Stochastic Distribution Model Research Articles

A Novel Failure-Distribution-Dependent Non-Fragile $H_\infty$ Fault-Tolerant Load Frequency Control for Faulty Multi-Area Power Systems

This paper studies the non-fragile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> fault-tolerant load frequency control problem for multi-area power systems with actuator failures. At first, considering the distribution characteristics of partial failures, a stochastic distribution model is established for actuator partial failures. Next, for the perturbations of controller gains, not only the additive uncertainties but also the multiplicative uncertainties are incorporated into the fault-tolerant controller design. The coupling items which hardly directly solved have turned into a W-problem in fault-tolerant load frequency control. Furthermore, a novel failure-distribution-dependent non-fragile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> fault-tolerant load frequency control algorithm is given by using linear matrix inequalities technology and Lyapunov-Krasovskii functional method. Finally, a numerical example with a three-area power system are given to show the effectiveness of the proposed methods.

Vibration response analysis of footbridge based on pedestrian perception

This article aims to study the influence of random crowd loading on the perceived vibration response of pedestrians. Firstly, a vertical vibration response analysis method considering pedestrian perception was established based on the random crowd walking model. Secondly, change rules of maximum vibration response of pedestrians, occurrence time and position interval under different random walk models were compared and analyzed. Finally, the vibration response reduction factor was defined by studying the correlation between the maximum vibration response of pedestrians and the peak acceleration of the structure, and the approximate calculation method of the maximum vibration response of pedestrians was proposed. The results show that the maximum acceleration perceived by pedestrians obeys the normal distribution under the four crowd walking models, the response distribution of ordered arrangement model (OAM) is larger than that of the other three models; The location and occurrence time of the maximum response depend on the distribution of pedestrian locations on the footbridge, and there is no significant change with the increase of population density. In addition, the distribution of OAM and stochastic arrival model (SAM) are consistent, which is concentrated in the middle of the total time-history. In contrast, the distribution of stochastic distribution model (SDM) and dynamic equilibrium model (DEM) are relatively uniform. The maximum error between the calculated acceleration maximum value and the actual acceleration value felt by the pedestrian is less than 5%. These results can provide reference for quantitative evaluation of pedestrian-induced vibration comfort.

Numerical Simulation in the Melt Pool Evolution of Laser Powder Bed Fusion Process for Ti6Al4V.

In order to track the free interface of the melt pool and understand the evolution of the melt pool, the flow of fluid, and the interface behavior of gas and liquid, a physical model is developed by using the VOF method in this paper. Its characteristics are a combined heat source model, including a parabolic rotation and a cylindrical distribution, and a powder bed stochastic distributed model with powder particle size. The unit interface between the metallic and gas phase in the laser-powder interaction zone can only be loaded by the heat source. Only the first and second laser scanning tracks are simulated to reduce the calculation time. The simulation results show that process parameters such as laser power and scanning speed have significant effects on the fluid flow and surface morphology in the melt pool, which are in good agreement with the experimental results. Compared with the first track, the second track has larger melt pool geometry, higher melt temperature, and faster fluid flow. The melt flows intensely at the initial position due to the high flow rate in the limited melt space. Because there is enough space for the metal flow, the second track can obtain smooth surface morphology more easily compared to the first track. The melt pool temperature at the laser beam center fluctuates during the laser scanning process. This depends on the effects of the interaction between heat conduction or heat accumulation or the interaction between heat accumulation and violent fluid flow. The temperature distribution and fluid flow in the melt pool benefit the analysis and understanding of the evolution mechanism of the melt pool geometry and surface topography and further allow regulation of the L-PBF process of Ti6Al4V.

Continuum modeling of dislocation channels in irradiated metals based on stochastic crystal plasticity

As a common feature observed in irradiated metallic materials, the formation of dislocation channels has been extensively studied and is considered to play a key role in irradiation embrittlement. However, modeling dislocation channels with the conventional crystal plasticity theory has been a theoretical challenge due to the difficulty of capturing microstructural inhomogeneities. Here a continuum crystal plasticity framework incorporating a stochastic distribution model of critical resolved shear stress (CRSS) is developed to describe the formation of dislocation channels and further plastic flow localization in irradiated materials. We show that the stochastic model is capable of capturing the heterogeneity of microscale plastic strain, which is an inherent feature of metallic materials during plastic deformation. It acts as an important microscale perturbation to trigger the dislocation channel nucleation in irradiated metals, especially for single crystals that lack mesoscale perturbations such as intergranular incompatibility and grain anisotropy. Without predetermining the potential nucleation position of dislocation channels, the stochastic irradiation crystal plasticity framework successfully simulates the dislocation channel formation and plasticity localization in both irradiated single- and polycrystalline copper (Cu), and further indicates the irradiation defect density threshold for the dislocation channel formation. This stochastic model broadens the application of the conventional crystal plasticity framework, and might provide new insights for other studies on plasticity localization, including shear bands formation of metals, mechanical behaviors with heterogeneous deformation and so on.

Numerical Simulation on Enhanced Heat Transfer of Metal Foam Based on LBM

Open cell foam metal has the characteristics of high porosity and large specific surface area. And it has developed rapidly in the related research of heat exchanger. Aiming at the convective heat transfer process of open cell metal structure with high porosity, a two-dimensional stochastic distribution model is established. Numerical simulation is carried out using the single-relaxation-time dual-distribution-function lattice-Boltzmann-method (BGK-DDF-LBM). For the non-ideal solid particles with unequal diameter and incomplete circular structure, the flow field is analyzed by taking the porosity of 0.964 as an example, and the dimensionless permeability is calculated. When the porosity is constant, the Nusselt number of the porous section increases with the increases of Reynolds number in the range of 10 to 100, which shows heat transfer performance. In addition, the Nusselt number of the porous section increases with the increase of porosity in the range of porosity from 0.900 to 0.980.

Ramp metering control under stochastic capacity in a connected environment: A dynamic bargaining game theory approach

This paper presents a dynamic predictive and cooperative ramp metering approach that considers stochastic breakdowns at merging bottlenecks. A stochastic microscopic model is used to estimate traffic state parameters based on speed, location, and travel time information from connected vehicles. Traffic state predictions are obtained on a lane by lane basis using an adaptive Kalman filter (AKF) that fuses fixed detector measurements with the model; the AKF then produces multiple step ahead predictions. The ramp metering problem in this paper is modeled as a stochastic distributed model predictive control (SDMPC) approach. The SDMPC problem is solved based on a bargaining game approach where each controller, a player in the game, receives traffic state and control decision information from other controllers to solve the local optimization problem based on expected local costs and constraints. The performance of the proposed model is evaluated for three aspects of efficiency: short-term and long-term equity and effectiveness compared to multiple control scenarios. The outcomes indicate that the proposed cooperative model with stochastic capacity considerations outperforms the deterministic capacity-based models in regard to effectiveness and equity properties. However, the centralized approach performs slightly better in respect to system-wide efficiency.

Параболическая модель в форме пространства состояний динамики накоплений

An important place in the theory of partial differential equations and its applications is occupied by the heat equation, a representative of the class of the so-called parabolic equations. It is known that to check the correctness of a mathematical model based on a parabolic equation, the existence of its solution is very important since a mathematical model is not always adequate to a specific phenomenon and the existence of a solution to a corresponding mathematical problem does not follow from the existence of a solution to a real applied problem. Therefore, methods for solving partial differential equations, both analytical and numerical, are always relevant. Nowadays, a computational experiment has become a powerful tool for theoretical research. It is carried out over a mathematical model of the object under study, but at the same time, other parameters are calculated using one of the parameters of the model and conclusions are drawn about the properties of the object or phenomenon under study. The problem of passive parametric identification of systems with distributed parameters for resource accumulation dynamics of many households using a stochastic distributed model in the form of a state space with regard to the white noise of the dynamics model of the object under study and the white noise of the model of a linear-type measuring system is considered in the paper. The use of the finite difference method allowed us to reduce the solution of partial differential equations of a parabolic type to the solution of a system of linear finite difference and algebraic equations represented by models in the form of a state space. It was also proposed to use a filtering algorithm based on the Kalman scheme for reliable estimation of the object behavior. Calculations were carried out using the Matlab mathematical system based on statistical data for five years, taken from the site “Agency for Strategic Planning and Reforms of the Republic of Kazakhstan Bureau of National Statistics”. Estimation of the coefficients of the equations for the household resource accumulation in the form of a state space using this technique is sufficiently universal and can be applied in other fields of science and technology.

Linear stochastic distributed model of moneyaccumulation in the form of a state space

The article deals with the problem of the passive parametric identification of systems for modeling the evolution of money savings income and expenses of one household using a linear stochastic distributed model in the form of a state space taking into account white noises model of the investigated object dynamics’ and white noises of the linear model measuring system of a distributed type. The use of the finite difference method allowed reducing the solution of partialdifferential equations to the solution of linear finite difference system with private derivatives to be reduced to the solution of a system of linear finite-difference and algebraic equations represented by models in the form of state space. It was proposed the use of a Kalman filtering algorithm for reliable evaluation of object behavior. The statement of the problem of estimating the coefficients of the equation of evolution of money savings income and expenses of one household is given. The structure of household income and expenses is described, taking into account additional additive white noise meters. An algorithm for numerical approbation of method for solving the problem of estimating the coefficients of an equation in the form of the state space for the evolution of money savings income and expenses of one household is considered. Calculations were carried out using the Matlab mathematical system based on statistical data for five years, taken from the site “Agency for Strategic planning and reforms of the Republic of Kazakhstan Bureau of National statistics”. The proposed method for solving the problem of coefficients assessment’s passive identification using the equations of money savings for one household in the form of a state space is sufficiently universal. Key words: linear finite-difference equation, model in the form of a state space, evolution of one household money savings, passive identification, Kalman filter, prediction estimates, filtering estimates.

Distributed stochastic model predictive control for cyber–physical systems with multiple state delays and probabilistic saturation constraints

In this paper, a stochastic distributed model predictive control (DMPC) architecture is investigated for cyber–physical systems subject to probabilistic input saturations. We present a systematic approach to design the stochastic DMPC by extending the deterministic DMPC. The input saturation constraints are relaxed and characterized by a Bernoulli-distributed white sequence, which can provide a trade-off between the satisfaction of input saturations and control performance. The probabilistic input constraints are transformed into a convex hull of linear feedback laws, therefore, can make the controller design less conservative. Then, the optimization problem of the stochastic DMPC is designed and cast into solving an online optimization problem. The probabilistic input saturations are dealt with a distributed fashion by developing an iterative algorithm of the DMPC. The recursive feasibility and closed-loop stability subject to probabilistic input saturations are given. Finally, a numerical example and an industrial electric heater system are used to demonstrate the effectiveness of the proposed approach.

Research on Optimal Solution of Correlation Properties of Solutions of Fractional Differential Equations Based on Cognitive Stochastic Distribution Model

Research on Optimal Solution of Correlation Properties of Solutions of Fractional Differential Equations Based on Cognitive Stochastic Distribution Model

Data-Driven Multiobjective Predictive Optimal Control of Refining Process With Non-Gaussian Stochastic Distribution Dynamics

The fiber length and the Canadian standard freeness (CSF) are two key indices in measuring pulp quality of the refining process with non-Gaussian stochastic distribution dynamics. Among them, it is defective to use the conventional 1-D average fiber length (AFL) as a pulp quality index because the AFL is insufficient to describe the 2-D probability density function (pdf) shaping of fiber length distribution (FLD) with non-Gaussian types. In this article, a data-driven multiobjective predictive optimal control method is proposed to control the 2-D pdf shaping of FLD and the 1-D CSF, simultaneously. First, a radial basis function neural network (RBF-NN) based stochastic distribution model is developed to approximate the 2-D pdf shaping of FLD, and the parameters of RBF basis functions are updated by an iterative learning rule. Then, taking the developed pulp quality models, including the 2-D pdf model of FLD and the model of 1-D CSF as two predictors, a multiobjective predictive controller is designed by solving the nonlinear programming problems with constraints. Then, the stability of the resulted closed-loop system is also analyzed. Ultimately, the industrial experiments demonstrate the effectiveness of the proposed method.

Stochastic distributed model predictive control of microgrid with uncertain PV power prediction

This paper is concerned with a stochastic distributed Model Predictive Control (MPC) technique for power management of a photovoltaic (PV) generators-installed microgrid. The photovoltaic power sup...

Modeling and Control Using Stochastic Distribution Control Theory for Intersection Traffic Flow

This work investigated stochastic distribution control theory-based traffic signal optimization to achieve a smooth and uniform flow of vehicles through signalized intersections. In this context, the static and linear dynamic stochastic distribution models were developed to express the relationship between the signal timing and the traffic queue length together with its probability density function. Two stochastic distribution control algorithms were designed to control the signal timing at intersections such that the probability density function of the traffic queue of each intersection road segment is made as narrow and as small as possible. Also, a recursive input-output traffic queue estimation model was proposed, which is data-driven and dynamic in nature, to calculate real-time traffic queue length using traffic signal timings and loop-detector data. The control algorithms were evaluated for a one-signal corridor, two-signal corridor, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> network of signalized intersections. MATLAB simulation examples are provided to demonstrate the use of the proposed algorithms and comparison to the existing widely-used semi-actuated control has been made. Desired results were obtained.

Prediction of tensile response of UHPC with aligned and ZnPh treated steel fibers based on a spatial stochastic process

This paper proposed a new method for predicting tensile response of UHPC based on a spatial stochastic strength distribution model. The steel fibers in UHPC were aligned by a developed device and chemically treated by ZnPh. A direct tension test was conducted to obtain the tensile response of UHPC with treated fibers. Image analysis was used to obtain the frequency of overall fiber orientation distribution. The spatial stochastic distribution model was proposed for cross sectional strength of UHPC based on the Ornstein-Uhlenbeck stochastic process. The model introduced some assumptions such as the correlation coefficient between the cracking strength and fiber bridging strength. Parametric analysis was conducted to obtain the crucial stochastic parameters in the model. Combining with the single fiber pullout model, tensile behavior of a single crack, and minimum crack spacing, the model predicted the strain hardening and multiple cracking behaviors with precise accuracy, as compared to experimental results.

An upscaled transport model for shale gas considering multiple mechanisms and heterogeneity based on homogenization theory

Because of the complex pore structure and multiple types of gas storage, the traditional Darcy permeability model is not valid for describing shale gas flow. In this paper, an upscaled transport model is established based on homogenization theory to consider multiple transport mechanisms and the heterogeneity of shale samples. This new transport model is employed to successfully explain pressure decay experimental data. The results show that absorbed gas cannot be ignored in pressure decay experiment and the pressure difference decreases rapidly when the absorbed gas is not considered. Then several critical conclusions have been drawn as follows. The permeability anisotropy for stochastic distribution model can be ignored and the effective permeability will be underestimated by double porosity model if surface diffusion dominates gas flow in shale reservoir. In addition, shale gas transport is dominated by Knudsen diffusion when the pore pressure is below 2 MPa and the contribution of surface diffusion increases as the pore pressure increases. The macroscopic effective permeability of the whole domain is dominated by the permeability of the connected phase; meanwhile, it can be influenced by the permeability of the disconnected phase. When the pore pressure is below 3.52 MPa, the effective permeability increases as the organic matter content (TOC) decreases. However, the effective permeability increases as the TOC increases when the pore pressure is above 3.52 MPa, which is different from traditionally believed when the relationship between the TOC and gas absorption capacity of the shale matrix is not considered. The effective permeability particularly increases at a high pore pressure as the Langmuir volume increases. In addition, the effective permeability increases as the Langmuir pressure decreases; however, this becomes apparent when the pore pressure is smaller.

Impacto Económico de Laringotraquitis Infecciosa Aviar en una Granja de Pollos de Carne en Lima, Perú

&lt;p&gt;El objetivo de este estudio fue cuantificar el impacto económico de la laringotraqueitis infecciosa aviar (LTI) en el rendimiento productivo y económico de pollos de engorde. Se evaluaron dos campañas consecutivas de 35 000 pollos criados hasta los 49 días de edad, donde la primera campaña estuvo afectada por LTI. Se realizó una encuesta para recopilar información sobre datos productivos, bioseguridad y costos de producción por campaña, así como los gastos adicionales que demandó el control de la enfermedad. El impacto económico se evaluó mediante la comparación de los datos de ambas campañas usando un modelo de distribución estocástica con el programa de análisis de riesgos @Risk 5.1&lt;sup&gt;®&lt;/sup&gt;. Además, se hizo un análisis estadístico para determinar diferencias entre datos productivos de cada campaña. En la campaña con LTI se incrementó la mortalidad en 3.51% y el índice de conversión en 16.8%, y la eficiencia productiva se redujo en 27.3% en comparación con la campaña sin LTI. Las pérdidas totales por la enfermedad sumaron S/. 88,805 Nuevos Soles. El análisis de riesgos mostró un rango de pérdidas de S/. 28,800.00 hasta S/. 149,300.00 Nuevos Soles con un 95% de probabilidad, para los 35,000 pollos de engorde con LTI.&lt;/p&gt;

Distribution Route Planning for Cold Chain Items under Variable Demand

AbstractThis paper discussed the planning and selection of an optimization model for distribution routing of cold chain items with variable customer demand. We established a distribution model of cold chain items to minimize the total distribution cost based on the model of vehicle routing problem (VRP) with time window. Distribution routing was then optimized by a saving algorithm. Finally, we compared the optimal routes planned by the stochastic distribution model (considering demand variation of customers) and the deterministic distribution model (based on a given demand expected value) by using a numerical example. Results show that (1) planning by using the stochastic model is superior to planning by using the deterministic model when demands fluctuate wildly and vice versa; (2) the total distribution costs obtained by the two models increase with the increase of the degree of demand change. Therefore, we proposed several suggestions to reduce the demand uncertainty of customers.

Stochastic Populations, Power Law and Fitness Aggregation in Genetic Algorithms

Natural populations are dynamic in both time and space. In biological populations such as insects, spatial distribution patterns are often studied as the first step to characterize population dynamics. In nature, the spatial distribution patterns of insect populations are considered as the emergent expression property of individual behaviors at population levels and are fine-tuned or optimized by natural selection. This inspiration prompts us to investigate the possibly similar mechanisms in Genetic Algorithms GA populations. In this study, we introduce the mathematical models for the spatial distribution patterns of insect populations to GA with the conjecture that the emulation of biological populations in nature may lead to computational improvement. In particular, we introduce three modeling approaches from the research of spatial distribution patterns of insect populations: i probability distribution modeling approach, ii aggregation index approach, and iii Taylor's 1961, 1977 Power Law, Iwao's 1968, 1976 Mean Crowding Model and Ma's 1991c population aggregation critical density PACD, to characterize populations in GA. With these three approaches, we investigate four mappings from the research field of insect spatial distribution patterns to GA populations in order to search for possible counterpart mechanisms or features in GA. They are: i mapping insect spatial distribution patterns to GA populations or allowing GA populations to be controlled by stochastic distribution models that describe insect spatial distributions; ii mapping insect population distribution to GA population fitness distribution via Power Law and PACD modeling; iii mapping population aggregation dynamics to GA fitness progression across generations or fitness aggregation dynamics in GA via insect population aggregation index; iv mapping insect population sampling model to optimal GA population sizing. With regard to the mapping i, the experiment results show the significant improvements in GA computational efficiency in terms of the reduced fitness evaluations and associated costs. This prompts us to suggest using probability distribution models, or what we call stochastic GA populations, to replace the fixed-size population settings. We also found the counterpart for the second mapping, the wide applicability of Power Law and Mean Crowding model to the fitness distribution in GA populations. The testing of the third and fourth mappings is very preliminary; we use example cases to suggest two further research problems: the potential to use fitness aggregation dynamics for controlling the number of generations iterated in GA searches, and the possibility to use fitness aggregation distribution parameters [obtained in mapping ii] in determining the optimum population size in GA. A third interesting research problem is to investigate the relationship between mapping i and iii, i.e., the controlling of both population sizes and population generations.

Stochastic model and synchronization analysis for large-scale oscillator networks and their applications

Networks of coupled large-scale oscillators have been studied in biology for a number of years. It has been recognized that transients in the nearest neighbour connected networks may take far too long to die out. It is considered that a few long-distance interconnections exist. Typically, these long-distance interconnections are considered to occur in a random way. In this paper, the synchronization problem for coupled oscillator networks is discussed. Then, the stochastic distribution model for the random long-distance connections is proposed and the validity is demonstrated by simulation. Furthermore, the proposed oscillator network is applied to the visual model of a dragonfly.

A stochastic distributed model of soil erosion by overland flow

AbstractA model has been built to simulate runoff and erosion on slopes of varying form with soil of varying hydraulic conductivity, porosity, storage capacity, and particle size distribution. The model is based on known physical laws and takes into account spatially dependent random variation in the initial conditions of the soil. The rainfall is similarly both random and autocorrelated in space.Detailed results show how runoff is generated as a result of slow conductivity and high water table, how this leads to erosion, the degradation of the land surface, the capture of flow lines, and the development of networks of rills. The last accords well with results from laboratory experiments. Changing the initial conditions produces results that accord with intuition and reality.