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This paper presents a linear and nonlinear stochastic distribution for the interactions in multi-agent systems (MAS). The interactions are considered for the agents to reach a consensus using hetero-homogeneous transition stochastic matrices. The states of the agents are presented as variables sharing information in the MAS dynamically. The paper studies the interaction among agents for the attainment of consensus by limit behavior from their initial states’ trajectories. The paper provides a linear distribution of DeGroot model compared with a nonlinear distribution of change stochastic quadratic operators (CSQOs), doubly stochastic quadratic operators (DSQOs) and extreme doubly stochastic quadratic operators (EDSQOs) for a consensus problem in MAS. The comparison study is considered for stochastic matrix (SM) and doubly stochastic matrix (DSM) cases of the hetero-homogeneous transition stochastic matrices. In the case of SM, the work’s results show that the DeGroot linear model converges to the same unknown limit while CSQOs, DSQOs and EDSQOs converge to the center. However, the results show that the linear of DeGroot and nonlinear distributions of CSQOs, DSQOs and EDSQOs converge to the center with DSM. Additionally, the case of DSM is observed to converge faster compared to that of SM in the case of nonlinear distribution of CSQOs, DSQOs and EDSQOs. In general, the novelty of this study is in showing that the nonlinear stochastic distribution reaches a consensus faster than all cases. In fact, the EDSQO is a very simple system compared to other nonlinear distributions.

We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class is in bijection with a subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the framework of perturbation theory, is based on an in-depth and original analysis of an intertwining relation that we establish between this class and a self-adjoint Markov semigroup, whose spectral expansion is expressed in terms of the classical Laguerre polynomials. As a by-product, we derive smoothness properties for the solution to the associated Cauchy problem as well as for the heat kernel. Our methodology also reveals a variety of possible decays, including the hypocoercivity type phenomena, for the speed of convergence to equilibrium for this class and enables us to provide an interpretation of these in terms of the rate of growth of the weighted Hilbert space norms of the spectral projections. Depending on the analytic properties of the aforementioned negative definite functions, we are led to implement several strategies, which require new developments in a variety of contexts, to derive precise upper bounds for these norms.

Since failure of steam turbines occurs frequently and can causes huge losses for thermal plants, it is important to identify a fault in advance. A novel clustering fault diagnosis method for steam turbines based on t-distribution stochastic neighborhood embedding (t-SNE) and extreme gradient boosting (XGBoost) is proposed in this paper. First, the t-SNE algorithm was used to map the high-dimensional data to the low-dimensional space; and the data clustering method of K-means was performed in the low-dimensional space to distinguish the fault data from the normal data. Then, the imbalance problem in the data was processed by the synthetic minority over-sampling technique (SMOTE) algorithm to obtain the steam turbine characteristic data set with fault labels. Finally, the XGBoost algorithm was used to solve this multi-classification problem. The data set used in this paper was derived from the time series data of a steam turbine of a thermal power plant. In the processing analysis, the method achieved the best performance with an overall accuracy of 97% and an early warning of at least two hours in advance. The experimental results show that this method can effectively evaluate the condition and provide fault warning for power plant equipment.

This paper investigates an uncommon technique by using the influence of the random function (Weiner process function), on a two-temperature problem, at the free surface of the semiconducting medium, by using the photo-thermoelasticity theory. Using the Silicon material as an example of a semiconducting medium under the influence of a magnetic field, the novel model can be formulated. To make the problem more logical, the randomness of the Weiner process function is aged to the governing stochastic equation. A combining stochastic process with the boundary of the variables is studied. In this case, the stochastic and deterministic solutions were obtained for all physical quantities. The additional noise is regarded as white noise. The problem is investigated according to a two-dimensional (2D) deformation. The normal mode method can be used mathematically to obtain numerically the deterministic, stochastic, and variance solutions of all physical quantities. Three sample paths are obtained by making a comparison between the stochastic and deterministic distributions of the field variables. The impacts of adding randomization to the boundary conditions are highlighted. The numerical results are shown graphically and discussed in consideration of the two-temperature parameter effect.

Fractures in the overburden induced by mining disturbances provide channels for heat-mass exchange between the subsurface environment and ground surface. Void fraction is an important characterization parameter to determine the difficulty of fluid flow and heat transfer. The three-dimensional stochastic distribution characteristics of the void fraction in the longwall mining-disturbed overburden are proposed based on the theoretical expressions of stratum and ground settlements and combined with a stochastic law with a normal distribution of void fractions obtained from statistical analyses from similar physical simulation experiments. The deterministic and stochastic distribution models and the discrete element numerical simulations show that the void fraction distribution is U-shaped in the cave zone and M-shaped in the bed separation zone. In the ground subsidence zone, the void fraction distribution of the horizontal fracture is M-shaped in the strike direction and an inverted U-shaped in the dip direction, and the void fraction presents an M-shaped distribution for the vertical fracture. As the depth decreases, the void fraction gradually decreases. As longwall mining progresses, the subsidence amount of stratum changes from a V-shaped into a U-shaped distribution, and the total void fraction transforms from an inverted V-shaped distribution to M-shaped distribution. The fracture distribution of the disturbed overburden forms into a fractured arch, and the fracture density gradually decreases from the foot to the top of the arch. The void fraction as a determinant parameter for stochastic distribution of permeability can provide valuable information for coal bed methane drainage, water inrush prevention, and coal fire control.

Multi-scale voids including fractures and bed separations will appear and dynamically develop as the underground mining-induced disturbance increases. The void fraction, which is an index for characterizing the void scale, is an important parameter for understanding the heat and mass transfer (including methane flow, coal spontaneous combustion, underground water flow) in the fractured overburden disturbed by underground mining of coal seam. The stochastic caving tests were conducted to simulate the roof caving and overburden movement induced by coal seam mining with different inclination angle and excavation length. The expectations and variances of random variables about the overall and local void fractions showed that the void fractions gradually increase with increases in excavation lengths and obey a normal distribution. The distribution fields of the mean and stochastic void fractions indicated that the rich voids present an arch-type distribution in the disturbed overburden. The random distribution field of void fractions obtained from stochastic inversion presents a small range of fluctuation around the mean values of void fractions and is more realistic to reflect the randomness of separation and caving of rock strata induced by underground mining of coal seam.

When the geological environment of rock masses is disturbed, numerous non-persisting open joints can appear within it. It is crucial to investigate the effect of open joints on the mechanical properties of rock mass. However, it has been challenging to generate realistic open joints in traditional experimental tests and numerical simulations. This paper presents a novel solution to solve the problem. By utilizing the stochastic distribution of joints and an enhanced-fractal interpolation system (IFS) method, rough curves with any orientation can be generated. The Douglas-Peucker algorithm is then applied to simplify these curves by removing unnecessary points while preserving their fundamental shape. Subsequently, open joints are created by connecting points that move to both sides of rough curves based on the aperture distribution. Mesh modeling is performed to construct the final mesh model. Finally, the RB-DEM method is applied to transform the mesh model into a discrete element model containing geometric information about these open joints. Furthermore, this study explores the impacts of rough open joint orientation, aperture, and number on rock fracture mechanics. This method provides a realistic and effective approach for modeling and simulating these non-persisting open joints.

Energy-awareness in the industrial sectors has become a global consensus in recent decades. Green scheduling is acknowledged as an effective weapon to reduce energy consumption in the industrial sectors. Therefore, this paper is devoted to the green scheduling of flexible manufacturing cells (FMC) with auto-guided vehicle transportation, where conflict-free routing of the vehicles is considered. To deal with this problem, a bi-objective optimization model is proposed to achieve the minimization of the maximum completion time and the total energy consumption in an FMC. The studied problem is an extension of flexible job shop problem which is NP-hard. Thus, an improved bi-objective salp swarm algorithm based on decomposition (IMOSSA/D) is proposed and applied to the problem. The approach is based on the decomposition of the bi-objective problem. Salp swarm intelligence along with three stochastic-distribution-based operators are incorporated into the approach, to enhance and balance its exploring and exploiting ability. Computational experiments are performed to compare the proposed approach with two state-of-the-art algorithms. This study allows the decision makers to better trade-off between energy savings and production efficiency in flexible manufacturing cellular environment.

The volume contains the proceedings of the international workshop on Concentration, Functional Inequalities and Isoperimetry, held at Florida Atlantic University in Boca Raton, Florida, from October 29-November 1, 2009. The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, to name but a few fields, with recent new applications in random matrices and information theory. This book should appeal to graduate students and researchers interested in the fascinating interplay between analysis, probability, and geometry.

In this paper, we investigate the problem of weight estimation and secure control for discrete stochastic distribution control (SDC) systems under sparse sensor attacks. Firstly, a Luenberger observer is designed for the linear SDC systems to perform the weight estimation under sparse sensor attacks. Then, a generalized proportional-integral (PI) tracking control strategy is proposed for the linear B-spline model. Furthermore, the tracking problem for output probability density functions (PDFs) is implemented, and the designed controller ensures that the closed-loop system is stable. Finally, the simulation results show the effectiveness of the proposed method.