Probabilistic Path Research Articles

Probabilistic Path Computation and Frequency Assignment to Mitigate Spectral Fragmentation in Elastic Optical Networks

Probabilistic Path Computation and Frequency Assignment to Mitigate Spectral Fragmentation in Elastic Optical Networks

Probabilistic Path Planning for UAVs in Forest Fire Monitoring: Enhancing Patrol Efficiency through Risk Assessment

Forest fire is a significant global natural disaster, and unmanned aerial vehicles (UAVs) have gained attention in wildfire prevention for their efficient and flexible monitoring capabilities. Proper UAV patrol path planning can enhance fire-monitoring accuracy and response speed. This paper proposes a probabilistic path planning (PPP) module that plans UAV patrol paths by combining real-time fire occurrence probabilities at different points. Initially, a forest fire risk logistic regression model is established to compute the fire probabilities at different patrol points. Subsequently, a patrol point filter is applied to remove points with low fire probabilities. Finally, combining fire probabilities with distances between patrol points, a dynamic programming (DP) algorithm is employed to generate an optimal UAV patrol route. Compared with conventional approaches, the experimental results demonstrate that the PPP module effectively improves the timeliness of fire monitoring and containment, and the introduction of DP, considering that the fire probabilities and the patrol point filter both contribute positively to the experimental outcomes. Different combinations of patrol point coordinates and their fire probabilities are further studied to summarize the applicability of this method, contributing to UAV applications in forest fire monitoring and prevention.

Human navigation strategies and their errors result from dynamic interactions of spatial uncertainties

Goal-directed navigation requires continuously integrating uncertain self-motion and landmark cues into an internal sense of location and direction, concurrently planning future paths, and sequentially executing motor actions. Here, we provide a unified account of these processes with a computational model of probabilistic path planning in the framework of optimal feedback control under uncertainty. This model gives rise to diverse human navigational strategies previously believed to be distinct behaviors and predicts quantitatively both the errors and the variability of navigation across numerous experiments. This furthermore explains how sequential egocentric landmark observations form an uncertain allocentric cognitive map, how this internal map is used both in route planning and during execution of movements, and reconciles seemingly contradictory results about cue-integration behavior in navigation. Taken together, the present work provides a parsimonious explanation of how patterns of human goal-directed navigation behavior arise from the continuous and dynamic interactions of spatial uncertainties in perception, cognition, and action.

Dynamic Event-Triggered Model Predictive Control With Guaranteed Rigorous Satisfaction of Probabilistic Path Constraints

Dynamic Event-Triggered Model Predictive Control With Guaranteed Rigorous Satisfaction of Probabilistic Path Constraints

Quantum simulation of non-Born–Oppenheimer dynamics in molecular systems by path integrals

A numerical algorithm based on the probabilistic path integral approach for solving Schrödinger equation has been devised to treat molecular systems without Born–Oppenheimer approximation in the nonrelativistic limit at zero temperature as an alternative to conventional variational and perturbation methods. Using high-quality variational trial functions and path integral method based on generalized Feynman–Kac method, we have been able to calculate the non-Born–Oppenheimer energy for hydrogen molecule for the [Formula: see text] state and hydrogen molecular ion. Combining these values and the value for ionization potential for atomic hydrogen, the dissociation energy and ionization potential for hydrogen molecules have been determined to be 36 113.672(3)[Formula: see text]cm[Formula: see text] and 124 446.066(10)[Formula: see text]cm[Formula: see text], respectively. Our results favorably compare with other theoretical and experimental results and thus show the promise of being a nonperturbative alternative for testing fundamental physical theories.

Multiple UAVs on a shared tether: Use cases, modeling, and probabilistic path planning

We analyze the concept of multiple unmanned aerial vehicles (UAVs) on a shared tether (MUST), where the UAVs act as control nodes for the shape of the tether, enabling the system to maneuver around obstacles without tangling or colliding for increased flexibility compared with single-tethered UAVs. MUST use cases are gathered from stakeholders in the military, public safety, and commercial domains. We present a model for the tether shape to use in collision checking and a model for the interactions among tether weight, size, and power, which we exercise to determine the maximum tether segment sizes. We apply three probabilistic path-planning algorithms from the literature to MUSTs, using a novel local planner and constraint set. In simulation, we show that probabilistic planners are a feasible approach to path planning for MUSTs with curved tether segments. We also show the first manual piloting modality of MUSTs.

Nondeterministic Evaluation Mechanism for User Recruitment in Mobile Crowd-Sensing

Based on the Internet of Behavior (IoB), mobile crowd-sensing (MCS) utilizes the Internet of Things (IoT) to recruit users by analyzing behavioral patterns. MCS is widely used in numerous large-scale and complex monitoring services, but it cannot provide stable and high-quality services due to nondeterministic user mobility and behaviors, which has a vital impact on recruiting high-quality users. In this article, a stochastic semi-algebraic hybrid system (SSAHS) model is constructed to characterize the user mobility and behaviors of the MCS systems. Based on the definition of probabilistic path and task execution rate, a nondeterministic evaluation mechanism is proposed to measure nondeterministic user mobility and behaviors and to give the probability of the user completing the MCS task under the specified time bound and space conditions. The greater the probability is, the higher the quality of the user. Furthermore, a user recruitment scheme based on a nondeterministic evaluation mechanism (NUR) is developed. The NUR employs historical user data to predict user mobility and behaviors; high-quality users are recruited to quickly upload reliable sensing data. We conduct simulation experiments based on a real-world user trace dataset, Geolife.The results show that compared with competing recruitment strategies, NUR achieves a higher quality of service for the same MCS sensing tasks.

Reinforcement Optimization Algorithm for Mobile Robot Sensor Networks Drive Motion Improvement

This paper proposed four optimization algorithms for mobile robot sensor networks that improve the kinematics drive motion in a reference map environment. The standard procedure followed in mobile robot sensor measurements considers a problem statement for relating the sensor measurements with a reference map. The initial path shows that the existing methods lack consideration of more sensor points without considering the boundary constraints and obstacles. The probabilistic path map can be rearranged according to the current location to improve the better drive motion, as well as to obey the fundamental kinematics equations. he obstacle crossing led to the development of new algorithms. Implementation of schemes is achieved in different map environments, and the accuracy of results outperforms conventional methods by 84.21 % to 96.94 %.

The Optimization Model of College Students’ Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory

Abstract College students can improve their physical fitness through sports activities. But physical activity requires long-term persistence. In this way, college students are required to carry out self-control. This paper studies the relationship between college students’ physical exercise motivation and self-control ability by using the mathematical model of probability theory. We use probabilistic path analysis to test the fit and difference of the relationship between the two. At the same time, the article uses Lyapunov’s characteristic function method to prove the correlation between physical exercise motivation and self-control ability again. The results show that the algorithm proposed in this paper can improve the self-management efficiency of college students.

Probabilistic Framework Allocation on Underwater Vehicular Systems Using Hydrophone Sensor Networks

This article emphasis the importance of constructing an underwater vehicle monitoring system to solve various issues that are related to deep sea explorations. For solving the issues, conventional methods are not implemented, whereas a new underwater vehicle is introduced which acts as a sensing device and monitors the ambient noise in the system. However, the fundamentals of creating underwater vehicles have been considered from conventional systems and the new formulations are generated. This innovative sensing device will function based on the energy produced by the solar cells which will operate for a short period of time under the water where low parametric units are installed. In addition, the energy consumed for operating a particular unit is much lesser and this results in achieving high reliability using a probabilistic path finding algorithm. Further, two different application segments have been solved using the proposed formulations including the depth of monitoring the ocean. To validate the efficiency of the proposed method, comparisons have been made with existing methods in terms of navigation output units, rate of decomposition for solar cells, reliability rate, and directivity where the proposed method proves to be more efficient for an average percentile of 64%.

Stochastic Primer Vector for Robust Low-Thrust Trajectory Design Under Uncertainty

Any space trajectories are subject to state uncertainty due to imperfect state knowledge, random disturbances, and partially known dynamical environments. Ideally, such uncertainty and associated risks must be properly quantified and taken into account in the process of trajectory design, ensuring a sufficiently low risk of causing hazardous events. To bridge the gap between the ideal goal and current practice in mission design, this paper extends Lawden’s primer vector theory and develops a solution method to solve the problem of low-thrust trajectory optimization under state uncertainty. The new primer vector, termed stochastic primer vector, provides an analytical open-loop optimal control law that respects a probabilistic path constraint with a user-specified confidence level (chance constraint). A numerical aspect of the indirect method is also extended by introducing a smoothing approach across constraint corner discontinuities, enabling efficient solution methods for constrained optimal control problems. The validity and effectiveness of the theoretical development are demonstrated with two numerical examples, which clarify the behavior of chance-constrained optimal low-thrust trajectories and confirm through Monte Carlo simulations that the designed trajectories indeed satisfy the imposed constraints under uncertainty with the prescribed confidence level.

Comprehensive Project Risk Management Methodology

The objective of this paper is to introduce and discuss the basics of a methodology called the Probabilistic Critical Path Method (PCPM) for managing the previously identified risks (uncertainty) of the three project management dimensions: time, cost and return (performance). An interactive Graphic User Interface (GUI) has been designed for visualizing the tradeoffs among these three dimensions as well as their uncertainties on a flat computer screen. The user can choose to visualize the probability of failure (exceeding some user given due date, budget or not exceeding a given Minimally Attractive Rate of Return – MARR) or the probability of success (not exceeding the due date and the budget and exceeding the MARR). PCPM allows for comprehensive project risk management and it constitutes a new integrative project risk management framework. This paper shows that it is possible to integrate all three project management dimensions (time, cost and return) and show their known risks as well as determining the optimal cost and the associated time and return for such optimal cost. Finally, it is possible to interactively show all this multidimensional information on a flat computer screen.

Dynamic Probability Analysis for Construction Schedule Using Subset Simulation

Schedule management is an essential part of construction project management. In practical management affairs, many uncertainties may lead to potential project delays and make the schedule risky. To quantify such risk, the Probabilistic Critical Path Method (PCPM) is used to compute the overdue probability. Survey shows it could help project managers understand the schedule better. However, two critical factors limited the application of PCPM: computational efficiency and timeliness. To solve these constraints, we combined subset simulation and statistical learning to build a computationally efficient and dynamic simulation system. Numerical experiment shows that this method can effectively improve the computation efficiency without losing any accuracy and outperforms the other approaches with the same assumptions. Besides, we proposed a machine learning‐based way to estimate task duration distributions in PCPM automatically. It collects real‐time progress data through user interactions and learns the best PERT‐Beta parameters based on these historical data. Our estimator provides our simulation system the ability to handle dynamic assessment without laborious human work. These improvements reduce the limitations of PCPM, making the application of PCPM in practical management affairs possible.

Reliability analysis of truss structures considering complete failure paths and using the FLHB model

abstract: The study of progressive collapse of structures using numerical models requires accurate modeling of geometrical nonlinearity and material failure behavior. Numerical models must demonstrate stability, such that localized member failures do not trigger numerical instabilities. Also, algorithms should be efficient, to limit the computational burden of analyzing multiple responses when considering the effects of uncertain loads, geometric and material variables. In this scientific domain, a comprehensive non-linear ductile-damage truss-element model has been recently presented by the authors. The model accounts for the geometrical and material nonlinearities observed during progressive collapse of structural systems. In this paper, the Felipe-Leonel-Haach-Beck (FLHB) model is calibrated to describe the response of Ultra-High-Performance Fiber Reinforced Concrete (UHPFRC). Based on a limited number of UHPFRC experimental curves, statistics of FLHB model parameters are obtained. These are employed in the probabilistic analysis of failure paths of truss structures under progressive collapse. Monte Carlo Simulation and the First Order Reliability Method are employed in the probabilistic failure path analyses. Six application examples demonstrate the accuracy, robustness, and efficiency of the FLHB model in evaluation of failure paths of realistic structural systems.

Probabilistic Path Prioritization for Hybrid Fuzzing

Hybrid fuzzing that combines fuzzing and concolic execution has become an advanced technique for software vulnerability detection. Based on the observation that fuzzing and concolic execution are complementary in nature, state-of-the-art hybrid fuzzing systems deploy “optimal concolic testing” and “demand launch” strategies. Although these ideas sound intriguing, we point out several fundamental limitations in them, due to unrealistic or oversimplified assumptions. Further, we propose a novel “discriminative dispatch” strategy and design a probabilistic hybrid fuzzing system to better utilize the capability of concolic execution. Specifically, we design a Monte Carlo-based probabilistic path prioritization model to quantify each path’s difficulty, and then prioritize them for concolic execution. Our model assigns the most difficult paths to concolic execution. We implement a prototype named <inline-formula><tex-math notation="LaTeX">${\sf DigFuzz}$</tex-math></inline-formula> and evaluate our system with two representative datasets and real-world programs. Results show that the concolic execution in <inline-formula><tex-math notation="LaTeX">${\sf DigFuzz}$</tex-math></inline-formula> outperforms than those in state-of-the-art hybrid fuzzing systems in every major aspect. In particular, the concolic execution in <inline-formula><tex-math notation="LaTeX">${\sf DigFuzz}$</tex-math></inline-formula> contributes to discovering more vulnerabilities (12 versus 5) and producing more code coverage (18.9 versus 3.8 percent) on the CQE dataset than the concolic execution in Driller.

A Bi-Level Probabilistic Path Planning Algorithm for Multiple Robots with Motion Uncertainty

For improving the system efficiency when there are motion uncertainties among robots in the warehouse environment, this paper proposes a bi-level probabilistic path planning algorithm. In the proposed algorithm, the map is partitioned into multiple interconnected districts and the architecture of proposed algorithm is composed of topology level and route level generating from above map: in the topology level, the order of passing districts is planned combined with the district crowdedness to achieve the district equilibrium and reduce the influence of robots under motion uncertainty. And in the route level, a MDP method combined with probability of motion uncertainty is proposed to plan path for all robots in each district separately. At the same time, the number of steps for each planning is dependent on the probability to decrease the number of planning. The conflict avoidance is proved, and optimization is discussed for the proposed algorithm. Simulation results show that the proposed algorithm achieves improved system efficiency and also has acceptable real-time performance.

Robust Superimposed Training Optimization for UAV Assisted Communication Systems

In this paper, we propose a superimposed training based two-phase robust channel estimation scheme for the unmanned aerial vehicle (UAV) assisted cellular communication system, in which various unitarily-invariant channel statistics errors are considered. Specifically, in the first phase, mobile station (MS) estimates the UAV-MS channel via the UAV training sequence, of which the robust design can be solved based on convex-concave theory. While in the second phase, the superimposed training scheme is considered at the ground base station (GBS) to improve spectrum efficiency. Then the robust GBS training sequence, the information signal power and the UAV amplifying factor are jointly optimized for the partially cascaded GBS-UAV-MS channel estimation subject to GBS and UAV transmit power constraints as well as the required information signal strength at the MS. To tackle this NP-hard problem, the optimal structures of involved variables are firstly derived, based on which the robust superimposed training design is simplified and proved to be quasi-convex in the UAV amplifying factor. Particularly, for Spectral norm and Nuclear norm bounded errors, the optimal training sequence can be obtained via convex-concave theory and Golden section searchWhile for Frobenius norm bounded error, a tractable upper-bounding scheme is proposed for the robust superimposed training design. Furthermore, we extend our work into the more general probabilistic path loss scenario of UAV-ground channels, and analyze the impacts of the probabilistic path loss and Rician $K$ -factor on channel estimation performance. Numerical results illustrate the excellent performance of the proposed superimposed training based two-phase channel estimation scheme.

Time-Cost Optimization Model with Probabilistic Path and Float Consumption Impact

Time-Cost Optimization Model with Probabilistic Path and Float Consumption Impact

Risk‐aware last‐minute data backup in inter‐datacenter networks

Network failure caused by disasters (both natural and man-made like earthquakes, floods, cyclones, electromagnetic pulse attacks etc.) result in communication disruption and huge amounts of data loss in the backbone datacenter (DC) networks. To prevent such large-scale network disruptions and quickly resume connectivity after the disaster, network operators require improved and efficient data-transfer algorithms in geographically distributed (geo-distributed) optical inter-DC networks. Minimising loss of infrastructure and preventing network disruption requires estimating the damage from a possible disaster. In this study, the authors consider a mutual backup model, where DCs can serve as backup sites of each other, thereby significantly reducing the backup duration (i.e. DC-Backup-Window (DC-B-Wnd)). They specifically consider the joint optimisation of probabilistic backup site selection and the amount of data to be backed up. They propose mixed-integer linear programming models for backup time minimisation using a single DC as well as dual DCs at backup sites. Further, they investigate the trade-off between DC-B-Wnd and the computational complexity of the proposed algorithms and perform extensive numerical simulations to show that, in the case of disasters, single and dual DC backups with risk-aware probabilistic path selection give shorter backup windows as compared to existing algorithms.

An efficient mechanical-probabilistic approach for the collapse modelling of RC structures

Abstract The reinforced concrete (RC) structures are widely utilized around the world. However, the modelling of its complex mechanical behaviour by efficient numerical approaches has been presented marginally in the literature. The efficient approaches enable the accurate and the realistic representation of the mechanical phenomena involved and are computationally efficient for analysing complex structures. In the present study, the improved version of the lumped damage model is coupled to the Monte Carlo simulation method to represent the mechanical-probabilistic behaviour of RC structures. In such model, the concrete cracking and reinforcements’ yield are represented accurately. Moreover, this damage approach enables the accurate modelling of failure scenarios, which are based on the damage variable. Furthermore, this coupled model enables the determination of the collapse modelling accounting for uncertainties, which is the main contribution of the present study. One simple supported RC beam and one 2D RC frame are analysed in the probabilistic context. The accurate results are obtained for the probabilistic collapse path as well as its changes as a function of the loading conditions and material properties uncertainties.