Estimator Selection: End-Performance Metric Aspects

Recently, a framework for application-oriented optimal experiment design has been introduced. In this context, the distance of the estimated system from the true one is measured in terms of a particular end-performance metric. This treatment leads to superior unknown system estimates to classical experiment designs based on usual pointwise functional distances of the estimated system from the true one. The separation of the system estimator from the experiment design is done within this new framework by choosing and fixing the estimation method to either a maximum likelihood (ML) approach or a Bayesian estimator such as the minimum mean square error (MMSE). Since the MMSE estimator delivers a system estimate with lower mean square error (MSE) than the ML estimator for finite-length experiments, it is usually considered the best choice in practice in signal processing and control applications. Within the application-oriented framework a related meaningful question is: Are there end-performance metrics for which the ML estimator outperforms the MMSE when the experiment is finite-length? In this paper, we affirmatively answer this question based on a simple linear Gaussian regression example.Comment: arXiv admin note: substantial text overlap with arXiv:1303.428

Input Design for System Identification via Convex Relaxation

This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal senses. In contrast to the majority of published work on this topic, we consider the problem in the time domain and subject to constraints on the amplitude of the input signal. This optimization problem is nonconvex. The main result of the paper is a convex relaxation that gives an upper bound accurate to within $2/\pi$ of the true maximum. A randomized algorithm is presented for finding a feasible solution which, in a certain sense is expected to be at least $2/\pi$ as informative as the globally optimal input signal. In the case of a single constraint on input power, the proposed approach recovers the true global optimum exactly. Extensions to situations with both power and amplitude constraints on both inputs and outputs are given. A simple simulation example illustrates the technique.Comment: Preprint submitted for journal publication, extended version of a paper at 2010 IEEE Conference on Decision and Contro

Optimal Multisine Probing Signal Design for Power System Electromechanical Mode Estimation

This paper proposes a methodology for the design of a probing signal used for power system electromechanical mode estimation. Firstly, it is shown that probing mode estimation accuracy depends solely on the probing signal’s power spectrum and not on a specific time-domain realization. A relationship between the probing power spectrum and the accuracy of the mode estimation is used to determine a multisine probing signal by solving an optimization problem. The objective function is defined as a weighting sum of the probing signal variance and the level of the system disturbance caused by the probing. A desired level of the mode estimation accuracy is set as a constraint. The proposed methodology is demonstrated through simulations using the KTH Nordic 32 power system model

Optimal Experiment Design for the Identification of One Module in the Interconnection of Locally Controlled Systems

International audienceIn this paper, we consider the problem of designing the least costly experiment that leads to a sufficiently accurate estimate of one module in a network of locally controlled systems. A module in such a network can be identified by exciting the corresponding local closed loop system. Such an excitation signal will not only perturb the input/output of the to-be-identified module, but also other modules due to the interconnection. Consequently, the cost of the identification can be expressed as the sum of the influence of the excitation signal on the inputs and outputs of all locally controlled systems. We develop a methodology to design the spectrum of the excitation signal in such a way that this cost is minimized while guaranteeing a certain accuracy for the identified model. We also propose an alternative identification configuration which can further reduce the propagation of the excitation signal to other modules and we make steps to robustify this optimal experiment design problem with respect to the cost of the identification

Iterative Decoupling Method for High-Precision Imaging of Complex Surfaces

Nonlinear systems and interaction forces are pervasive in many scientific fields, such as nanoscale metrology and materials science, but their accurate identification is challenging due to their complex behaviour and inaccessibility of measured domains. This problem intensifies for continuous systems undergoing distributed, coupled interactions, such as in the case of topography measurement systems, measuring narrow and deep grooves. Presented is a method to invert a set of nonlinear coupled equations, which can be functions of unknown distributed physical quantities. The method employs a successive approach to iteratively converge to the exact solution of the set of nonlinear equations. The latter utilizes an approximate yet invertible model providing an inexact solution, which is evaluated using the hard-to-invert exact model of the system. This method is applied to the problem of reconstructing the topography of surface contours using a thin and long vibrating fiber. In nanoscale metrology, measuring inaccessible deep and narrow grooves or steep walls becomes difficult and singular when attempting to extract distributed nonlinear interactions that depend on the topography. We verify our method numerically by simulating the Van der Waals (VdW) interaction forces between a nanofiber and a nanoscale deep groove, and experimentally by exploiting magnetic interactions between a magnetic topography and a vibrating, elastic beam. Our results validate the ability to accurately reconstruct the topography of normally inaccessible regions, making it a possible enhancement for traditional point based AFM measurements, as well as for other nonlinear inverse problems