Dariusz Uciński

D-optimal design of a monitoring network for parameter estimation of distributed systems

This paper addresses the design of a network of observation locations in a spatial domain that will be used to estimate unknown parameters of a distributed parameter system. We consider a setting where we are given a finite number of possible sites at which to locate a sensor, but cost constraints allow only some proper subset of them to be selected. We formulate this problem as the selection of the gauged sites so as to maximize the log-determinant of the Fisher information matrix associated with the estimated parameters. The search for the optimal solution is performed using the branch-and-bound method in which an extremely simple and efficient technique is employed to produce an upper bound to the maximum objective function. Its idea consists in solving a relaxed problem through the application of a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for optimal design. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional convective diffusion process.

Time–Optimal Path Planning of Moving Sensors for Parameter Estimation of Distributed Systems

A general approach to the optimization of the observation horizon of moving sensor trajectories for parameter estimation of distributed systems is presented. Two problems are formulated here. The first consists in maximizing the determinant of the information matrix for a specified duration of observations and an open initial time, and the other constitutes its generalization to the case where the elapsed observation time is minimized subject to a guaranteed D-efficiency of the experiment. The approach is to convert the problem to an optimal control one in Mayer form, in which both the control forces of the sensors and the initial sensor positions are optimized in addition to the limits of the observation horizon.

Sensor network design for the estimation of spatially distributed processes

Sensor network design for the estimation of spatially distributed processes In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical processes underlying the observed phenomena. The present work aims at bridging this gap and meeting the needs created in the context of the source identification problem. We assume that the paths of the moving sources are unknown, but they are sufficiently smooth to be approximated by combinations of given basis functions. This parametrization makes it possible to reduce the source detection and estimation problem to that of parameter identification. In order to estimate the source and medium parameters, the maximum-likelihood estimator is used. Based on a scalar measure of performance defined on the Fisher information matrix related to the unknown parameters, which is commonly used in optimum experimental design theory, the problem is formulated as an optimal control one. From a practical point of view, it is desirable to have the computations dynamic data driven, i.e., the current measurements from the mobile sensors must serve as a basis for the update of parameter estimates and these, in turn, can be used to correct the sensor movements. In the proposed research, an attempt will also be made at applying a nonlinear model-predictive-control-like approach to attack this issue.

Optimal mobile sensor motion planning under non-holonomic constraints for parameter estimation of distributed systems

This paper presents a numerical solution for a mobile sensor motion trajectory scheduling problem under non-holonomic constraints of a project named Mobile Actuator-Sensor network (MAS-net). The motivation of the MAS-net project, at the first stage, is to estimate diffusion system parameters by networked mobile sensors. Each sensor is mounted on a differentially driven mobile robot to observe the diffusing fog. In other words, this project requires the observation of a parabolic Distributed Parameter System (DPS) by non-holonomic networked mobile sensors. This paper reformulates this problem in the framework of optimal control and proposes a procedure to obtain a numerical solution by using RIOTS and Matlab PDE Toolbox. The objective function of this method is designed to minimise the effect of the sensing noise. Extensive simulation results are presented for illustration.

Experimental Design for Time-Dependent Models with Correlated Observations

We describe an algorithm for the construction of optimum experimental designs for the parameters in a regression model when the errors have a correlation structure. Our example is drawn from chemical kinetics, so that the model is nonlinear. Our algorithm has been implemented to be used when the model consists of a set of differential equations for which only numerical solutions ar available. However, the algorithm can also be used for standard regression models when the errors are correlated. The paper concludes with some discussion of outstanding issues in optimum design with correlated errors.

D-optimal trajectory design of heterogeneous mobile sensors for parameter estimation of distributed systems

An approach is proposed to joint optimization of trajectories and measurement accuracies of mobile nodes in a sensor network collecting measurements for parameter estimation of a distributed parameter system. The problem is cast as maximization of the log-determinant of the information matrix associated with the estimated parameters over the set of all feasible information matrices, which yields a formulation in terms of convex optimization. This makes it possible to employ powerful tools of optimum experimental design theory to characterize the optimal solution and adapt the Wynn-Fedorov algorithm to construct its numerical approximation. As a crucial subtask in each iteration, a nontrivial optimal control problem must be solved, which is accomplished using the MATLAB PDE toolbox and the RIOTS_95 optimal control toolbox which handles various constraints imposed on the sensor motions. The effectiveness of the method is illustrated with a numerical example regarding a two-dimensional diffusion equation.

Configuring A Sensor Network for Fault Detection in Distributed Parameter Systems

Configuring A Sensor Network for Fault Detection in Distributed Parameter Systems The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.

Sensor Motion Planning in Distributed Parameter Systems Using Turing's Measure of Conditioning

We present a technique for planning sensor motions in a specified two-dimensional spatial domain in such a way as to make the Hessian of the parameter estimation cost well conditioned. The framework is based on the use of Turings measure of conditioning, whose minimization yields the confidence regions for the parameters as spherical as possible. Since this does not necessarily guarantee a high information content in the measurements, an additional constraint is imposed on the D-efficiency of the solutions. Then the approach converts the problem to an optimal control one in which both the control forces of the sensors and the initial sensor positions are optimized. Numerical solutions are then obtained using the MATLAB PDE toolbox and the RIOTS_95 optimal control toolbox which handles various constraints imposed on the sensor motions

OPTIMAL ACTIVATION STRATEGY OF DISCRETE SCANNING SENSORS FOR FAULT DETECTION IN DISTRIBUTED-PARAMETER SYSTEMS

Abstract The problem under consideration is to determine an activation policy of discrete scanning sensors in such a way as to maximize the power of a simple parametric hypothesis test, which verifies the nominal state of the considered distributed system specified over a given multi-dimensional spatial domain. The optimal locations of sensors are determined based on the D s -optimality criterion defined on the respective Fisher Information Matrix. The proposed approach exploits the notion of directly constrained design measures recently introduced in modern optimum experimental design theory which leads to an extremely fast iterative procedure of exchange type. In this work, a general scheme of such an approach leading to maximization of the fault detection efficiency in distributed-parameter systems is delineated and tested via computer simulations regarding an advection-diffusion problem.

Optimal location of discrete scanning sensors for parameter estimation of distributed systems

Abstract We investigate possibilities of choosing an activation policy of discrete scanning sensors in such a way as to maximize the accuracy of parameter estimation of a distributed system defined in a given multidimensional domain. A general functional defined on the Fisher information matrix is used as the design criterion. The setting examined here corresponds to situations where one has many sensors and activates only some of them during a given time interval, or alternatively, has several sensors which are mobile. The proposed approach, which has been suggested by Fedorovs idea of directly constrained design measures, consists in imposing constraints on the sensor density in a given spatial domain. As a result, an extremely fast iterative procedure is obtained whose each step reduces to replacing less informative sensor locations with points which furnish more informaton about the parameters. The performance of the proposed algorithm is evaluated by numerical experiments.