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Diagnosability is a fundamental consideration when designing an interconnected network. The PMC and MM ∗ fault diagnosis models are the two most commonly used models. Both the g -good-neighbour diagnosability and g -extra diagnosability of an interconnection network have been two of the hot topics in the intersectional research areas of Graph theory and Computer Science, which become increasingly attractive for new solutions to real-world problems. However, there are still some problems in the transformation from the concepts of Computer Science to that of mathematics. In this paper, we systematically study such problems and give a strict proof from concepts to mathematical conclusions. In the terms of results, we not only give the relationship between g -good-neighbour diagnosabilities of the network under PMC model and MM ∗ model, but also between g -extra diagnosabilities of the network under PMC and MM ∗ models. To apply our results, we give an application on the enhanced hypercube in the end and derive a lemma explaining whether these are 3-cycles in enhanced hypercubes and how many common neighbours for two vertices of enhanced hypercubes under different values of k in the meantime. [ABSTRACT FROM AUTHOR]

There are hundreds of various sensors used for online Prognosis and Health Management (PHM) of LREs. Inspired by the fact that a limited number of key sensors are selected for inflight control purposes in LRE, it is practical to optimal placement of redundant sensors for improving the diagnosability and economics of PHM systems. To strike a balance between sensor cost, real-time performance and diagnosability of the fault diagnosis algorithm in LRE, this paper proposes a novel Optimal Sensor Placement (OSP) method. Firstly, a Kernel Extreme Learning Machine-based (KELM) two-stage diagnosis algorithm is developed based on a system-level failure simulation model of LRE. Secondly, hierarchical diagnosability metrics are constructed to formulate the OSP problem in this paper. Thirdly, a Hierarchy Ranking Evolutionary Algorithm-based (HREA) two-stage OSP method is developed, achieving further optimization of Pareto solutions by the improved hypervolume indicator. Finally, the proposed method is validated using failure simulation datasets and hot-fire test-run experiment datasets. Additionally, four classical binary multi-objective optimization algorithms are introduced for comparison. The testing results demonstrate that the HREA-based OSP method outperforms other classical methods in effectively balancing the sensor cost, real-time performance and diagnosability of the diagnosis algorithm. The proposed method in this paper implements system-level OSP for LRE fault diagnosis and exhibits the potential for application in the development of reusable LREs. [ABSTRACT FROM AUTHOR]

Fault detection and localization are vital for ensuring the stability of data center networks (DCNs). Specifically, adaptive fault diagnosis is deemed a fundamental technology in achieving the fault tolerance of systems. The highly scalable data center network (HSDC) is a promising structure of server-centric DCNs, as it exhibits the capacity for incremental scalability, coupled with the assurance of low cost and energy consumption, low diameter, and high bisection width. In this paper, we first determine that both the connectivity and diagnosability of the m-dimensional complete HSDC, denoted by H S D C m (m) , are m. Further, we propose an efficient adaptive fault diagnosis algorithm to diagnose an H S D C m (m) within three test rounds, and at most N + 4 m (m − 2) tests with m ≥ 3 (resp. at most nine tests with m = 2 ), where N = m · 2 m is the total number of nodes in H S D C m (m) . Our experimental outcomes demonstrate that this diagnosis scheme of HSDC can achieve complete diagnosis and significantly reduce the number of required tests. [ABSTRACT FROM AUTHOR]

With the expansion of network scale, it is essential to study network reliability through connectivity and diagnosability. For Hypercube, DCell, BCube, and other networks, their connection modes are specific and different, so it is necessary to use different methods to study the properties of networks. This paper proposes a class of topological structure—cycle composition networks (CCNs), which not only contains k-ary n-cube and BC graph, but also includes the data center network CamCube and many other unknown networks. We then study their diameters and path construction algorithm in them. Furthermore, we establish their classical connectivity and diagnosability under the PMC and the MM ∗ models, respectively. Finally, we give the 1-good-neighbor connectivity and diagnosability of the CCNs under the PMC model for n ⩾ 3 and l = 2 . [ABSTRACT FROM AUTHOR]

Structural analysis, a model-based fault diagnosis approach, has been extensively highlighted since it does not depend on an exact analytical system model. The structural analysis approach focuses on obtaining the required information for fault detection and fault-tolerant control from the structural model of the control system. Diagnosability is a design attribute that indicates the fault diagnosis capabilities. Diagnosability design not only guarantees that the structure of the control system gives adequate fault information but also that the control system achieves the fault diagnosis with the least cost and the most excellent efficiency. In this paper, in combination with the research progress of structural analysis, the study first designs the structural diagnosability model of the control system based on structural analysis; secondly, the essential techniques of diagnosability evaluation and diagnosability design based on structural analysis are analyzed and summarized, and the diagnosability index system based on structural analysis is designed based on the structural detectability and structural isolation; this lays the foundation for the development of the diagnosability; lastly, the study summarizes the problems of diagnosability research based on structural analysis and the future development direction. [ABSTRACT FROM AUTHOR]

A reconfigurable manufacturing system (RMS) can provide a customised manufacturing process to complete changes in operational requirements or machine status. The effective development of an RMS is supported by dynamic reconfiguration management that detects errors in the process and explores the reconfiguration strategy. However, existing studies on reconfiguration focus on production while ignoring inspection. In the RMS, a reconfigurable inspection system (RIS) is developed for data-oriented detection of product quality with the minimally sufficient number of inspection machines. We propose a key feature-based method for designing the RIS's configuration to achieve a satisfactory RIS design, which detects different processes and satisfies the inspection requirement for each phase of the RMS's lifecycle. The key features of the RIS (i.e. modularity, integrability, customisation, scalability, convertibility and diagnosability) are identified based on the RMS's detection mechanism. An example of the RMS for a spindle box is presented to validate the method. [ABSTRACT FROM AUTHOR]

Diagnosability of a discrete event system is usually dealt at the system level entailing synchronous composition of component automata leading to state explosion problem. However, many of the systems are modular in nature allowing localized detection and isolation of faults. Moreover, developments in sensor technology allow direct detection of faults based on sensor output which are denoted as observations in this paper. Combining modularity and observations, we propose a new concept of O-diagnosability based on observations at the subsystem or component level to make the diagnosability verification less complex. The concepts of monolithic (system) O-diagnosability and CO-diagnosability (system to component) are introduced and necessary and sufficient conditions for O-diagnosability are derived. Theoretical results on the relation between monolithic O-diagnosability and CO-diagnosability support the system level diagnosability verification through component level analysis in a progressive way. Computational complexity for the proposed diagnosability verification is shown to be of the order of n2 where n is the largest number of diagnoser states of a component of the system. [ABSTRACT FROM AUTHOR]

Diagnosability is often considered as an important factor for measuring the self-diagnostic ability of network systems. However, classic system-level diagnosis focuses only on processor faults and ignores the objective reality of communication faults. Under real circumstances, missing edges and node failures usually occur simultaneously in multiprocessor systems (called hybrid fault circumstances). Therefore, it is important to study the diagnosability of multiprocessor systems under hybrid fault circumstances. In this paper, we propose several diagnosabilities of interconnection networks with missing edges and faulty nodes. By exploring some important relationships between diagnosability and the minimum degree of a network under hybrid fault circumstances, we present and prove the diagnosability of several classic interconnection networks, including BC (bijective connection) networks, star graphs, folded hypercubes, exchanged hypercubes, exchanged crossed cubes, k-ary n-cubes, bubble-sort star graphs and balanced hypercubes, with missing edges and broken-down nodes under the PMC (Preparata, Metze and Chien) and MM* (Maeng and Malek) models. [ABSTRACT FROM AUTHOR]

There are hundreds of various sensors used for online Prognosis and Health Management (PHM) of LREs. Inspired by the fact that a limited number of key sensors are selected for inflight control purposes in LRE, it is practical to optimal placement of redundant sensors for improving the diagnosability and economics of PHM systems. To strike a balance between sensor cost, real-time performance and diagnosability of the fault diagnosis algorithm in LRE, this paper proposes a novel Optimal Sensor Placement (OSP) method. Firstly, a Kernel Extreme Learning Machine-based (KELM) two-stage diagnosis algorithm is developed based on a system-level failure simulation model of LRE. Secondly, hierarchical diagnosability metrics are constructed to formulate the OSP problem in this paper. Thirdly, a Hierarchy Ranking Evolutionary Algorithm-based (HREA) two-stage OSP method is developed, achieving further optimization of Pareto solutions by the improved hypervolume indicator. Finally, the proposed method is validated using failure simulation datasets and hot-fire test-run experiment datasets. Additionally, four classical binary multi-objective optimization algorithms are introduced for comparison. The testing results demonstrate that the HREA-based OSP method outperforms other classical methods in effectively balancing the sensor cost, real-time performance and diagnosability of the diagnosis algorithm. The proposed method in this paper implements system-level OSP for LRE fault diagnosis and exhibits the potential for application in the development of reusable LREs.

Fault detection and localization are vital for ensuring the stability of data center networks (DCNs). Specifically, adaptive fault diagnosis is deemed a fundamental technology in achieving the fault tolerance of systems. The highly scalable data center network (HSDC) is a promising structure of server-centric DCNs, as it exhibits the capacity for incremental scalability, coupled with the assurance of low cost and energy consumption, low diameter, and high bisection width. In this paper, we first determine that both the connectivity and diagnosability of the m-dimensional complete HSDC, denoted by HSDCm(m), are m. Further, we propose an efficient adaptive fault diagnosis algorithm to diagnose an HSDCm(m) within three test rounds, and at most N+4m(m−2) tests with m≥3 (resp. at most nine tests with m=2), where N=m·2m is the total number of nodes in HSDCm(m). Our experimental outcomes demonstrate that this diagnosis scheme of HSDC can achieve complete diagnosis and significantly reduce the number of required tests.

The notion of diagnosability of stochastic discrete‐event systems (SDESs) was introduced in the literature, but the method for verifying the diagnosability of SDESs was exponential. However, is there a sufficient condition of diagnosability of SDESs that can be tested with polynomial method? In this paper, we present a sufficient condition of diagnosability of SDESs based on a constructive testing automaton, and a polynomial method is proposed to test the condition. [ABSTRACT FROM AUTHOR]

Motivated by two typical ways to construct multiprocessor systems, matching composition networks and cycle composition networks, we generalize the definition of the Cartesian product of networks and consider the classical diagnosability of the generalized Cartesian product of networks (GCPNs). In this paper, we determine the accurate value of the classical diagnosability of the generalized Cartesian product of networks (GCPNs) under the PMC model and the MM * model. [ABSTRACT FROM AUTHOR]

The diagnosability problem has been extensively studied over the past two decades for discrete event systems associated with intermittent faults. Diagnosability is a property that requires a large number of sensors for fault detection, which leads to expensive system deployment. To alleviate the above drawbacks, we propose a new property called intermittent fault manifestability, which is a weaker observation requirement for diagnosing the occurrence of intermittent faults. In order to verify the property, we consider fault events and their corresponding reset events and introduce two properties of f-manifestability and r-manifestability, respectively. Based on an intermittent fault pattern automaton, we first propose a diagnoser structure to track the occurrence of intermittent faults and prove that the verification of intermittent fault diagnosability can be transformed into the problem of detecting an intermittent fault language. Then, we present a pair verifier constructed by the strict composition of a fault diagnoser and a normal diagnoser, which are the subparts of the diagnoser with respect to the fault events and the normal events, respectively. Finally, we introduce necessary and sufficient conditions for verifying intermittent fault manifestability. [ABSTRACT FROM AUTHOR]

We study here the diagnosability of networks under two models of self-diagnosis: PMC model introduced by Preparata, Metze and Chien (IEEE Trans Electronic Computers 16(12):848–854 (1967)) and MM ∗ model introduced by Sengupta and Dahbura (IEEE Trans Computers 41(11):1386–1396 (1992)) which is the variant of the comparison model (1980). The diagnosability of a network of processors is the maximum number of faulty processors that can be identified by the network itself. Lee and Hsieh (IEEE Trans Dependable Secure Comput 8(2):246–255 (2011)) considered the diagnosability of networks obtained by connecting two networks of the same order by two perfect matchings and got the lower bounds. Usually, there is a gap between the lower bound and the exact value of the diagnosability. In this paper, we completely determine the diagnosability of this family of matching composition networks. [ABSTRACT FROM AUTHOR]

Today's supercomputers contain thousands of processing cores. As the number of processing units grows, the probability of failing some processing units increases. Therefore, finding faulty units has become a concern in these systems which depends on the diagnosability of the interconnection network that connects processing units. In this paper, we investigate the g-good-neighbor diagnosability of triangle-free graphs under the MM ∗ and PMC models. We show that if G is a connected triangle-free graph with minimum degree δ , its diagnosability under the MM ∗ model, i.e., t MM ∗ (G) , is either δ - 2 , δ - 1 , or δ . Also, the 1-good-neighbor diagnosability of G, i.e., t 1 MM ∗ (G) , is at least δ - 1 if it does not contain any subgraph isomorphic to K δ , δ . Moreover, we show that if G does not contain a subgraph isomorphic to K δ - 1 , δ - 1 , then it is 1-good-neighbor δ + 1 -diagnosable under PMC model when | V (G) | > 2 δ + 2 . Our results give lower bounds on the diagnosability and 1-good-neighbor diagnosability of triangle-free graphs which covers a broad class of interconnection networks. [ABSTRACT FROM AUTHOR]

Fault-freeness is one of the necessary guarantees for healthy and stable operations of discrete event systems. Traditional diagnostic models may fail since sensors may suffer electronic component failures, communication failures, or atmospheric electromagnetic interference. Robust diagnosis problem has attracted more and more attention since it improves reliability of the diagnosis technology. When generating the Petri net reachability graph necessary for constructing a reachability diagnoser, one may face the state explosion problem. As a Petri net gets more complicated, the complexity of its reachability graph also increases exponentially. With the basis reachability graph, a lightweight diagnoser named a basis reachability diagnoser is developed, together with a robust basis reachability diagnoser obtained by dilating the basis reachability graph. Compared with reachability graphs, the advantages of basis reachability graphs in construction complexity are confirmed and the efficiency in robust diagnosability analysis is improved.

Structural analysis, a model-based fault diagnosis approach, has been extensively highlighted since it does not depend on an exact analytical system model. The structural analysis approach focuses on obtaining the required information for fault detection and fault-tolerant control from the structural model of the control system. Diagnosability is a design attribute that indicates the fault diagnosis capabilities. Diagnosability design not only guarantees that the structure of the control system gives adequate fault information but also that the control system achieves the fault diagnosis with the least cost and the most excellent efficiency. In this paper, in combination with the research progress of structural analysis, the study first designs the structural diagnosability model of the control system based on structural analysis; secondly, the essential techniques of diagnosability evaluation and diagnosability design based on structural analysis are analyzed and summarized, and the diagnosability index system based on structural analysis is designed based on the structural detectability and structural isolation; this lays the foundation for the development of the diagnosability; lastly, the study summarizes the problems of diagnosability research based on structural analysis and the future development direction.

With the rapid and continuous development of network technology, a multiprocessor system, consisting of multiple processors and communication links, plays an significant role in big data era. The topology of a multiprocessor system is a basic architecture of great influence on the network performance. Multiprocessor systems should have some good performances such as low communication costs, high network reliability, and friendly resource sharing. Therefore, designing a high-performance network architecture is of great significance to multiprocessor systems. In this paper, we propose a more general class of balanced hypercubes with two more general edge-disjoint sets of perfect matchings as cross edges. Then we explore some basic properties of G B H n. Furthermore, we show the connectivity, super connectivity, extra connectivity and (extra) diagnosability of G B H n , respectively. [ABSTRACT FROM AUTHOR]

The generalizations of traditional connectivity and diagnosability, h -component connectivity and diagnosability along with h -extra connectivity and diagnosability are significant parameters to characterize invulnerability of multiprocessor systems. In this paper, we determine that h -extra connectivity of bubble sort networks B n is κ h (B n) = (h + 1) (n − 1) − h (h + 3) 2 for 0 ≤ h ≤ n 2. Afterwards, we show that h -extra diagnosability of B n under PMC model and MM⁎ model is t h (B n) = (h + 1) (n − 1) − h (h + 3) 2 + h. In addition, we prove that (h + 1) -component connectivity of B n is c κ h + 1 (B n) = h (n − 1) − h (h + 1) 2 + 1 , and h -component diagnosability of B n under PMC model and MM⁎ model is c t h (B n) = h (n − 1) − h (h + 1) 2 + 1 for 1 ≤ h ≤ n 2. [ABSTRACT FROM AUTHOR]

In practical systems, due to reasons such as sensor faults, sensor limitations and packet losses in networks, the observation of events becomes nondeterministic, and makes observing system behavior particularly complex. Aiming at the problem that the same event string might have multiple observations in discrete event systems and the same event observations might be different in different states, this paper proposed a method for fault diagnosis and verification under nondeterministic observations. Firstly, it formalized the diagnosability of discrete event systems under nondeterministic observations. Secondly, it constructed a verifier for the above fault diagnosis verification. Based on the verifier, it proposed a necessary and sufficient conditions and the verification algorithm for the system to be diagnosable under nondeterministic observations. Finally, an example illustrates the application of the fault diagnosis verification algorithm under nondeterministic observations. Compared with the existing research, the observation value of the fault event is not constrained in this proposed method, and it can be zero or more observations, which makes the application of this method more extensive. [ABSTRACT FROM AUTHOR]

In this paper, a new method for fault diagnosability research based on information geometry is proposed. The problem of the diagnosability evaluation of dynamic system faults is transformed into a distance calculation problem on a manifold. The Fisher information distance is used to realize a quantitative judgment of diagnosability, and a quantitative evaluation index of the fault diagnosability of a satellite attitude determination system is designed. This includes a fault detectability index and a fault isolability index. The validity and superiority of the new indexes are verified through a mathematical simulation. In addition, the fault information is visually presented by the geodesics of the fault manifold, and the properties and behavior of the fault are mined and analyzed on the fault information manifold, which lays a foundation for further exploration of fault information through geometric methods. [ABSTRACT FROM AUTHOR]

In fault diagnosis, we study model‐based approaches to diagnose the discrete event system that efficiently represents the determined ambiguity, unpredictability, and the observation and judgment of several real‐life problems. Diagnosability is a crucial task for system reliability. This article presents a strategy for verifying the diagnosability of discrete event systems (DESs) using conjunctive normal form (CNF). This strategy introduces CNF‐based finite state machine (FSM). First, the scheme considers the model of the system for diagnosis, and CNF represents all transitions of the DES. CNF‐based FSM constructs a diagnoser known as CNF‐based diagnoser. Diagnoser tests whether faulty events can be detected or not in a given system model, that is, DES. The diagnoser verifies the diagnosability of the given DES‐based FSM using the resolve rule. The construction of diagnoser and diagnosability verification with respect to a real‐world industrial system is illustrated. The complexity of the diagnoser construction and diagnosability verification are shown to be efficient. [ABSTRACT FROM AUTHOR]

This article investigates diagnosability and $T$ -diagnosability for discrete-event systems modeled by unambiguous max-plus automata (UMPAs). More precisely, diagnosability requires that the occurrence of any fault can be detected within a finite number of events after the fault has occurred. $T$ -diagnosability requires that the occurrence of any fault can be detected within a delay of at most $T$ time units after its occurrence. First, we propose a polynomial-time algorithm based on the construction of a nondeterministic finite automaton over a weighted alphabet for diagnosability verification of a UMPA. Second, we prove that $T$ -diagnosability of a UMPA can be studied by reducing it to the problem of diagnosability. Third, we introduce an approach to calculate the upper on the time needed for detecting fault occurrence for a diagnosable UMPA, and its complexity is of sixth order in the number of states of the UMPA. [ABSTRACT FROM AUTHOR]

• The MMCD-based method for the quantitative evaluation of diagnosability is proposed. • The TSA-based design strategy for diagnosability optimization is proposed. • The advantage of quantitative evaluation of diagnosability was obtained experimentally. • The diagnosability of UAVs is analyzed and optimized. This study presents a proposed strategy for optimizing diagnosability in unmanned aerial vehicles (UAVs) through a combination of Structural Analysis (SA) and Maximum Mean Covariance Difference (MMCD). Initially, diagnosability is qualitatively assessed using SA. Residuals are then designed based on the minimal structural overdetermination (MSO) using the sequential residual generation approach. Subsequently, diagnosability is reframed as a measurement of residual variance in the probability distribution. To address the absence of Maximum Mean Difference (MMD) in covariance difference measurement, Maximum Covariance Difference (MCD) is introduced. Furthermore, a method for quantitatively evaluating diagnosability based on MMCD is proposed, incorporating both MMD and MCD. Finally, an optimization model for diagnosability is established to ensure the efficient completion of fault diagnostic tasks with minimal cost and maximum effectiveness. The proposed method's rationality and effectiveness are validated through simulation using the Tree Seed Algorithm (TSA) on a fixed-wing UAV model. [ABSTRACT FROM AUTHOR]

Today, a high volume of operation interval data can be efficiently captured by a diverse range of measurements including sensors, control signals and meters, which are deployed in building automation systems (BAS). Hence, advanced data analytics tools such as fault detection and diagnostic (FDD) can be developed to analyze the operational performance of heating, ventilation and air conditioning (HVAC) systems. In the past, enormous efforts have been made to develop various FDD approaches, assuming interval data contains essential information for identifying fault signatures. However, a "data rich, but information poor" phenomenon exists due to the fact that not all measurements are sensitive to faults in HVAC systems. This highlights a significant research gap, the lack of systematic analysis of measurement sensitivity to different HVAC system faults, which is vital for FDD development, measurement deployment optimization, and control system design. To address this gap, this study introduces a novel approach to assess the sensitivity of BAS measurements in relation to various HVAC fault types. We propose two sensitivity indices (SI), the SI of fault (SI_fault) and the global measurement SI (SI_measurement_global) to quantify measurement sensitivities. The SI_fault quantifies the measurement's sensitivity to a particular fault, while the SI_measurement_global assesses its sensitivity across all fault types. These indices integrate probability distributions, enhancing the interpretability and scalability. Utilizing the HVACSIM+ fault simulation dataset, which includes 15 common faults at varying severity levels and 89 different measurements within an HVAC system, we conducted an extensive analysis of measurement sensitivities by looking at the proposed SIs. [Display omitted] • A novel method was developed to evaluate measurement sensitivities to faults in an HVAC system. • Two new sensitivity indices (SI) were proposed to quantify the measurement sensitivity under faults. • Data representing 15 common faults with different severity levels was used to analyze measurement sensitivities. • A use case is illustrated to indicate that the developed SI can be used to identify fault signatures. [ABSTRACT FROM AUTHOR]

Reconfigurable manufacturing systems are complex systems that are prone to malfunctions and performance decay. Thus, such systems need to be safeguarded against quality issues and decline in production efficiency to ensure the optimal health of machines. The product quality and health of a reconfigurable manufacturing system can be analyzed by using the diagnosability characteristic. This study examines the diagnosability characteristic in a multi-stage reconfigurable manufacturing system. The aim is to understand the impact of time-based diagnostics on the functionality performance of a reconfigurable manufacturing system and the level of inventory used during production. The diagnosability is analyzed regarding product variation and system diagnosability. A mathematical model is proposed, and it is subsequently applied in deterministic and stochastic settings. The deterministic setting is examined through a set of two problem-specific heuristics. The stochastic setting, subject to the gamma process, is examined by using a simulation-based optimization approach. The results suggest that the use of line replacement units can restore a reconfigurable system to optimal functionality, reduce the level of inventory, and complete production in a minimum time at the expense of additional cost. These findings apply to the context of healthcare emergency response systems, reconfigurable supply chains, reconfigurable integrated manufacturing systems, etc. Finally, a conclusion and future research avenues are provided.

• To improve the local diagnosability of a vertex, we propose a new structure for a vertex to be locally t -diagnosable. • We also provide the corresponding diagnosis algorithm for the new structure. • We provide a sufficient and necessary condition for a vertex to be locally optimal diagnosed in faulty hypercubes. • We also give a sufficient and necessary condition for a vertex to be locally optimal diagnosed in faulty folded hypercubes. PMC model is the test-based diagnosis which a vertex performs the diagnosis by testing the neighbor vertices via the edges between them. If we only care about the status of a particular vertex, instead of doing global diagnosis, Hsu and Tan introduced the concept of local diagnosis and proposed two structures to diagnose a vertex. The local diagnosability of a vertex is upper bounded by its degree in the system. If the local diagnosability of a vertex is equal to its degree then we say it is locally optimal diagnosable. Usually, there is a gap between the local diagnosability and the lower bound guaranteed by the two structures mentioned above. Herein, we propose a new testing structure and corresponding diagnosis algorithm to diagnose a vertex under PMC model to better evaluate the local diagnosability. And this diagnosis algorithm takes linear time. Based on this new structure, we give a sufficient condition for a vertex to be locally optimal diagnosable. As its applications, we consider the sufficient and necessary condition for a vertex of hypercubes (resp. folded hypercubes) with faulty edges to be locally optimal diagnosable. [ABSTRACT FROM AUTHOR]

Rough‐toothed dolphins (Steno bredanensis) have a global tropical and subtropical distribution with oceanic, neritic, and island‐associated populations. To inform conservation and management for this species, we used sequences from the mtDNA control region (n = 360), mitogenomes (n = 19), and six nuclear introns (n = 35) to provide multiple lines of evidence to critically evaluate the potential taxonomic status of rough‐toothed dolphins. Using samples from the Pacific, Indian, and Atlantic Oceans, we examined the null hypothesis that rough‐toothed dolphins are one panmictic species and the alternate hypothesis of oceanic subspecies. Phylogenetic analyses of mitogenomes revealed a private Atlantic clade sister to a larger cosmopolitan clade including individuals from all tropical and subtropical oceans. We dated the split between the Atlantic clade and the cosmopolitan clade to 890,000 years ago. We determined that Atlantic rough‐toothed dolphins could be correctly diagnosed with 98% accuracy with the mtDNA control region and calculated the net nucleotide divergence as 0.02. Population level analyses revealed significant genetic differentiation using mtDNA among most regions, while significant differentiation using nuclear markers occurred only between the Atlantic and the Indian/Pacific regions. Therefore, the oceanic divergence and diagnosability of rough‐toothed dolphins in the Atlantic and the Indian/Pacific Oceans meet proposed criteria for recognition as two subspecies. [ABSTRACT FROM AUTHOR]

Diagnosability is an essential parameter for a multiprocessor system when measuring the reliability of an interconnection network. The g -extra diagnosability of a system G denoted by t ˜ g (G) was introduced by Zhang et al., which constrains that each fault-free component G i owns | V (G i) | ≥ g + 1 fault-free nodes. The n -dimensional wheel network C W n has advantages as a typical topological structure in interconnection networks. The paper establishes the 2-extra diagnosability of C W n to be 6 n − 10 for n ≥ 6 when the PMC model and MM⁎ model are employed. • The n -dimensional wheel network C W n is tightly 6 n − 12 super 2-extra connected. • The 2-extra diagnosability of the n -dimensional wheel network C W n under the PMC model is 6 n − 10 for n ≥ 6. • The 2-extra diagnosability of the n -dimensional wheel network C W n under the MM⁎ model is 6 n − 10 for n ≥ 6. [ABSTRACT FROM AUTHOR]

A faulty vertex may probably affect its neighbors and further causes them being faulty, which makes a subnetwork (structure) fail. Therefore, looking into the effect caused by some structures becoming faulty is meaningful. The connectivity and diagnosability are two important parameters to evaluate the fault-tolerability of networks. The connectivity of a network is the minimum number of vertices whose removal will disconnect the network or trivial. We call the network to be t -diagnosable if the number of faulty vertices does not exceed t and all faulty vertices can be identified without a replacement. Let Q n be the n -dimensional hypercube and E H (s , t) be the exchanged hypercube, which is the variant of hypercube. In this paper, we study connectivity, diagnosability, and 1-good-neighbor conditional diagnosability based on structure faults, respectively. Specifically, we first determine the connectivity (1 ≤ k ≤ n − 1 and n ≥ 3) and diagnosability (1 ≤ k ≤ n − 1 and n ≥ 4) of Q n − Q k under the PMC model. Then, we determine the connectivity (2 ≤ k ≤ min ⁡ { s , t }) and diagnosability (2 ≤ k ≤ min ⁡ { s , t } and min ⁡ { s , t } ≥ 3) of E H (s , t) − Q k under the PMC model. Finally, we show that the 1-good-neighbor conditional diagnosability of Q n − Q k is 2 n − 3 for n ≥ 5 and 1 ≤ k ≤ n − 1 under the PMC model, which is almost twice as the traditional diagnosability for a large n. • We study fault-tolerability of two important interconnection networks when a hypercube-based subnetwork fails. • We prove that they preserve good fault-tolerability when a hypercube-based subnetwork fails. • The method to study the fault-tolerability of the two interconnection networks can be generalized to other networks. [ABSTRACT FROM AUTHOR]

• The g -extra connectivity κ g (F C Q n) of folded crossed cubes F C Q n is explored. • κ g (F C Q n) is determined for every g with 0 ≤ g ≤ ⌊ n 2 ⌋. • The g -extra conditional fault-diagnosability of F C Q n under PMC model is obtained. There are various ways to measure the reliability and fault tolerance of diverse networks. The g -extra connectivity κ g (G) of a connected graph G is the minimal cardinality of vertex set F , if any, whose deletion disconnects G and every remaining component of G − F has at least g + 1 vertices. Folded crossed cubes F C Q n , a kind of interconnection network, has more reliable properties. In this paper, we explore the g -extra connectivity of n -dimensional folded crossed cubes. It is shown that when 0 ≤ g ≤ ⌊ n 2 ⌋ , κ g (F C Q n) = (g + 1) n − g − ( g 2 ) + 1 for n ≥ 8. As a byproduct, we get g -extra conditional fault-diagnosability t g p ˜ (F C Q n) = (g + 1) n − ( g 2 ) + 1 of F C Q n under PMC model. [ABSTRACT FROM AUTHOR]

We generalise an approach to deriving diagnosability results of various interconnection networks in terms of the popular g-good-neighbour and g-extra fault-tolerant models, as well as mainstream diagnostic models such as the PMC and the MM* models. As demonstrative examples, we show how to follow this constructive, and effective, process to derive the g-extra diagnosabilities of the hypercube, the (n , k) -star, and the arrangement graph. These results agree with those achieved individually, without duplicating structure independent technical details. Some of them come with a larger applicable range than those already known, and the result for the arrangement graph in terms of the MM* model is new. [ABSTRACT FROM AUTHOR]

Motivated by two typical ways to construct multiprocessor systems, matching composition networks and cycle composition networks, we generalize the definition of the Cartesian product of networks and consider the classical diagnosability of the generalized Cartesian product of networks (GCPNs). In this paper, we determine the accurate value of the classical diagnosability of the generalized Cartesian product of networks (GCPNs) under the PMC model and the MM* model.

Fault diagnosis is an important issue of partially observed discrete event systems (DESs). In this problem, fault detection and isolation are two associated tasks, where a fault is diagnosable if it can be detected certainly with a finite delay occurrence and a system is diagnosable if any type of faults can be distinguished with the observed information. Existing researches for fault diagnosis tend to regard faults as unobservable faulty events or states. In this paper, there exists a key conversion, denoting faults by accessible changes of state transition, and then obtains a normative and a faulty construction of given systems. Specially, we establish algebraic structures of composite automata with the help of semi-tensor product and propose a definition of diagnosability based on algebraic state space. Notice that the definition is so different from existing results that provide a new opportunity to fault diagnosis when existing criteria fail. Besides, we construct matrix observers to summarize the requisite information in the evolutionary process and present corresponding theorems to the verification of diagnosability. We apply the exhaust gas recirculation system and the heating system to illustrate the matrix approach in this paper is feasible.

A new technique is presented for diagnosing faults in a Discrete Event System (DES) when the state of the system under diagnosis (SUD) is uncertain upon commencement of the diagnosis process. Specifically, a diagnoser is developed that detects, identifies, and isolates faults in a DES relative to an initial belief state : a set of states in which the SUD could be located at the diagnoser's time of activation. The diagnoser does not need to be synchronously initialized with the SUD. Rather, it can be activated anytime before or after a fault in the SUD occurs, as it does not require knowledge of the SUD's behavior pre-activation. This form of analysis can be understood as fault diagnosis under uncertain initial conditions. The construction procedure for the diagnoser is given and the new concept of semi-asynchronous diagnosability is introduced. The latter requires all failures in the SUD to be diagnosable by observing the behaviors of the SUD after the diagnoser is activated. Moreover, necessary and sufficient conditions for semi-asynchronous diagnosability of a DES are provided. The semi-asynchronous diagnosis technique presented herein is compared with classical synchronous diagnosis approaches. Illustrative examples are provided in order to explain the introduced concepts and the developed approach. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a notion of diagnosability for labeled weighted automata over a class of dioids which admit both positive and negative numbers as well as vectors. The weights can represent diverse physical meanings such as time elapsing and position deviations. We also develop an original tool called concurrent composition to verify diagnosability for such automata. These results are fundamentally new compared with the existing ones in the literature. In a little more detail, diagnosability is characterized for a labeled weighted automaton A D p over a special dioid D p called progressive , which can represent diverse physical meanings such as time elapsing and position deviations. In a progressive dioid, the canonical order is total, there is at least one eventually dominant element, there is no zero divisor, and the cancellative law is satisfied, where the functionality of an eventually dominant element t is to make every nonzero element a arbitrarily large by multiplying a by t for sufficiently many times. A notion of diagnosability is formulated for A D p . By developing a notion of concurrent composition , a necessary and sufficient condition is given for diagnosability of automaton A D p . It is proven that the problem of computing the concurrent composition for an automaton A Q _ is NP -complete, then the problem of verifying diagnosability of A Q _ is proven to be coNP -complete, where the NP -hardness and coNP -hardness results even hold for deterministic, deadlock-free, and divergence-free automaton A N _ , where Q _ and N _ are the max-plus dioids having elements in Q ∪ { − ∞ } and N ∪ { − ∞ } , respectively. Several extensions of the main results have also been obtained. [ABSTRACT FROM AUTHOR]

The subject of study is the physical processes of translational and angular motion of a two-wheeled experimental sample. The goal is to develop physical, mathematical, and graphic models of the translational and angular motions of a two-wheeled experimental sample as an object of automatic control. The objectives: to form physical models of a two-wheeled experimental sample; to develop a nonlinear mathematical description of the processes of translational and angular sample`s motions using the Lagrange approach; to obtain a linearized mathematical sample`s description as an object of automatic control in the state space and frequency domain; to generate graphic models in the form of structural diagrams in the time and frequency domains; to analyze the functional properties of an object of automatic control: stability, controllability, observability, structural and signal diagnosability concerning violations of the functional properties of electric drives and sensors of the angular position of the body and wheels. The methods of the study: the Lagrange method, Taylor series, state-space method, Laplace transformations, Lyapunov, Kalman criteria, and diagnosability criterion. The results: physical models of a two-wheeled experimental sample have been obtained in the form of a kinematic diagram of the mechanical part and the electric circuit of an electric drive; mathematical descriptions of translational and angular motions have been developed in nonlinear and linearized forms; structural diagrams have been developed; functional characteristics of a two-wheeled experimental model as an object of automatic control have been analyzed to solve problems of control algorithms synthesis. Conclusions. The scientific novelty lies in obtaining new models that describe the translational and angular motion of a two-wheeled experimental model as an object of automatic control. The obtained models differ from the known ones by considering the dynamic properties of sensors and electric drives, as well as the relationship of movements.

Checking the diagnosability of a timed discrete-event system usually consists in determining whether a single fault event can always be identified with certainty after a finite amount of time. The aim of this article is to extend this type of analysis to more complex behaviors, called event patterns, and to propose an effective method to check diagnosability with the use of model-checking techniques. To do so, we propose to convert the pattern diagnosability problem into checking a linear-time property over a specific time Petri net. Note to Practitioners—This article is motivated by the problem of improving the monitoring and the supervision of systems, such as automated and robotized manufacturing systems. Based on a model of the system, this article proposes a method to assert with certainty whether the available set of sensors will always provide enough information to ensure that a complex and unexpected behavior has not happened in the system. The proposed method uses a publicly available model-checking tool to perform this analysis. [ABSTRACT FROM AUTHOR]

The diagnosability of a multiprocessor system is an important measure of the reliability of the interconnection network. In 2016, Zhang et al. proposed the g -extra diagnosability of G that requires every component of G − S to have at least (g + 1) vertices. In this paper, we show that the g -extra diagnosability of the Möbius cube M Q n is (n + 1) (g + 1) − 1 2 g (g + 3) − 1 under the PMC model for n ≥ 6 and 0 ≤ g ≤ ⌈ n 2 ⌉ and the MM⁎ model for n ≥ 8 and 0 ≤ g < 1 2 (n − 2). [ABSTRACT FROM AUTHOR]

Diagnosis plays an important role in measuring the reliability of an interconnection network, and the diagnosability of interconnection networks has been widely investigated. For a system G , Zhang et al. introduced h -extra conditional diagnosability, denoted by t h ̃ (G) , which is a novel measure of diagnosability. In this paper, several new structural properties of balanced hypercubes have been derived. Based on these properties, the 3-extra conditional diagnosability of an n -dimensional balanced hypercube is determined to be t ̃ 3 (B H n) = 4 n − 1 for n ≥ 5 under the MM ∗ model. [ABSTRACT FROM AUTHOR]

System diagnosis is process of identifying faulty nodes in a system. An efficient diagnosis is crucial for a multiprocessor system. The BGM diagnosis model is a modification of the PMC diagnosis model, which is a test-based diagnosis. In this paper, we present a specific structure and propose an algorithm for diagnosing a node in a system under the BGM model. We also give a polynomial-time algorithm that a node in a hypercube-like network can be diagnosed correctly in three test rounds under the BGM diagnosis model. [ABSTRACT FROM AUTHOR]