Reduced-order modeling and state estimation applied to gas distribution systems

A reduced-order model for complex multifeed gas networks has been developed which is based on an aggregation procedure. The reduced model is then used with an estimation scheme to determine the pressure distribution in the network from a limited number of measurements. The results obtained show that the model yields good steady-state data over a range of operating conditions, and hence a robust estimation scheme has been developed.     

Real time distributed parameter state estimation applied to a two dimensional heated ingot

A distributed parameter state estimator, implemented via a minicomputer, was used to estimate the radial and axial temperature distribution of a stainless steel cylindrical ingot being heated in a three zone furnace. The filter estimates as well as the estimate covariances were calculated by reduction of the distributed equations to ordinary differential equations via modal decomposition. The filter was shown to be robust and rapidly convergent even in cases of high measurement noise, few sensors, and poor initial conditions. The on line computations were accomplished in less than half of real-time. Since typical industrial applications involve time constants which are two orders of magnitude larger than for this laboratory system, the feasibility of such estimation algorithms in a multiprocess industrial environment seems assured.     

Joint state and parameter robust estimation of stochastic nonlinear systems

Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez–Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non‐Gaussian distributions is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Stubborn state estimation for nonlinear distributed parameter systems subject to measurement outliers

In this article, the state estimation problem is investigated for a class of distributed parameter systems (DPSs). In order to estimate the state of DPSs, we give a partition of spatial interval with a finite sequence and, on each subinterval, one sensor is placed to receive the measurements from the DPS. Due to the unexpected environment changes, the measurements will probably contain some outliers. To eliminate the effects of the possibly occurring outliers, we construct a stubborn state estimator where the innovation is constrained by a saturation function. By using Lyapunov functional, Wirtinger inequality and piecewise integration, some sufficient conditions are obtained under which the resulting estimation error system is exponentially stable and the performance requirement is satisfied. According to the obtained analysis results, the desired state estimator is designed in terms of the solution to a set of matrix inequalities. Finally, a numerical simulation example is given to verify the effectiveness of the proposed state estimation scheme.     

Identification of non-linear stochastic systems by state dependent parameter estimation

The paper outlines how improved estimates of time variable parameters in models of stochastic dynamic systems can be obtained using recursive filtering and fixed interval smoothing techniques, with the associated hyper-parameters optimized by maximum likelihood based on prediction error decomposition. It then shows how, by exploiting special data re-ordering and back-fitting procedures, similar recursive parameter estimation techniques can be utilized to estimate much more rapid State Dependent Parameter (SDP) variations. In this manner, it is possible to identify and estimate a widely applicable class of nonlinear stochastic systems, as illustrated by several examples that include simulated and real data from chaotic processes. Finally, the paper points out that such SDP models can form the basis for new methods of signal processing, automatic control and state estimation for nonlinear stochastic systems.     

Parameter estimation applied to physiological systems

Parameter estimation techniques are of ever-increasing interest in the fields of medicine and biology, as greater efforts are currently being made to describe physiological systems in explicit quantitative form. Although some of the techniques of parameter estimation as developed for use in other engineering and scientific problems may be carried over into physiology, it has nevertheless been necessary to re-examine the entire procedure of estimation, from model formulation to computer selection. The results of this re-examination, as set forth in this paper, give some guidance as to the selection of techniques for the estimation of the parameters of physiological systems.     

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H_∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.     

Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.     

Intelligent state changing applied to multi-robot systems

The target searching problem is a situation where a formation of multi-robot systems is set to search for a target and converge towards it when it is found. This problem lies in the fact that the target is initially absent and the formation must search for it in the environment. During the target search, false targets may appear dragging the formation towards it. Therefore, in order to avoid the formation following a false target, this paper presents a new methodology using the Takagi–Sugeno type fuzzy automaton (TS-TFA) in the area of formation control to solve the target searching problem. The TS fuzzy system is used to change the formation through the modifications in the states of the automaton. This change does not only switch the rules and therefore the state of each robot, but also the controllers and cost functions. This approach amplifies the versatility of the formation of mobile robots in the target searching problem. In this paper, the TS-TFA is presented and its implications in the formation are explained. Simulations and results with real robot are presented where it can be noticed that the formation is broken to maximize the perception range based on each robot’s observation of a possible target. Finally this work is concluded in the last section.     

Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory

This paper combines polynomial chaos theory with maximum likelihood estimation for a novel approach to recursive parameter estimation in state-space systems. A simulation study compares the proposed approach with the extended Kalman filter to estimate the value of an unknown damping coefficient of a nonlinear Van der Pol oscillator. The results of the simulation study suggest that the proposed polynomial chaos estimator gives comparable results to the filtering method but may be less sensitive to user-defined tuning parameters. Because this recursive estimator is applicable to linear and nonlinear dynamic systems, the authors portend that this novel formulation will be useful for a broad range of estimation problems.     

Distributed parameter and state estimation in petroleum reservoirs

In this paper, we describe some of the key elements of the data assimilation problem for multiphase flow in petroleum reservoirs that make the problem distinctly different from data assimilation problems in weather or oceanography. Most importantly, the reservoir is often initially in a state of static equilibrium, the number of model parameters may be greater than the number of state variables, and the evolution of some of the state variables proceed monotonically from the initial state (low water saturation) to a final state (high water saturation). As a result of the differences, data assimilation is sometimes applied with a focus on estimation of model parameters.     

Maximum-likelihood parameter estimation of bilinear systems

This paper addresses the problem of estimating the parameters in a multivariable bilinear model on the basis of observed input-output data. The main contribution is to develop, analyze, and empirically study new techniques for computing a maximum-likelihood based solution. In particular, the emphasis here is on developing practical methods that are illustrated to be numerically reliable, robust to choice of initialization point, and numerically efficient in terms of how computation and memory requirements scale relative to problem size. This results in new methods that can be reliably deployed on systems of nontrivial state, input and output dimension. Underlying these developments is a new approach (in this context) of employing the expectation-maximization method as a means for robust and gradient free computation of the maximum-likelihood solution.     

Structural parameter estimation in power systems

A new class of algorithms for the estimation of structural parameters of a continuous-time linear system excited by random natural disturbances is presented in the paper. All these algorithms are based on fitting the autocorrelation function of the system output; differences among them arise from the various possible formulations of the fit-criterion. Thus, the asymptotic statistical properties of the estimate are analyzed in order to have a choice tool among the class of algorithms and to compare them with other existing estimation methods. A further relevant subject is the statement of a robust test to verify the correctness of the tentative model assumed for the sake of the estimation procedure. Then the above algorithm is applied to the problem of estimating structural parameters (i.e. natural frequencies and damping factors) of the Italian and Yugoslavian power systems by recording some main electrical quantities during the normal operation of the system.Capability of dealing with structural systems affected by an unknown number of oscillatory modes and simplicity of use by non-statistical people are interesting features of the present approach, emphasized by the application.     

Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

In the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.     

Suboptimal sensors location in the state estimation problem for stochastic non-linear distributed parameter systems

The present paper deals with the minimal number sensor choice and their optimal location for the estimation in non-linear stochastic distributed parameter systems described by parabolic and hyperbolic partial differential equations. The necessary condition for the optimal sensor location by using the matrix minimum principle was obtained. In turn, the computational algorithm of the sensors location was determined on the basis of the necessary condition, applying the optimal control theory. The computational efficiency of this algorithm is defined by the suboptimal filtering algorithm which does not require solving of the matrix Riccati equation for the filter error covariance. Finally, one example is given to demonstrate the effectiveness of the present approach.     

Modular approach to parameter estimation in geared and linear resonant systems

This paper proposes a unified approach to the estimation of the physical parameters defining both geared and linear resonant systems, namely the dead-zone, inertia, stiffness and damping parameters. Although the technique is based on discrete-time models, it allows extraction of the continuous-time parameters from the discrete coefficients. This is facilitated by a modular procedure, involving separate locked- and unlocked-load measurements. The difference equation coefficients associated with the discrete model become trivial functions of the physical system parameters, which are computed using predetermined polynomial approximations. The reduced-order estimation modules improve noise immunity and simplify the estimation routines. Very accurate experimental results verify the utility of the approach.     

A novel approach to robust parameter estimation using neurofuzzy systems

A novel approach for solving robust parameter estimation problems is presented for processes with unknown-but-bounded errors and uncertainties. An artificial neural network is developed to calculate a membership set for model parameters. Techniques of fuzzy logic control lead the network to its equilibrium points. Simulated examples are presented as an illustration of the proposed technique. The result represent a significant improvement over previously proposed methods.     

Optimal state estimation for networked systems with random parameter matrices,correlated noises and delayed measurements

In this paper, the optimal least-squares state estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with state transition and measurement random parameter matrices and correlated noises. It is assumed that at any sampling time, as a consequence of possible failures during the transmission process, one-step delays with different delay characteristics may occur randomly in the received measurements. The random delay phenomenon is modelled by using a different sequence of Bernoulli random variables in each sensor. The process noise and all the sensor measurement noises are one-step autocorrelated and different sensor noises are one-step cross-correlated. Also, the process noise and each sensor measurement noise are two-step cross-correlated. Based on the proposed model and using an innovation approach, the optimal linear filter is designed by a recursive algorithm which is very simple computationally and suitable for online applications. A numerical simulation is exploited to illustrate the feasibility of the proposed filtering algorithm.     

Ellipsoidal parameter or state estimation under model uncertainty

Ellipsoidal outer-bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown-but-bounded state perturbations and measurement noise. The technique described in this paper applies to linear discrete-time dynamic systems; it can also be applied to weakly non-linear systems if non-linearity is replaced by uncertainty. Many difficulties arise because of the non-convexity of feasible sets. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis. Analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented, which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.