Probabilistic Interval Research Articles

Stochastic Modeling and Forecasting of Load Demand for Electric Bus Battery-Swap Station

Electric-vehicle (EV) battery-swap stations (BSSs) have become important infrastructures for the development of EVs to extend their driving range. Due to the randomness of batteries' swapping and charging patterns, the load demand of the BSS has a stochastic nature. It is necessary to investigate the charging load characteristics of BSS to guide the coordinated battery charging for mitigating the impact of disorderly charging behaviors on the distribution network. Under the uncontrolled swapping and charging scenario, four variables are essential: 1) hourly number of EVs for battery swapping; 2) the charging start time; 3) the travel distance; and 4) the charging duration. Taking these factors into account, a novel model based on Monte Carlo simulation is presented to estimate uncontrolled energy consumption of the BSS. Then, a generic nonparametric method for the estimation of prediction uncertainty of charging load demand is introduced. Adopting an actual typical BSS as an example, the simulation results show that the proposed prediction methods of the BSS charging load and probabilistic interval are suitable for forecasting the horizon 24 h ahead.

Observer-based networked control with probabilistic interval input delays

In this paper, the problem of observer-based control is investigated for networked control systems (NCSs) with probabilistic interval distribution communication delays. In the presence of network-induced delays and packet dropouts in the sensor-to-controller and controller-to-actuator connections, a new model for an observer-based NCS is established, which is then converted to an equivalent linear system with two random time-varying delays satisfying Bernoulli distributions. By utilizing information concerning the probability distribution of the delays and by adopting a tighter bounding technique, less conservative asymptotic mean-square stable sufficient conditions are derived in the form of linear matrix inequalities (LMIs). Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Hybrid Probabilistic and Non-Probabilistic Dynamic Analysis of Vehicle-Bridge Interaction System with Uncertainties

A hybrid probabilistic interval dynamic analysis of vehicle-bridge interaction system with a mixture of random and interval properties is studied based on finite element analysis framework. A half car model is used to represent a moving vehicle and the bridge is modeled as a simply supported Euler-Bernoulli beam. The vehicle’s parameters are considered as interval variables and the bridge’s parameters are treated as random variables. The mathematical model of vehicle-bridge interaction system is established based on the finite element model. By introducing the random interval perturbation method into the dynamic analysis of vehicle-bride interaction system, the expressions for the mean value and variance of the bridge dynamic response are developed. Examples are used to illustrate the effectiveness of the presented method. The accuracy and effectiveness of the numerical results are verified by a hybrid simulation method combining direct simulations for interval variables and Monte-Carlo simulations for random variables.

Optimal Prediction Intervals of Wind Power Generation

Accurate and reliable wind power forecasting is essential to power system operation. Given significant uncertainties involved in wind generation, probabilistic interval forecasting provides a unique solution to estimate and quantify the potential impacts and risks facing system operation with wind penetration beforehand. This paper proposes a novel hybrid intelligent algorithm approach to directly formulate optimal prediction intervals of wind power generation based on extreme learning machine and particle swarm optimization. Prediction intervals with associated confidence levels are generated through direct optimization of both the coverage probability and sharpness to ensure the quality. The proposed method does not involve the statistical inference or distribution assumption of forecasting errors needed in most existing methods. Case studies using real wind farm data from Australia have been conducted. Comparing with benchmarks applied, experimental results demonstrate the high efficiency and reliability of the developed approach. It is therefore convinced that the proposed method provides a new generalized framework for probabilistic wind power forecasting with high reliability and flexibility and has a high potential of practical applications in power systems.

Hybrid probabilistic interval dynamic analysis of vehicle–bridge interaction system with uncertainties

This paper presents the hybrid probabilistic interval dynamic analysis of vehicle–bridge interaction system with a mixture of random and interval properties. The vehicle's parameters are considered as interval variables and the bridge's parameters are treated as random variables. A half car model is used to represent a moving vehicle and the bridge is modeled as a simply supported Euler–Bernoulli beam. By introducing the random interval moment method (RIMM) into the dynamic analysis of vehicle–bride interaction system, the expressions for the mean value and standard deviation of the random interval bridge dynamic response are developed. The midpoint and interval width of the first two statistical moments are then determined. Examples are used to illustrate the effectiveness of the presented method. A hybrid simulation method combining direct simulations for interval variables and Monte Carlo simulations for random variables is implemented to validate the computational results. The effects of individual system parameters on bridge response are also investigated.

A simple model for probabilistic interval forecasts of wind power chaotic time series

Integration of wind power into grids requires accurate forecasting, however, traditional wind power point forecast errors are unavoidable and they cannot be eliminated due to the highly volatile and uncertain in the chaotic time series of wind power. Unlike point prediction, which conveys no information about the prediction accuracy, probabilistic interval forecasts can provide a range, within which the target will lie with a certain probability, for estimating the potential impacts and risks facing the system operation. Most existing prediction interval (PI) construction methods are often placed after a deterministic forecasting model with or without prior assumptions, this paper propose a novel lower-upper bound estimation approach using extreme learning machine to directly construct PIs for wind power series. Based on the analysis of the interval forecasting error information in training dataset, a new problem formulation is developed in this method to get better PIs. In addition, in order to obtain the global optimal solution of the above model, a quantum bacterial foraging optimization algorithm is proposed by introducing the theory of quantum mechanics into bacteria foraging behavior. The testing results from two real wind farms with different confidence probability and optimization criterion demonstrate the excellent quality of PIs in terms of both reliability and sharpness, which provide a support for the steady operation of power system with wind power integration.

A Hybrid Approach for Probabilistic Forecasting of Electricity Price

The electricity market plays a key role in realizing the economic prophecy of smart grids. Accurate and reliable electricity market price forecasting is essential to facilitate various decision making activities of market participants in the future smart grid environment. However, due to the nonstationarities involved in market clearing prices (MCPs), it is rather difficult to accurately predict MCPs in advance. The challenge is getting intensified as more and more renewable energy and other new technologies emerged in smart grids. Therefore transformation from traditional point forecasts to probabilistic interval forecasts can be of great importance to quantify the uncertainties of potential forecasts, thus effectively supporting the decision making activities against uncertainties and risks ahead. This paper proposes a hybrid approach to construct prediction intervals of MCPs with a two-stage formulation. In the first stage, extreme learning machine (ELM) is applied to estimate point forecasts of MCPs and model uncertainties involved. In the second stage, the maximum likelihood method is used to estimate the noise variance. A generalized and comprehensive evaluation framework for probabilistic electricity price forecasting is proposed in this paper. The effectiveness of the proposed hybrid method has been validated through comprehensive tests using real price data from Australian electricity market.

Interval design point method for calculating the reliability of structural systems

The evaluation of reliability for structural system is important in engineering practices. In this paper, by combining the design point method, JC method, interval analysis theory, and increment load method, we propose a new interval design point method for the reliability of structural systems in which the distribution parameters of random variables are described as interval variables. The proposed method may provide exact probabilistic interval reliability of structures whose random variables can have either a normal or abnormal distribution form. At last, we show the feasibility of the proposed approach through a typical example.

Fuzzy Filtering With Randomly Occurring Parameter Uncertainties, Interval Delays, and Channel Fadings

In this paper, the H∞ fuzzy filtering problem is investigated for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with randomly occurring uncertainties and randomly occurring interval time-varying delays, as well as channel fadings. A sequence of random variables obeying the Bernoulli distribution is utilized to govern the randomly occurring uncertainties and probabilistic interval time-varying delays. Simultaneously, the Rice fading model is employed to describe the phenomena of channel fadings by setting different values of the channel coefficients. Our attention is focused on the design of an H∞ fuzzy filter such that the filtering error dynamics is exponentially mean-square stable and the disturbance rejection attenuation is constrained to a given level by means of the H∞-performance index. In the presence of the randomly occurring phenomena, sufficient conditions are derived, via stochastic analysis and Lyapunov functional approach, for the existence of desired filter ensuring both the exponential mean-square stability and the prescribed H∞ performance. The filter parameters can be obtained by solving a convex optimization problem via the semidefinite program method. Finally, a numerical example is utilized to illustrate the usefulness and effectiveness of the proposed design technique.

Probabilistic Upper Bounds for the Matrix Two-Norm

We develop probabilistic upper bounds for the matrix two-norm, the largest singular value. These bounds, which are true upper bounds with a user-chosen high probability, are derived with a number of different polynomials that implicitly arise in the Lanczos bidiagonalization process. Since these polynomials are adaptively generated, the bounds typically give very good results. They can be computed efficiently. Together with an approximation that is a guaranteed lower bound, this may result in a small probabilistic interval for the matrix norm of large matrices within a fraction of a second.

Reconstructing Past Populations With Uncertainty From Fragmentary Data

Current methods for reconstructing human populations of the past by age and sex are deterministic or do not formally account for measurement error. We propose a method for simultaneously estimating age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data that incorporates measurement error. Inference is based on joint posterior probability distributions that yield fully probabilistic interval estimates. It is designed for the kind of data commonly collected in modern demographic surveys and censuses. Population dynamics over the period of reconstruction are modeled by embedding formal demographic accounting relationships in a Bayesian hierarchical model. Informative priors are specified for vital rates, migration rates, population counts at baseline, and their respective measurement error variances. We investigate calibration of central posterior marginal probability intervals by simulation and demonstrate the method by reconstructing the female population of Burkina Faso from 1960 to 2005. Supplementary materials for this article are available online and the method is implemented in the R package “popReconstruct.”

Continuous–discrete confidence interval observer – Application to vehicle positioning

In vehicle positioning applications, the confidence level in the position and velocity estimates can be even more significant than accuracy. In this study, a probabilistic interval method is proposed, which combines, through union and intersection operations, the information from a possibly uncertain predictor (the vehicle model) and measurement sensors. The proposed method is compared to Kalman filtering and to guaranteed interval estimation in the context of railway vehicles where security is the key objective.

Probabilistic Interval Perturbation Methods for Hybrid Uncertain Acoustic Field Prediction

For the hybrid uncertain acoustic field prediction with random and interval variables, the random interval dynamic equilibrium equation is established and two hybrid probabilistic interval perturbation methods, named as hybrid perturbation Monte Carlo method (HPMCM) and hybrid perturbation vertex method (HPVM), are present. In HPMCM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and Monte Carlo method. In HPVM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and the vertex method. Numerical results on a 2D acoustic tube, the 2D acoustic cavity of a car and a 3D acoustic cavity verify the effectiveness and the high efficiency of HPVM when compared with HPMCM. HPVM can be considered as an effective engineering method to quantify the effects of parametric uncertainty on the sound pressure response.

Delay-dependent absolute stability criterion for Lurie system with probabilistic interval time-varying delay

In this paper, the absolute stability of Lurie control system with probabilistic time-varying delay is studied. By using a new extended Lyapunov-Krasovskii functional, an improved stability criterion based on LMIs is presented and its solvability heavily depends on the sizes of both the delay range and its derivatives, which has wider application fields than those present results. The efficiency and reduced conservatism of the presented results can be demonstrated by two numerical examples with giving some comparing results.

Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling

This technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.

Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time‐varying delays

SUMMARYThis paper investigates the global asymptotic synchronization in an array of coupled neural networks with random coupling strengths, probabilistic interval time‐varying coupling delays as well as unbounded distributed delays (mixed delays). Two important integral inequalities that include the Jensen's inequality as a special case are developed. On the basis of the developed inequalities, the properties of random variables and Lyapunov functional method, several delay‐dependent sufficient synchronization criteria are derived for the considered model. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using MATLAB LMI Toolbox. Some existing results are improved and extended by taking different values of parameters of the obtained results. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Robust [formula omitted] control for T–S fuzzy systems with probabilistic interval time varying delay

In this paper, we are concerned with the problem of robust H∞ control for the Takagi–Sugeno (T–S) fuzzy system with probabilistic interval time-varying state delay. Considering the distribution property of time-varying delay, a new stochastic fuzzy model is first proposed. Then, a delay-distribution-dependent H∞ performance analysis result is established for the closed-loop stochastic fuzzy systems via the Lyapunov–Krasovskii functional method and linear matrix inequality (LMI) technique. Based on the derived H∞ performance analysis results, H∞ controller is designed in terms of LMIs. An illustrative example is proposed to show the effectiveness and feasibility of the proposed method.

CLUSTER SYNCHRONIZATION OF DISCRETE-TIME STOCHASTIC COMPLEX DYNAMICAL NETWORKS WITH PROBABILISTIC INTERVAL TIME-VARYING DELAYS

The paper investigates the cluster synchronization in discrete-time complex networks with stochastic nonlinearities and probabilistic interval time-varying delays. Based on the stochastic analysis techniques and the properties of the Kronecker product, delay-dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities. The solvability of derived conditions depends on not only the probability of the binary switch between nonlinear functions, but also the size of the delay and the probability of the delay taking values in some intervals. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed criterion.

H<inf>∞</inf>-based fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

The fault detection problem for the nonlinear networked control system (NCS) with packet dropout and delay is inves- tigated. A nonlinear stochastic system model is proposed to account for the NCS with random packet dropout and network- induced non-uniformly distributed time-varying delay in both from sensor to controller (S/C) and from controller to actuator (C/A). Based on the obtained NCS model, employing an observer-based fault detection filter as the residual generator, the addressed fault detection problem is converted into an auxiliary nonlinear H∞ control problem. Then, with the help of Lyapunov functional ap- proach, a sufficient condition for the desired fault detection filter is constructed in terms of certain linear matrix inequalities, which depend on not only the delay interval but also the delay interval occurrence rate and successful packet communication rate. Es- pecially, a trade-off phenomenon between the maximum allowable delay bound and successful data packet transmission rate is found, which is typically resulted from the limited bandwidth of commu- nication networks. The effectiveness of the proposed method is demonstrated by a simulation example.

Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays

The synchronization problem for a class of complex dynamical networks with stochastic disturbances and probabilistic interval time-varying delays is investigated. Based on the stochastic analysis techniques and properties of the Kronecker product, some delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities (LMIs). The solvability of derived conditions depends not only on the size of the delay, but also on the probability of Bernoulli stochastic variables. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.