Direct Parameter Identification of Distributed Parameter Systems

A new direct approach to identifying the parameters of distributed parameter systems from noise corrupted data is introduced. The model of the system which takes the form of a set of nonlinear partial differential equations is assumed known with the exception of a set of constant parameters. Using finite difference approximations of the spatial derivatives the original equation is transformed into a set of ordinary differential equations. The identification approach involves smoothing the measured data and estimating the temporal derivatives using a fixed interval smoother. A least squares method is then employed to estimate the unknown parameters. Three examples that illustrate the applicability of the proposed approach are presented and discussed

Parameter estimation of large flexible aerospace structures with application to the control of the Maypole Deployable Reflector

Systems such as the Maypole deployable reflector have a distributed parameter nature. The flexible column and hoop structure and the circular antenna of 30-100 meter diameter which it supports are described by partial, rather than ordinary, differential equations. Progress completed in reduced order modelling andd controller design and digital parameter estimation and control is summarized. Topics covered include depolyment and on-orbit operation; quasi-static (steady state) operation; dynamic distributed parameter system; autoregressive moving average identification; frequency domain procedures; direct or implicit active control; adaptive observers; parameter estimation using a linear reinforcement learning factor; feedback control; and reduced order modeling for nonlinear systems

Identification for distributed parameter systems

This thesis considers the parameter identification problem for systems governed by partial differential equations. The various identification methods sire grouped into three disjoint classes namely: "Direct Methods", "Reduction to a Lumped Parameter System", and "Reduction to an Algebraic Equation". The major subject investigated here is concerned with the applicability of stochastic approximation algorithms for identifying distributed parameter systems (DPS) operating in a stochastic environ­ment, where no restriction on probability distributions is imposed. These algorithms are used as a straightforward identification procedure, converge to the real value of the parameters with probability one, and are suitable for on-line applications. In this way, a new identification method is developed for DPS described by linear models, driven by random inputs, and observed through noisy measurements. The very real case of noisy observations taken at a limited number of discrete points located in the spatial domain is considered. The proposed identifica­tion method assumes that a previous system classification has been performed, such that the model to be identified is known up to a set of space-varying parameters, where extraneous terms may be included

Adaptive Method for the Experimental Detection of Instabilities

Motivated by numerical bifurcation detection, we present a methodology for the direct location of bifurcation points in nonlinear dynamic laboratory experiments. The procedure involves active, adaptive use of the bifurcation parameter(s) as control variable(s), coupled with the on-line identification of low-order nonlinear dynamic models from experimental time-series data. Application of the procedure to such “hard” transitions as saddle-node and subcritical Hopf bifurcations is demonstrated through simulated experiments of lumped as well as spatially distributed systems

Model reduction for the dynamics and control of large structural systems via neutral network processing direct numerical optimization

Three neural network processing approaches in a direct numerical optimization model reduction scheme are proposed and investigated. Large structural systems, such as large space structures, offer new challenges to both structural dynamicists and control engineers. One such challenge is that of dimensionality. Indeed these distributed parameter systems can be modeled either by infinite dimensional mathematical models (typically partial differential equations) or by high dimensional discrete models (typically finite element models) often exhibiting thousands of vibrational modes usually closely spaced and with little, if any, damping. Clearly, some form of model reduction is in order, especially for the control engineer who can actively control but a few of the modes using system identification based on a limited number of sensors. Inasmuch as the amount of 'control spillover' (in which the control inputs excite the neglected dynamics) and/or 'observation spillover' (where neglected dynamics affect system identification) is to a large extent determined by the choice of particular reduced model (RM), the way in which this model reduction is carried out is often critical

Electromechanical actuator bearing fault detection using empirically extracted features

Model parameter estimation when coupled with Principal Component Analysis (PCA) and Bayesian classification techniques form a potentially effective fault detection scheme for Electromechanical Actuators (EMAs). This work uses parameter estimation algorithms based on linear system identification methods, derives a novel feature extraction algorithm based on PCA and analyzes its performance through simulations and experiments. A Bayesian classifier is used to create well defined EMA health classes from the extracted features. Research contributions on fault detection in EMAs are significant because EMA faults and their detection are not yet well understood. Potential future applications - such as in primary flight control actuation in aircraft - require that quality fault detection systems be in place. Therefore, fault detection of EMAs is a vast area of ongoing research where highly capable solutions are gradually becoming available. Prior work in parameter estimation methods for feature extraction in DC motor drives - which includes EMAs - are amongst those available. While PCA is a popular feature extraction solution in a number of frequency-based fault detection approaches, the use of PCA for feature extraction from model parameters for detecting bearing faults in EMAs has not been previously reported. In this work, a linear difference model is applied to the EMA system data such that fault information is distributed amongst the estimated model parameters. A direct comparison of the parameter estimates from healthy and degraded systems offers little insight into health conditions because of the weak effects of faults on the signal data. However, the application of PCA to uncorrelate the linearly correlated model parameters while minimizing the loss of variance information from the data effectively brings out fault information. The present algorithm is successfully applied to data collected from a Moog MaxForce EMA. The results are consistent and display effective fault detection characteristics, making the developed approach a suitable starting point for future work

Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed we ag-gregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the ad-vantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart

Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods

Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thoré basin and used as a relatively simple (synthetic observations) but didactic application case. It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting