Search Results (84)

In this work, we propose a definition of the random fractional Riemann–Liouville integral operator, where the order of integration is given by a random variable. Within the framework of random operator theory, we study this integral with a random kernel and establish results on the measurability of the random Riemann–Liouville integral operator, which we show to be a random endomorphism of $L^1[a,b]$. Additionally, we derive the semigroup property for these operators as a probabilistic version of the constant-order Riemann–Liouville integral. To illustrate the behavior of this operator, we present two examples involving different random variables acting on specific functions. The sample trajectories and estimated probability density functions of the resulting random integrals are then explored via Monte Carlo simulation. Full article

In today’s dynamic and highly uncertain environment, organizations, particularly in the aviation sector, face increasing challenges that demand resilient, flexible, and data-driven change management decisions. Responding to the growing need for structured approaches to managing complex uncertainties—geopolitical tensions, economic volatility, social shifts, rapid technological advancements, environmental pressures and regulatory changes—this research proposes a theoretical change management model for aviation service providers, such as airports. Integrating three analytical approaches, the model offers a robust, multi-method approach for supporting sustainable transformation under uncertainty. Normative analysis using Bayesian decision theory identifies influential external environmental factors, capturing probabilistic relationships, and revealing causal links under uncertainty. Prescriptive planning through scenario theory explores alternative future pathways and helps to identify possible predictions, offer descriptive evaluation employing fuzzy comprehensive evaluation, and assess decision quality under vagueness and complexity. The proposed four-stage model—observation, analysis, evaluation, and response—offers a methodology for continuous external environment monitoring, scenario development, and data-driven, proactive change management decision-making, including the impact assessment of change and development. The proposed model contributes to the theoretical advancement of the change management research area under uncertainty and offers practical guidance for aviation organizations (airports) facing a volatile external environment. This framework strengthens aviation organizations’ ability to anticipate, evaluate, and adapt to multifaceted external changes, supporting operational flexibility and adaptability and contributing to the sustainable development of aviation services. Supporting aviation organizations with tools to proactively manage systemic uncertainty, this research directly supports the integration of sustainability principles, such as resilience and adaptability, for long-term value creation through change management decision-making. Full article

Accurate extraction of representative operating conditions is crucial for optimizing systems in renewable energy applications. This study proposes a novel framework that combines the Parzen window estimation method, ideal for nonparametric modeling of wind, solar, and load datasets, with a game theory-based time scale selection mechanism. The novelty of this work lies in integrating probabilistic density modeling with multi-indicator evaluation to derive realistic operational profiles. We first validate the superiority of the Parzen window approach over traditional Weibull and Beta distributions in estimating wind and solar probability density functions. In addition, we analyze the influence of key meteorological parameters such as wind direction, temperature, and solar irradiance on energy production. Using three evaluation metrics, the main result shows that a 3-day representative time scale offers optimal accuracy when determined through game theory methods. Validation with real-world data from Inner Mongolia confirms the robustness of the proposed method, yielding low errors in wind, solar, and load profiles. This study contributes a novel 3-day typical profile extraction method validated on real meteorological data, providing a data-driven foundation for optimizing energy storage systems under renewable uncertainty. This framework supports energy sustainability by ensuring realistic modeling under renewable intermittency. Full article

The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article

The water–energy nexus (WEN) is of great significance due to the strong interdependence between the energy and water sectors. Nevertheless, water leakage in water distribution networks (WDNs), which is often ignored in existing WEN operation models, causes notable water and energy losses. In this research, a cooperative operation model for WEN considering WDN water leakage is put forward. A hybrid stochastic–information gap decision theory (IGDT) method was tailored in this study to properly manage the probabilistic uncertainties associated with renewable generation, electrical and water demand in the WEN, and water leakage with limited information to enhance the robustness of the operation strategies of the WEN under complex operational conditions. The proposed model and method were validated on a modified IEEE 33-bus system integrated with a 15-node commercial WDN. The co-optimization model reduced the operational cost by 23.01% compared to the independent operation model. When considering water leakage, the joint optimization resolved the water supply shortage issue caused by ignoring leakage and reduced the water purchase volume by 94.44 cubic meters through coordinated optimization. These quantitative results strongly demonstrate the effectiveness of the proposed framework. Full article

General aviation trajectory prediction plays a crucial role in enhancing safety and operational efficiency at non-towered airports. However, current research faces multiple challenges including variable weather conditions, complex aircraft interactions, and flight pattern constraints specified by general aviation regulations. This paper proposes a deep learning method based on stochastic processes aimed at addressing uncertainty issues in general aviation trajectory prediction. First, we design a probabilistic encoder–decoder structure enabling the model to output trajectory distributions rather than single paths, with regularization terms based on Lyapunov stability theory to ensure predicted trajectories maintain stable convergence while satisfying flight patterns. Second, we develop a multi-layer attention mechanism that accounts for weather factors, enhancing the model’s responsiveness to environmental changes. Validation using the TrajAir dataset from Pittsburgh-Butler Regional Airport (KBTP) not only advances deep learning applications in general aviation but also provides new insights for solving trajectory prediction problems. Full article

The failure mode and effect analysis (FMEA) method, which estimates the risk levels of systems or components solely based on the multiplication of simple risk rating indices, faces several limitations. These include the risk of inaccurate risk level judgment and the potential for misjudgments due to human factors, both of which pose significant threats to the safe operation of aircraft. Therefore, a Probabilistic Language based on a cumulative prospect theory (Probabilistic Language, PL) risk assessment strategy was proposed, combining the technique for order preference with similarity to an ideal solution (TOPSIS). The probabilistic language term value and probability value were fused in the method through the cumulative prospect theory, and a new PL measure function was introduced. The comprehensive weights of evaluation strategies were determined by calculating the relevant weights of various indicators through the subjective expert weight and objective entropy weight synthesis. So, a weighted decision matrix was constructed to determine the ranking order close to the ideal scheme. Finally, the risk level of each failure mode was ranked according to its close degree to the ideal situation. Through case validation, the consistency of risk ranking was improved by 23.95% compared to the traditional FMEA method. The rationality of weight allocation was increased by 18.2%. Robustness was also enhanced to some extent. Compared with the traditional FMEA method, the proposed method has better rationality, application, and effectiveness. It can provide technical support for formulating a new generation of airworthiness documents for the risk level assessment of civil aircraft and its subsystem components. Full article

Addressing the critical challenges of sealing integrity and operational optimization in aquifer gas storage (AGS), this study focuses on a block within the Qianjiang Basin to systematically investigate geological modeling and injection–production strategies. Utilizing 3D seismic interpretation, drilling, and logging data, a stochastic geological modeling approach was employed to construct a high-resolution 3D reservoir model, elucidating the distribution of reservoir properties and trap configurations. Numerical simulations optimized the gas storage parameters, yielding an injection rate of 160 MMSCF/day (40 MMSCF/well/day) over 6-month-long hot seasons and a production rate of 175 MMSCF/day during 5-month-long cold seasons. Interval theory was innovatively applied to assess fault stability under parameter uncertainty, determining a maximum safe operating pressure of 23.5 MPa—12.3% lower than conventional deterministic results. The non-probabilistic reliability analysis of caprock integrity showed a maximum 11.1% deviation from Monte Carlo simulations, validating the method’s robustness. These findings establish a quantitative framework for site selection, sealing system evaluation, and operational parameter design in AGS projects, offering critical insights to ensure safe and efficient gas storage operations. This work bridges theoretical modeling with practical engineering applications, providing actionable guidelines for large-scale AGS deployment. Full article

This study establishes a novel mathematical framework for stochastic maintenance optimization in production systems by integrating Markov decision processes (MDPs) with convex programming theory. We develop a Z-transformation-based dual-space decomposition method to reconstruct MDPs into a solvable linear programming form, resolving the inherent instability of traditional models caused by uncertain initial conditions and non-stationary state transitions. The proposed approach introduces three mathematical innovations: (i) a spectral clustering mechanism that reduces state-space dimensionality while preserving Markovian properties, (ii) a Lagrangian dual formulation with adaptive penalty functions to handle operational constraints, and (iii) a warm start algorithm accelerating convergence in high-dimensional convex optimization. Theoretical analysis proves that the derived policy achieves stability in probabilistic transitions through martingale convergence arguments, demonstrating structural invariance to initial distributions. Experimental validations on production processes reveal that our model reduces long-term maintenance costs by 36.17% compared to Monte Carlo simulations (1500 vs. 2350 average cost) and improves computational efficiency by 14.29% over Q-learning methods. Sensitivity analyses confirm robustness across Weibull-distributed failure regimes (shape parameter $\beta \in$ [1.2, 4.8]) and varying resource constraints. Full article

The vigorous development of urban air mobility (UAM) is reshaping the urban travel landscape, but it also poses severe challenges to the safe and efficient operation of dense and complex airspace. Potential conflicts between flight plans have become a core bottleneck restricting its development. Traditional flight plan adjustment and management methods often rely on deterministic trajectory predictions, ignoring the inherent temporal uncertainties in actual operations, which may lead to the underestimation of potential risks. Meanwhile, existing global optimization strategies often face issues of inefficiency and overly broad adjustment scopes when dealing with large-scale plan conflicts. To address these challenges, this study proposes an innovative flight plan conflict management framework. First, by introducing a probabilistic model of flight time errors, a new conflict detection mechanism based on confidence intervals is constructed, significantly enhancing the ability to foresee non-obvious conflict risks. Furthermore, based on complex network theory, the framework accurately identifies a small number of “critical flight plans” that play a core role in the conflict network, revealing their key impact on chain reactions of conflicts. On this basis, a phased optimization strategy is adopted, prioritizing the adjustment of spatiotemporal parameters (departure time and speed) for these critical plans to systematically resolve most conflicts. Subsequently, only fine-tuning the speeds of non-critical plans is required to address remaining local conflicts, thereby minimizing interference with the overall operational order. Simulation results demonstrate that this framework not only significantly improves the comprehensiveness of conflict detection but also effectively reduces the total number of conflicts. Additionally, the proposed phased artificial lemming algorithm (ALA) outperforms traditional optimization algorithms in terms of solution quality. This work provides an important theoretical foundation and a practically valuable solution for developing robust and efficient UAM dynamic scheduling systems, holding promise to support the safe and orderly operation of large-scale urban air traffic in the future. Full article

In the framework of quasi-Hermitian quantum mechanics, the eligible operators of observables may be non-Hermitian, $A_j\ne A_j^{†}$, $j=1,2,\dots ,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $\mathsf{\Theta }\ne I$, guaranteeing the quasi-Hermiticity $A_j^{†}\mathsf{\Theta }=\mathsf{\Theta }{A}_j$. The task is easy at $K=1$ because there are many eligible metrics $\mathsf{\Theta }=\mathsf{\Theta }\left(A_1\right)$. In our paper, the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric, $\mathsf{\Theta }=\mathsf{\Theta }(A_1,A_2)$, are presented and discussed. Full article

To rectify significant heading calculation errors in polarized light navigation for unmanned aerial vehicles (UAVs) under tilted states, this paper proposes a method for compensating horizontal attitude angles based on horizon detection. First, a defogging enhancement algorithm that integrates Retinex theory with dark channel prior is adopted to improve image quality in low-illumination and hazy environments. Second, a dynamic threshold segmentation method in the HSV color space (Hue, Saturation, and Value) is proposed for robust horizon region extraction, combined with an improved adaptive bilateral filtering Canny operator for edge detection, aimed at balancing detail preservation and noise suppression. Then, the progressive probabilistic Hough transform is used to efficiently extract parameters of the horizon line. The calculated horizontal attitude angles are utilized to convert the body frame to the navigation frame, achieving compensation for polarization orientation errors. Onboard experiments demonstrate that the horizontal attitude angle estimation error remains within 0.3°, and the heading accuracy after compensation is improved by approximately 77.4% relative to uncompensated heading accuracy, thereby validating the effectiveness of the proposed algorithm. Full article

In the oil and gas IIoT environment, fire detection systems heavily depend on fire sensor data, which can be prone to inaccuracies due to faulty or unreliable sensors. These sensor issues, such as noise, missing values, outliers, sensor drift, and faulty readings, can lead to delayed or missed fire predictions, posing significant safety and operational risks in the oil and gas industrial IoT environment. This paper presents an approach for handling faulty sensors in edge servers within an IIoT environment to enhance the reliability and accuracy of fire prediction through multi-sensor fusion preprocessing, machine learning (ML)-driven probabilistic model adjustment, and uncertainty handling. First, a real-time anomaly detection and statistical assessment mechanism is employed to preprocess sensor data, filtering out faulty readings and normalizing data from multiple sensor types using dynamic thresholding, which adapts to sensor behavior in real-time. The proposed approach also deploys machine learning algorithms to dynamically adjust probabilistic models based on real-time sensor reliability, thereby improving prediction accuracy even in the presence of unreliable sensor data. A belief mass assignment mechanism is introduced, giving more weight to reliable sensors to ensure they have a stronger influence on fire detection. Simultaneously, a dynamic belief update strategy continuously adjusts sensor trust levels, reducing the impact of faulty readings over time. Additionally, uncertainty measurements using Hellinger and Deng entropy, along with Dempster–Shafer Theory, enable the integration of conflicting sensor inputs and enhance decision-making in fire detection. This approach improves decision-making by managing sensor discrepancies and provides a reliable solution for real-time fire predictions, even in the presence of faulty sensor readings, thereby mitigating the fire risks in IIoT environments. Full article

To reduce the burden on individuals with disabilities when operating a Wheelchair Mounted Robotic Arm (WMRA), many researchers have focused on inferring users’ subsequent task intentions based on their “gazing” or “selecting” of scene objects. In this paper, we propose an innovative intention reasoning method for users’ action sequences by fusing object task and object action affordances based on Dempster–Shafer Theory (D-S theory). This method combines the advantages of probabilistic reasoning and visual affordance detection to establish an affordance model for objects and potential tasks or actions based on users’ habits and object attributes. This facilitates encoding object task (OT) affordance and object action (OA) affordance using D-S theory to perform action sequence reasoning. Specifically, the method includes three main aspects: (1) inferring task intentions from the object of user focus based on object task affordances encoded with Causal Probabilistic Logic (CP-Logic); (2) inferring action intentions based on object action affordances; and (3) integrating OT and OA affordances through D-S theory. Experimental results demonstrate that the proposed method reduces the number of interactions by an average of 14.085% compared to independent task intention inference and by an average of 52.713% compared to independent action intention inference. This demonstrates that the proposed method can capture the user’s real intention more accurately and significantly reduce unnecessary human–computer interaction. Full article

Power consumption management is crucial to maintaining the reliable operation of power grids, especially in the context of the decarbonization of the electric power industry. Managing power consumption of industrial enterprises by personnel proved ineffective, which required the development and implementation of automatic energy consumption management systems. Optimization of power consumption behavior requires comprehensive and reliable information on the parameters of the technological processes of an industrial enterprise. The paper explores the specific features of non-stationary conditions of output production and assesses the potential for power consumption management under these conditions. The analysis of power consumption modes was carried out based on the consideration of random factors determined by both internal and external circumstances, subject to the fulfillment of the production plan. This made it possible to increase the efficiency of power consumption in mechanical engineering production by taking into account the uncertainty of seasonal and technological fluctuations by 15–20%, subject to the fulfillment of the production plan. This study presents a justification for utilizing the theory of level-crossings of random processes to enhance the reliability of input information. The need to analyze the specific features of technological processes based on the probabilistic structure and random functions is proven. This is justified because it becomes possible to fulfill the production plan with technological fluctuations in productivity and, accordingly, power consumption, which exceeds the nominal values by more than 5%. In addition, the emission characteristics are clear, easy to measure, and allow the transition from analog to digital information presentation. The algorithm and methods developed to analyze the power consumption patterns of industrial enterprises can be used to develop automatic power consumption management systems. Full article