Stochastic Model Uncertainty Research Articles

Robust state estimation and fault detection for Autonomous Underwater Vehicles considering hydrodynamic effects

Autonomous Underwater Vehicles (AUVs) are designed to operate in complex external environments, making fault detection crucial to overall safety. While a general kinetic model can be applied to describe the dynamics of an AUV, obtaining accurate parameters for the dynamic model is challenging due to the complexity of the outline structure of the AUV and external influence factors. In addition, environmental influence on model parameters is usually time-varying and stochastic, which is different from simple model uncertainties. In this paper, we model external perturbations as stochastic model uncertainties that share some characteristics with noise. We also apply an improved robust filtering method to estimate system states and alleviate the effects of stochastic system uncertainties. Based on the proposed filtering approach, a residual signal is computed based on reconstruction errors of the observations and smoothed using a sliding-window technique, which is directly applied to the fault detection problem. Finally, simulation experiments demonstrate the effectiveness of the proposed method in detecting actuator faults in several cases.

A stochastic SPOD-Galerkin model for broadband turbulent flows

The use of spectral proper orthogonal decomposition (SPOD) to construct low-order models for broadband turbulent flows is explored. The choice of SPOD modes as basis vectors is motivated by their optimality and space-time coherence properties for statistically stationary flows. This work follows the modeling paradigm that complex nonlinear fluid dynamics can be approximated as stochastically forced linear systems. The proposed stochastic two-level SPOD-Galerkin model governs a compound state consisting of the modal expansion coefficients and forcing coefficients. In the first level, the modal expansion coefficients are advanced by the forced linearized Navier-Stokes operator under the linear time-invariant assumption. The second level governs the forcing coefficients, which compensate for the offset between the linear approximation and the true state. At this level, least squares regression is used to achieve closure by modeling nonlinear interactions between modes. The statistics of the remaining residue are used to construct a dewhitening filter that facilitates the use of white noise to drive the model. If the data residue is used as the sole input, the model accurately recovers the original flow trajectory for all times. If the residue is modeled as stochastic input, then the model generates surrogate data that accurately reproduces the second-order statistics and dynamics of the original data. The stochastic model uncertainty, predictability, and stability are quantified analytically and through Monte Carlo simulations. The model is demonstrated on large eddy simulation data of a turbulent jet at Mach number $M=0.9$ and Reynolds number of $Re_D\approx 10^6$.

Energy-Storage-Based Intelligent Frequency Control of Microgrid With Stochastic Model Uncertainties

With the increasing proportion of renewable power generations, the frequency control of microgrid becomes more challenging due to stochastic power generations and dynamic uncertainties. The energy storage system (ESS) is usually used in microgrid since it can provide flexible options to store or release power energy. In this paper, an intelligent control strategy completely based on the adaptive dynamic programming (ADP) is developed for the frequency stability, which is designed to adjust the power outputs of micro-turbine and ESS when photovoltaic (PV) power generation is connected into the microgrid. Further, considering the changes of PV power and load demand in a day, the full utilization of PV power and the recycling of energy storage are realized through the proposed regulation strategy. Numerical simulation results validate the energy-storage-based intelligent frequency control strategy for the microgird with stochastic model uncertainties, and comparative studies based on PID, LQR and fuzzy logic control illustrate the superiority of the proposed control strategy.

Fault Detection for a Class of Uncertain Linear Discrete-time Systems with Intermittent Measurements and Probabilistic Actuator Failures

This paper deals with fault detection (FD) problem for linear discrete-time systems subject to random intermittent measurements, probabilistic actuator failures, norm-bounded model uncertainty, and stochastic model uncertainty. By taking into account the probabilistic actuator failures, a new reference residual model is proposed to formulate the FD issue as an H∞, model-matching problem. The corresponding reference residual is generated through maximizing a stochastic H–/H∞ or H∞/H∞ performance index via solving an algebraic Riccati equation (ARE). By the aid of the linear matrix inequality (LMI) techniques, a fault detection filter (FDF) is constructed such that the residual is sensitive to fault but insensitive to unknown inputs, mixed model uncertainties, random intermittent measurements and stochastic actuator failures. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Bounding Integrity Risk for Sequential State Estimators with Stochastic Modeling Uncertainty

A new method is introduced to upper bound integrity risk for sequential state estimators when the autocorrelation functions of measurement noise and disturbance inputs are subject to bounded uncertainties. Integrity risk is defined as the probability of the state estimate error exceeding predefined bounds of acceptability. In the first part of the paper, a new expression is derived that relates the measurement noise and disturbance input autocorrelation functions to the state estimate error vector. Using this relation, an efficient algorithm is developed in the second part of the paper to upper bound the estimation integrity risk when each input autocorrelation function is known to lie between upper and lower bounding functions. Numerical simulations for a one-dimensional position and velocity estimation problem are conducted to demonstrate the practical feasibility and effectiveness of this new bounding method.

Decentralized Control for Arbitrarily Interconnected Systems over Lossy Network

Abstract This paper deals with the control of arbitrarily topological interconnected systems where information communicated between subsystems may be lost due to unreliable links. First, the stochastic variable that is responsible for the communication status of lossy network is regarded as a source of model uncertainty. The system is modeled in the framework of linear fractional transformation with a deterministic nominal system and a stochastic model uncertainty. Then, the robust control theory is employed for system analysis. The largest probability of communication failure, tolerated by the interconnected systems keeping mean square stable, can be obtained by solving a μ synthesis optimization problem. Decentralized state feedback controllers are designed to ensure that the whole system is mean square stable for a given communication failure rate, based on the technique of linear matrix inequalities. An illustrative example is presented finally to verify the effectiveness of the proposed model and method.