Continuous-time Model Identification Research Articles

Data-based mechanistic rainfall-runoff continuous-time modelling in urban context

This paper presents a data-based mechanistic modelling (DBM) approach to rainfall-runoff modelling based on the direct identification and estimation of continuous-time models from discrete-time series. It is argued that many mechanistic model parameters are more naturally defined in the context of continuous-time, differential equation models. As a results, there are advantages if such models are identified directly in this continuous-time form rather than being formulated and identified as discrete-time models. An illustrative example based on the analysis of rainfall-flow data from the Kerinou catchment in Brest demonstrates the relevance of the proposed modelling approach.

The CONTSID toolbox for Matlab: extensions and latest developments

This paper describes the latest developments for the CONtinuous-Time System IDentification (CONTSID) toolbox to be run with Matlab which includes time-domain identification methods for estimating continuous-time models directly from sampled data. The main additions to the new version aim at extending the available methods to handle wider practical situations in order to enhance the application field of the CONTSID toolbox. The toolbox now includes routines to solve errors-in-variables and closed-loop identification problems, as well as non-linear continuous-time model identification techniques.

An optimal instrumental variable method for continuous-time fractional model identification

this paper deals with continuous-time system identification using fractional differentiation models in a noisy output context. The simplified refined instrumental variable for continuous-time systems (srivc) is extended to fractional models. Monte Carlo simulation analysis are used to demonstrate the performance of the proposed optimal instrumental variable scheme.

Gray-Box Identification of Continuous-Time Models of Flexible Structures

A noniterative algorithm is proposed to identify the continuous-time state space model of lightly damped flexible structures. This paper is motivated by the need for accurate dynamic models to be used in design of active vibration control systems for, e.g., large space structures and aeronautical structures. A gray-box approach is adopted to preserve the physical meaning of the model parameters and to naturally impose physical constraints to the model, e.g., passivity and reciprocity. The procedure consists of two stages both in the frequency domain; first, a subspace method is applied to estimate the dynamic matrix, then, the input and output matrices are identified by solving a weighted least square problem, both in the colocated and noncolocated case. A numerical case study is carried out to illustrate the features of the algorithm and experimental results are presented by reporting and validating the identified model of a stiffened aeronautical panel in a broad frequency range. The experimental case study serves also for carrying out a comparison between the proposed identification procedure and some of the already existing algorithms.

An optimal IV technique for identifying continuous-time transfer function model of multiple input systems

An instrumental variable method for continuous-time model identification is proposed for multiple input single output systems where the characteristic polynomials of the transfer functions associated with each input are not constrained to be identical. An associated model order determination procedure is shown to be reasonably successful. Monte Carlo simulation analyses are used to demonstrate the properties and general robustness of the model order selection and parameter estimation schemes. The results obtained to model a winding process and an industrial binary distillation column illustrate the practical applicability of the proposed identification scheme.

Continuous-time model identification for closed loop control performance assessment

The paper describes a system identification procedure for continuous-time transfer function models and demonstrates how it can be used for control performance assessment. Two normalized indices are derived for detecting oscillations and sluggish performance. The methods are designed for single-input single-output (SISO) control loops that experience periodic setpoint changes. An advantage of the system identification procedure is that it can operate on irregularly sampled data. The paper presents results from simulation tests and from tests on an heating, ventilating, and air-conditioning (HVAC) system serving a large commercial office building.

SAMPLED-DATA MODELS FOR STOCHASTIC NONLINEAR SYSTEMS

To carry out identification of continuous-time models one inevitably needs to work with a sampled-data description of a system. In this paper a sampled-data model to represent continuous-time stochastic nonlinear systems is proposed. The model is simple to obtain and accurate in a well defined sense. It is based on numerical solution of stochastic differential equations, and shows some connections to the linear case. The results here extend previous work by the authors for the (nonlinear) deterministic case.

Box-Jenkins identification revisited—Part II: Applications

Part I of this series of two papers handles the identification of discrete-time and continuous-time Box-Jenkins models on arbitrary frequency grids in an open and closed loop setting. Part II (i) discusses the practical calculation of the estimators developed in Part I, (ii) illustrates some theoretical results via simulation, and (iii) applies the modeling technique to a real life problem.

Comments on: “Continuous time model identification from sampled data: implementation and performance evaluation”, Garnier, Mensler and Richard (2003)

This note extends the discussion of the above paper with respect to the finite time integration method of data preparation for continuous time system identification of linear systems.

Authors' reply to “Comments on ‘Continuous-time model identification from sampled data: implementation issues and performance evaluation’ by E. Boje”

We would like to thank Professor E. Boje for his interest in our article (Garnier et al. 2003). His comments lead us to the three following points: 1. We take note of the paper by Eitelberg (1988) ...

ROBUSTNESS ISSUES IN CONTINUOUS-TIME SYSTEM IDENTIFICATION FROM SAMPLED DATA

This paper explores the robustness issues that arise in the identification of continuous-time systems from sampled data. A key observation is that, in practice, one cannot rely upon the fidelity of the model at high frequencies. This implies that any result which implicitly or explicitly depends upon the folding of high frequency components down to lower frequencies will be inherently non-robust. We illustrate this point by referring to the identification of continuous-time auto-regressive stochastic models from sampled data. We argue that traditional approaches to this problem are sensitive to high frequency modelling errors. We also propose an alternative maximum likelihood procedure in the frequency domain, which is robust to high frequency modelling errors.

Integral-equation-based continuous-time model identification of a magnetostrictive actuator

The problem of the continuous-time model identification of a magnetostrictive actuator is considered. An integral-equation-based least squares method is proposed. The identification is based on the sampled data of an input-output measurement with high frequency coloured noise. The main idea of the method is to transform a differential equation into an integral equation so that the effect of the high-frequency coloured noise can be ignored. The method is successfully applied to parameter identification in a continuous-time model of a magnetostrictive actuator.

Regularization aspects in continuous-time model identification

This paper presents an analysis of some regularization aspects in continuous-time model identification. The study particulary focuses on linear filter methods and shows that filtering the data before estimating their derivatives corresponds to a regularized signal derivative estimation by minimizing a compound criterion whose expression is given explicitly. A new structure based on a null phase filter corresponding to a true regularization filter is proposed and allows to discuss the filter phase effects on parameter estimation by comparing its performances with those of the Poisson filter-based methods. Based on this analysis, a formulation of continuous-time model identification as a joint system input–output signal and model parameter estimation is suggested. In this framework, two linear filter methods are interpreted and a compound criterion is proposed in which the regularization is ensured by a model fitting measure, resulting in a new regularization filter structure for signal estimation.

A Time-Domain Approach to Continuous-Time Model Identification of Highly-Resonant Wide-Band Systems

The purpose of this paper is to present some issues that arise when applying a traditional continuous-time model identification technique to highly resonant systems over a large bandwidth. A scheme based on the use of frequency localising basis functions to improve the numerical conditioning of the identification problem is examined. Examples are presented showing the superior performance of the proposed method when applied to wideband estimation problems.

A sufficient condition for the convergence of adaptive observer in continuous-time model identification

This paper proposes a new method to identify a continuous-time model from sampled I/O data by using an adaptive observer. The boundedness of the parameter estimate and the exponential convergence of the parameter estimation error to 0 under the assumption of Persistently exciting (PE) signals are guaranteed. In order to identify the plant from a finite number of I/O data, an adaptive observer for a backward system is also proposed. In noise-free cases, the magnitude of the parameter estimation error can be made arbitrarily small if the sampling period is smaller than a certain value.

適応観測器を用いた連続時間モデル同定

Abstract This paper proposes a continuous-time model identification from sampled I/O data by using an adaptive observer, The boundedness of the parameter estimate and the exponential convergence of the parameter estimate error to 0 under the PE assumption are guaranteed, In order to identify the plant from a finite number of the I/O data, an adaptive observer of a backward system is also proposed.

Identification of continuous time models using discrete time data

Continuous-discrete stochastic state space models in the form of nonlinear partially observed Itô stochastic differential equations (SDE's) with measurement noise are advocated for modelling dynamic systems in continuous time using discrete time data. Such models provide a decomposition of the noise affecting the system into a process noise term and a measurement noise term, and this prediction error decomposition (PED) allows unknown parameters to be estimated from experimental data in a prediction error (PE) setting, which gives less biased and more reproductible results in the presence of significant process noise than the more commonly used output error (OE) setting. To facilitate the use of continuous-discrete stochastic state space models, a PE estimation scheme that features maximum likelihood (ML) and maximum a posteriori (MAP) estimation is presented along with a software implementation. To illustrate the superiority of PE estimation over OE estimation a case study is given, which demonstrates the higher sensitivity of OE estimates to process noise.

Continuous-time model identification by using adaptive observer

This paper proposes a continuous-time model identification from sampled I/O data by using an adaptive observer, The boundedness of the parameter estimate and the exponential convergence of the parameter estimate error to 0 under the PE assumption are guaranteed, In order to identify the plant from a finite number of the I/O data, an adaptive observer of a backward system is also proposed.

Identification of simple continuous-time models from relay feedback

In this paper it is presented a procedure for the estimation of a first order plus deadtime (FOPDT) model using a relay test and a relay test with an integrator. Exact expressions for the limit cycle in each case are obtained. The time constant and dead-time are computed by solving two equations from Poincaré map analysis of time-delay systems. The process gain is then estimated using three different approaches. Simulation examples illustrates the procedure in the presence of unmodelled dynamics and noise.

Unbiased identification of continuous-time parametric models using a time-weighted integral transform

A time-weighted integral transform is presented to identify a continuous SISO or MIMO parametric model based on a single dynamic test under open-loop or closed-loop operation. Moving-horizon algorithms are proposed to obtain unbiased estimates of the model parameters. The off-line algorithm in a least-squares form and the on-line algorithm in a recursive form are provided. An effective technique based on pattern recognition is also developed to determine the system order and time delay from observed data in a simple manner. Furthermore, the proposed method can be easily applied as a model reduction technique that results in an ideal model with delay for any specified order.