Effective fault detection of complex systems can significantly enhance safety, availability, and maintainability. Recently, graph neural networks (GNNs), which leverage spatial structures among variables, have gained substantial attention due to advancements over previous data-driven methods. However, existing GNN-based fault detection models primarily focus on adjacent neighborhood for feature fusion, neglecting the long-range dependencies in graphs. Moreover, these models often utilize undirected correlational graphs, potentially limiting their applicability and modeling efficiency for target systems. In this work, a causal graph-based bidirectional Graphormer (BiGraphormer) is proposed for complex systems fault detection. The causal relationships among monitoring variables are mined and represented as a directed acyclic causal graph, in which nodes denote variables and directed edges indicate causal influence. Then, the dependencies including the global spatial structure, the node and edge information are encoded and fused using the proposed BiGraphormer. By incorporating both ancestral cause and descendant effect nodes along the directed causal graphs, comprehensive representations are constructed for system fault detection. To validate the effectiveness of the proposed framework, a case study concerning real monitoring data of high-speed train braking systems is conducted, with the results showing efficacy of the proposed method.

This brief develops a degradation-based imperfect maintenance policy considering both positive effect and negative effect for a deteriorating system with variations of operating conditions. The proposed method improves the positive effect on the imperfect maintenance, which further considers the impact of resource on the distribution function of the positive effect after each maintenance process. The positive effect induces the system state into a random interval which is related to maintenance resource applied into each preventive maintenance action and actual maintenance times. Meanwhile, a new negative deteriorating effect model for describing the impacts of imperfect maintenance actions is established. The new model considers that the degradation rate increases after each imperfect maintenance process; meanwhile, it includes the impacts of variations of operating condition bringing to the degradation rate which is described as a distribution subjected to stress as well. Therefore, a condition-based adaptive maintenance policy is applied for a deteriorating system. The optimal maintenance cost allocation and maintenance threshold are determined by maximizing an availability function. Finally, a numerical example is illustrated to demonstrate the application of our maintenance model and policy.

Serious sealing problems cause premature retirement of Lithium-ion punch cells in the service stage. This paper mainly investigates the sealing failure behavior of Li-ion punch cell. A non-linear peeling model was established with experimental verification to explain the failure behavior of sealing cohesive zone. Based on the peeling model, a sealing life prediction method is proposed by describing the decrease of key parameters (σ̂, δc) in the force peeling model. Besides, the accelerated degradation test was conducted for acquiring parameters of life prediction model. Finally, a commercial Li-ion punch cell illustrated is used to validate our method. The result shows that our method can provide a significant reference for the sealing life prediction of Li-ion pouch cell working in different variable loads.

Opportunistic spectrum access (OSA) that allows secondary users to independently search for and exploit instantaneous spectrum availability is considered. The design objective is to maximize the throughput of a secondary user while limiting the probability of colliding with primary users. Integrated in the joint design are three basic components: a spectrum sensor that identifies spectrum opportunities, a sensing strategy that determines which channels in the spectrum to sense, and an access strategy that decides whether to access based on potentially erroneous sensing outcomes. This joint design is formulated as a constrained partially observable Markov decision process (POMDP), and a separation principle is established. The separation principle reveals the optimality of myopic policies for the design of the spectrum sensor and the access strategy, leading to closed-form optimal solutions. Furthermore, it decouples the design of the sensing strategy from that of the spectrum sensor and the access strategy, and reduces the constrained POMDP to an unconstrained one. Numerical examples are provided to study the tradeoff between sensing time and transmission time, the interaction between the physical layer spectrum sensor and the MAC layer sensing and access strategies, and the robustness of the ensuing design to model mismatch.

We design opportunistic spectrum access strategies for improving spectrum efficiency. In each slot, a secondary user chooses a subset of channels to sense and decides whether to access based on the sensing outcomes. Incorporating the secondary user's residual energy and buffer state, we formulate this sequential decision-making problem as a partially observable Markov decision process (POMDP). Within the POMDP framework, we obtain stationary optimal sensing and access policies. By exploiting the rich structure of the underlying problem, we develop monotonicity results for the optimal policies, which accelerate the computations. Numerical results are provided to study the impact of the secondary user's packet arrival rate and residual energy on the optimal sensing and access decisions.

We propose decentralized cognitive MAC protocols that allow secondary users to independently search for spectrum opportunities without a central coordinator or a dedicated communication channel. Recognizing hardware and energy constraints, we assume that a secondary user may not be able to perform full-spectrum sensing or may not be willing to monitor the spectrum when it has no data to transmit. We develop an analytical framework for opportunistic spectrum access based on the theory of partially observable Markov decision process (POMDP). This decision-theoretic approach integrates the design of spectrum access protocols at the MAC layer with spectrum sensing at the physical layer and traffic statistics determined by the application layer of the primary network. It also allows easy incorporation of spectrum sensing error and constraint on the probability of colliding with the primary users. Under this POMDP framework, we propose cognitive MAC protocols that optimize the performance of secondary users while limiting the interference perceived by primary users. A suboptimal strategy with reduced complexity yet comparable performance is developed. Without additional control message exchange between the secondary transmitter and receiver, the proposed decentralized protocols ensure synchronous hopping in the spectrum between the transmitter and the receiver in the presence of collisions and spectrum sensing errors

This paper addresses optimal sensor scheduling for maximizing network lifetime. We formulate this problem as a stochastic shortest-path multi-armed bandit problem. The optimal transmission scheduling policy is thus to choose the sensor with the largest Gittins index. Exploiting the underlying structure of the sensor scheduling problem, we derive a closed-form expression for the Gittins index. We show that choosing the sensor with the most residual energy is an optimal strategy when the channel fading is independently and identically distributed across sensors.

Moments of the equal gain combiner (EGC) output signal-to-noise ratio (SNR) are only known for independent and exponentially correlated Nakagami-m fading channels. We derive the moments of the EGC output SNR in equally correlated Nakagami-m fading channels. Our moment expressions can be used to evaluate the outage and the average error rate of EGC as well as purely moments-based measures such as the average output SNR and the amount of fading as functions of the fading correlation. Numerical results that illustrate the effect of fading correlation on the distribution of the EGC output SNR are also provided. The average output SNR increases with the fading correlation.

Few theoretical results are known about the joint distribution of three or more arbitrarily correlated Rayleigh random variables (RVs). Consequently, theoretical performance results are unknown for three- and four-branch equal gain combining (EGC), selection combining (SC), and generalized SC (GSC) in correlated Rayleigh fading. This paper redresses this gap by deriving new infinite series representations for the joint probability density function (pdf) and the joint cumulative distribution function (cdf) of three and four correlated Rayleigh RVs. Bounds on the error resulting from truncating the infinite series are derived. A classical approach, due to Miller, is used to derive our results. Unfortunately, Miller's approach cannot be extended to more than four variates and, in fact, the quadrivariate case considered in this paper appears to be the most general result possible. For brevity, we treat only a limited number of applications in this paper. The new pdf and cdf expressions are used to derive the outage probability of three-branch SC, the moments of the EGC output signal-to-noise ratio (SNR), and the moment generating function of the GSC(2,3) output SNR in arbitrarily correlated Rayleigh fading. A novel application of Bonferroni's inequalities allows new outage bounds for multibranch SC in arbitrarily correlated Rayleigh channels.

The recent literature has thoroughly treated two-branch selection combining (SC) over correlated Rayleigh fading and three-branch SC over exponentially correlated Rayleigh fading. However, a long-standing open problem involves the three-branch SC performance over arbitrarily correlated Rayleigh fading. We solve this problem completely by deriving new infinite series expressions for the cumulative distribution function, the probability density function, and the moment generating function (mgf) of the three-branch SC output signal-to-noise ratio (SNR). The output mgf can be used to derive the average symbol-error rate for any two-dimensional digital modulations. The outage probability and the higher moments of the SC output SNR are also derived. These analytical results are canonical, in that the three-branch SC performance is now completely solved for arbitrary correlation. Some previous results are shown to be special cases of our new results.

Few theoretical results are known about the joint distribution of three or more correlated Rayleigh random variables (RVs). Consequently, theoretical results for the performance of 3-branch and 4-branch equal gain combining (EGC), selection combining (SC) and generalized SC (GSC) over arbitrarily correlated Rayleigh fading channels are not known. This paper derives new infinite series representations of the joint probability density function (pdf) and the joint cumulative distribution function (edf) of the tri-variate and a certain class of quadri-variate correlated Rayleigh distribution. The new pdf and cdf expressions are used to derive the outage probability of 3-branch SC and the moments of the 3-branch EGC output signal-to-noise ratio (SNR) over arbitrarily correlated Rayleigh fading. New bounds for the complementary cdf (ccdf) of the L-branch SC output SNR are also derived. These long-standing diversity theory problems, which have resisted a solution, can now be completely solved.

Despite the importance of the Rician fading model in describing microcellular, picocellular and mobile satellite channels, few theoretical results are known about the performance of selection combining (SC) and equal gain combining (EGC) in correlated Rician fading channels. In this paper, we develop a novel approach for performance analysis of L-branch diversity systems in equally correlated Rician fading channels. This approach involves transforming a set of equally correlated branch gains into a set of conditionally independent branch gains, analyzing the performance for the independent case and averaging the conditional results. Consequently, we derive novel expressions for the average error rates of various digital modulations and the output moments for both SC and EGC. We find that the performance of diversity systems in correlated Rician fading channels can be worse than that in correlated Rayleigh fading channels, which has never been observed for the independent fading case.

Emerging very high-data-rate wireless communications requires that traditional diversity systems be adapted so that some performance is sacrificed for complexity reduction. With this goal in mind, we investigate the recently-developed absolute threshold generalized selection combining (AT-GSC). We show that AT-GSC has poor bit-error rate (BER) performance when the average branch signal-to-noise ratio (SNR) is comparably lower than the preset threshold. This paper therefore develops a new diversity combining scheme, referred to as switching GSC (S- GSC). This scheme combines all branches whose SNR's exceed a preset threshold and if all the branches drop below the threshold, the output is the single branch with the maximum SNR. We prove that for any two-dimensional amplitude/phase linear modulation schemes, the symbol error rate (SER) of S-GSC lies between those of maximal ratio combining (MRC) and selection combing (SC). Importantly, the complexity of S-GSC is only slightly above that of AT-GSC. We derive the moment generating function (mgf) of the S-GSC output SNR over independent fading channels. For identically and independently distributed (i.i.d.) Rayleigh fading channels, we also derive the output probability density function (pdf) and cumulative distribution function (cdf) and analyze the error rate and the outage probability performance of S-GSC. Higher order moments of the S-GSC output SNR are also derived. These theoretical results are sufficient to completely characterize the performance of S-GSC and enable one to compare S-GSC with conventional diversity schemes.

We develop a novel approach to derive the cumulative distribution functions (cdfs) of the selection-combining (SC) output signal-to-noise ratio (SNR) in equally correlated Rayleigh, Ricean, and Nakagami-m fading channels. We show that a set of equally correlated channel gains can be transformed into a set of conditionally independent channel gains. Single-fold integral expressions are, therefore, derived for the cdfs of the SC output SNR. Infinite series representations of the output cdfs are also provided. New expressions are applied to analyze the average error rate, the outage probability, and the output statistics of SC. Numerical and simulation results that illustrate the effect of fading correlation on the performance of L-branch SC in equally correlated fading channels are provided.