Modern control concepts in hydrology

Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations (identification of lifting rotor system parameters from transient response data), Phase 7-B

System identification methods have been applied to rotorcraft to estimate stability derivatives from transient flight control response data. While these applications assumed a linear constant coefficient representation of the rotorcraft, the computer experiments used transient responses in flap-bending and torsion of a rotor blade at high advance ratio which is a rapidly time varying periodic system. It was found that a simple system identification method applying a linear sequential estimator also called least square estimator or equation of motion estimator, is suitable for this periodic system and can be used directly if only the acceleration data are noise polluted. In the case of noise being present also in the state variable data the direct application of the estimator gave poor results

On the optimality of a new class of 2D recursive filters

summary:The purpose of this paper is to prove the minimum variance property of a new class of 2D, recursive, finite-dimensional filters. The filtering algorithms are derived from general basic assumptions underlying the stochastic modelling of an image as a 2D gaussian random field. An appealing feature of the proposed algorithms is that the image pixels are estimated one at a time; this makes it possible to save computation time and memory requirement with respect to the filtering procedures based on strip processing. Experimental results show the effectiveness of the new filtering schemes

The theory of multiple measurements techniques in distributed parameter systems

A comprehensive theory of multiple measurements for the optimum on-line state estimation and parameter identification in a class of noisy, dynamic distributed systems, is developed in this study. Often in practical monitoring and control problems, accurate measurements of a critical variable are not available in a desired form or at a desired sampling rate. Rather, noisy independent measurements of related forms of the variable may be available at different sampling rates. Multiple measurements theory thus involves the optimum weighting and combination of different types of available measurements. One of the contributions of this work is the development of a unique measurement projection method by which off-line measurements may be optimally utilized for on-line estimation and control. The analysis of distributed systems often requires the establishment of monitoring stations. Another contribution of this study is the development of a measurement strategy, based on statistical experimental design techniques, for the optimum spatial monitoring stations in a class of distributed systems. By incorporating in the optimization criterion, terms representing the realistic costs of making observations, an algorithm is developed for an estimator indicator whose values dictate an observation strategy for the optimum number and temporal intervals of observations. This, along with the optimum measurement stations thus provides a comprehensive monitoring policy on which the estimation and control of a distributed system may be based. By employing the measurement projection scheme and the monitoring policy, algorithms are further developed for Kalmantype distributed filters for the estimation of the state profiles based on all available on-line and off-line measurements. In the interest of a realistic engineering application, the developments in this study are based on a specific class of distributed systems representable by the mass transport models in environmental pollution systems. However, the techniques developed are equally applicable to a broader class of systems, including process control, where measurements may be characterized by noisy on-line instrumentation and off-line empirical laboratory tests. Although pertinent field data were not available for the research, the multiple measurements techniques developed were applied to several simulated numerical examples that do represent typical engineering problems. The results obtained demonstrate the consistent superiority of the techniques over existing estimation methods. Methods by which the results of this work may be integrated into real engineering problems are also discussed

Neural network directed Bayes decision rule for moving target classification

Includes bibliographical references.In this paper, a new neural network directed Bayes decision rule is developed for target classification exploiting the dynamic behavior of the target. The system consists of a feature extractor, a neural network directed conditional probability generator and a novel sequential Bayes classifier. The velocity and curvature sequences extracted from each track are used as the primary features. Similar to hidden Markov model (HMM) scheme, several hidden states are used to train the neural network, the output of which is the conditional probability of occurring the hidden states given the observations. These conditional probabilities are then used as the inputs to the sequential Bayes classifier to make the classification. The classification results are updated recursively whenever a new scan of data is received. Simulation results on multiscan images containing heavy clutter are presented to demonstrate the effectiveness of the proposed methods.This work was funded by the Optoelectronic Computing Systems (OCS) Center at Colorado State University, under NSF/REC Grant 9485502

Online Natural Gradient as a Kalman Filter

We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural gradient descent on the log-likelihood of the observations. In the i.i.d. case, this relation is a consequence of the "information filter" phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant interpretations for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.Comment: 3rd version: expanded intr

Methods Studies on System Identification from Transient Rotor Tests

Some of the more important methods are discussed that have been used or proposed for aircraft parameter identification. The methods are classified into two groups: Equation error or regression estimates and Bayesian estimates and their derivatives that are based on probabilistic concepts. In both of these two groups the cost function can be optimized either globally over the entire time span of the transient, or sequentially, leading to the formulation of optimum filters. Identifiability problems and the validation of the estimates are briefly outlined, and applications to lifting rotors are discussed