Optimization of a joint sensor placement and robust estimation scheme for distributed parameter processes subject to worst case spatial disturbance distributions

2004 ◽  
Author(s):  
M.A. Demetriou ◽  
J. Borggaard
Keyword(s):  
Robust Estimation ◽  
Sensor Placement ◽  
Distributed Parameter ◽  
Worst Case ◽  
Estimation Scheme

scholarly journals Robust Universal Inference

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 773
Author(s):  
Amichai Painsky ◽  
Meir Feder
Keyword(s):  
Robust Estimation ◽  
Minimax Estimator ◽  
Worst Case ◽  
Capacity Theory ◽  
Alternative Approach ◽  
True Model ◽  
Finite Set ◽  
Universal Prediction ◽  
Estimation Scheme

Learning and making inference from a finite set of samples are among the fundamental problems in science. In most popular applications, the paradigmatic approach is to seek a model that best explains the data. This approach has many desirable properties when the number of samples is large. However, in many practical setups, data acquisition is costly and only a limited number of samples is available. In this work, we study an alternative approach for this challenging setup. Our framework suggests that the role of the train-set is not to provide a single estimated model, which may be inaccurate due to the limited number of samples. Instead, we define a class of “reasonable” models. Then, the worst-case performance in the class is controlled by a minimax estimator with respect to it. Further, we introduce a robust estimation scheme that provides minimax guarantees, also for the case where the true model is not a member of the model class. Our results draw important connections to universal prediction, the redundancy-capacity theorem, and channel capacity theory. We demonstrate our suggested scheme in different setups, showing a significant improvement in worst-case performance over currently known alternatives.

A Robust Method for Parameter Estimation from Catch and Effort Data

1989 ◽  
Vol 46 (1) ◽  
pp. 137-144 ◽  
Author(s):  
D. Ludwig ◽  
C. J. Walters
Keyword(s):  
Parameter Estimation ◽  
Robust Estimation ◽  
Robust Method ◽  
Amount Of Information ◽  
Surplus Production ◽  
Production Models ◽  
Composite Estimation ◽  
Estimation Scheme

The problem of robust estimation of optimal effort levels from surplus production models is considered. A variety of models are used to generate data, for the purpose of testing estimation schemes. The result of an estimation is an estimate of the optimal effort. These efforts are compared using the expected discounted value of a deterministic stock, which corresponds to the model used to generate the data. Such a criterion takes into account not only the loss due to bias in the estimated optimal effort, but also the loss due to the variance of the estimator. Estimation is difficult if there is a lack of informative variation in effort levels or stock sizes. In such cases, the estimation scheme which maximizes the criterion described above sacrifices realism in the representation of the stock-production relationship in order to reduce the variance of the estimate of optimal effort. We present a composite estimation scheme which performs acceptably in all the cases we have examined, and whose performance degrades slowly as the amount of information in the data decreases.

A Robust Optimization Method for Systems With Significant Nonlinear Effects

1993 ◽  
Author(s):  
Jyh-Cheng Yu ◽  
Kosuke Ishii
Keyword(s):  
Heat Treatment ◽  
Robust Optimization ◽  
Nonlinear Effects ◽  
Optimization Method ◽  
Post Heat Treatment ◽  
Worst Case ◽  
Estimation Scheme ◽  
Optimization Methodology ◽  
Major Factors ◽  
The Cost

Abstract This paper describes a robust optimization methodology for design involving either complex simulations or actual experiments. The proposed procedure optimizes the worst case response that consists of a weighted sum of expected mean and response variance. The estimation scheme for expected mean and variance adopts the modified 3-point Gauss quadrature integration to assure superior accuracy for systems with significant nonlinear effects. We apply the proposed method to the robust design of geometric parameters of heat treated parts to minimize the cost of post heat treatment operations. The paper investigates the major factors influencing geometric distortions due to heat treatment and the rules of thumb in design. The study focuses on relating dimensional distortion to the design of part geometry. To illustrate the utility of the proposed method, we present the formulation of a case study on allocation of dimensions of preheat treated (green) shafts to minimize the cost of post heat treatment operations. The final result is not presented yet pending the completion of further experiments.

Optimal Sensor Configuration for Bridge Structures Following a Probabilistic Approach

2012 ◽  
Vol 594-597 ◽  
pp. 1098-1104
Author(s):  
Tao Yin ◽  
Hong Ping Zhu ◽  
Dian Qing Li
Keyword(s):  
Information Entropy ◽  
Optimization Technique ◽  
Probabilistic Approach ◽  
Sensor Placement ◽  
Entropy Method ◽  
Distributed Parameter ◽  
Coordinate Systems ◽  
Fe Method ◽  
Bridge Model ◽  
Sensor Configuration

In this paper, a statistical methodology is introduced for identifying the most effective way to install a limited number of sensors on a typical distributed-parameter system, i.e., a three-span continuous bridge model with two elastic supports to extract as much information as possible. This is performed by minimizing the uncertainties associated with the identified bridge modeling parameters. In the proposed methodology, the information entropy is employed as a measure to quantify the uncertainty of the identified structural modeling parameters. The problem of optimal sensor placement is then formulated as a continuous optimization problem, in which the information entropy is minimized, with the sensor configurations as the minimization variables. The generally used discrete-coordinate systems modeled by the finite element (FE) method can only approximate their actual dynamic behavior, which would in turn influence the sensor configuration results, and the sensors are confined to be only put on discrete nodes related to the coarse mesh scheme usually employed. For structures such as bridges belonging to typical distributed-parameter systems, it’s more reasonable and convenient to be modeled as continues-coordinate system with analytical formulation. It’s the main purpose of this paper to develop a sensor placement method for continues-coordinate systems following the Bayesian theorem and the information entropy method, with the binary-encoded genetic algorithm (GA) employed as the optimization technique.

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