how the MDD models are generated and evaluated to obtain the mission reliability measures. Performance of the MDD-based method is compared with an existing binary decision diagram (BDD)-based method for MFPMS analysis through several examples and a comprehensive benchmark study. Empirical results show that the proposed MDD-based method can offer lower computational complexity and simpler model construction and evaluation algorithms than the BDD-based method, and it can be effectively applied to large practical cases.

Recently, Z. Tang, and J. B. Dugan proposed a new algorithm (DEP-BDD) based on binary decision diagrams (BDD) for reliability analysis of phased-mission systems (PMS) with multimode failures. Although the variable ordering is very important from a practical point of view, it has not been treated directly. This paper develops four ordering heuristics for DEP-BDD based on two ordinary schemes, and evaluates these schemes & heuristics with hundreds of randomly generated fault trees having different sizes and structure properties. As a synthesis of the obtained performance results, we propose a heuristic selection strategy.

We present a generalized analysis methodology for binary decision diagram-based fault tree analysis of a wide range of phased-mission systems, with various mission requirements, and structure characteristics. This methodology includes 1) four alternative variable ordering schemes: forward/backward phased dependent operations, and forward/backward concatenation; 2) a strategy to choose an adequate ordering scheme to process a new phased-mission system instance depending on its phase and mission configuration; and 3) efficient generation and evaluation algorithms for generalized phased-mission system binary decision diagrams adopting any arbitrary ordering scheme. The advantages of this methodology are in the low computational complexity, broad applicability, and easy implementation.

The application domain, such as communication networks and embedded controllers for telephony, automobiles, trains and avionics systems, requires very high quality reactive systems, so an important phase in the development of reactive systems is the verification of their conceptual models before implementation. Normally in the requirement analysis phase, system property can be represented as an input and output labeled transition system (IOLTS), which is a transition system labeled by inputs and outputs between the system and the environment. This paper describes an attempt to propose an approach to verify Statechart specifications for reactive systems given IOLTS property specifications. We develop a suitable semantics model — observable semantics, an abstract semantics model only which describes outside observable behavior and suffers from less state explosion problem by reducing infinite or large state spaces to small ones. Then we propose two methods to verify the conformance between a given IOLTS property specification and a Statechart specification: two-phase verification and on-the-fly verification. Compared with two-phase verification, on-the-fly verification needs less storage and computation-time, especially when the target Statechart specification is very large or likely to have many errors.