Continuous-time Model Identification Research Articles

Continuous-time Hammerstein model identification utilizing hybridization of Augmented Sine Cosine Algorithm and Game-Theoretic approach

The widespread use of dynamic systems has greatly simplified various human-operated tasks. However, the complex and nonlinear nature of these systems has posed challenges in determining their structure due to heavy reliance on modeling for theoretical and empirical purposes in academic and practical contexts. This challenge is particularly evident in the Hammerstein model, which is well-known for its recognition of structural nonlinearity. To address the limitations of uncovering an optimized continuous-time Hammerstein model, researchers have explored the practical application of the Augmented Sine Cosine Algorithm-Game Theoretic (ASCA-GT). By combining the Game Theoretic (GT) and Sine Cosine Algorithm (SCA), this hybrid approach aims to achieve a nonlinear position-updated process for improved exploration and exploitation, while effectively overcoming issues like local optima trapping. The performance of ASCA-GT was evaluated using 13 benchmark functions and mathematical scenarios, as well as the Twin-Rotor System (TRS) and Electro-Mechanical Positioning System (EMPS). The effectiveness of the proposed technique was assessed using Wilcoxon's rank test, which confirmed the superior performance of ASCA-GT compared to other metaheuristic optimization methods in determining the continuous-time Hammerstein model.

Continuous-time model identification of the subglottal system

Mathematical models that accurately simulate the physiological systems of the human body serve as cornerstone instruments for advancing medical science and facilitating innovative clinical interventions. One application is the modeling of the subglottal tract and neck skin properties for its use in the ambulatory assessment of vocal function, by enabling non-invasive monitoring of glottal airflow via a neck surface accelerometer. For the technique to be effective, the development of an accurate building block model for the subglottal tract is required. Such a model is expected to utilize glottal volume velocity as the input parameter and yield neck skin acceleration as the corresponding output. In contrast to preceding efforts that employed frequency-domain methods, the present paper leverages system identification techniques to derive a parsimonious continuous-time model of the subglottal tract using time-domain data samples. Additionally, an examination of the model order is conducted through the application of various information criteria. Once a low-order model is successfully fitted, an inverse filter based on a Kalman smoother is utilized for the estimation of glottal volume velocity and related aerodynamic metrics, thereby constituting the most efficient execution of these estimates thus far. Anticipated reductions in computational time and complexity due to the lower order of the subglottal model hold particular relevance for real-time monitoring. Simultaneously, the methodology proves efficient in generating a spectrum of aerodynamic features essential for ambulatory vocal function assessment.

Continuous-Time Model Identification of the Subglottal System

Continuous-Time Model Identification of the Subglottal System

Long-memory recursive prediction error method for identification of continuous-time fractional models

This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models.

Direct identification of continuous-time LPV state-space models via an integral architecture

In this paper, we present a block-structured architecture for direct identification of continuous-time Linear Parameter-Varying (LPV) state-space models. The proposed architecture consists of an LPV model followed by an integral block. This structure is used to approximate the continuous-time LPV system dynamics. The unknown LPV model matrices are estimated along with the state sequence by minimizing a properly constructed dual-objective criterion. A coordinate-descent algorithm is employed to optimize the desired objective, which alternates between computing the unknown LPV matrices and estimating the state sequence. Thanks to the linear parametric structure induced by the LPV model, the optimization variables within each coordinate-descent step can be updated analytically via ordinary least squares. Furthermore, in order to handle large-size datasets, we discuss how to perform optimization based on short-size subsequences. The effectiveness of the proposed methodology is demonstrated via an academic example and two case studies. The first case study consists of identifying an LPV model describing the behaviour of an electronic bandpass filter from benchmark experimental data. The second case study involves identification of the plasma safety factor from a tokamak plasma simulator.

Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part

Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems.

An integral architecture for identification of continuous-time state-space LPV models

Abstract This paper presents an integral architecture for direct identification of continuous-time linear parameter-varying (LPV) state-space models. The main building block of the proposed architecture consist of an LPV model followed by an integral block, which is used to approximate the continuous-time state map of an LPV representation. The unknown LPV model matrices are estimated along with the state sequence by minimizing a properly constructed dual-objective criterion. A coordinate descent algorithm is employed to optimize the desired objective, which alternates between computing the unknown LPV matrices and estimating the state sequence. Thanks to the linear parametric structure induced by the LPV models, the unknown parameters within each coordinate descent step can be computed analytically via ordinary least squares. The effectiveness of the proposed methodology is assessed via a numerical example.

Continuous-Time Model Identification From Filtered Sampled Data: Error Analysis

In this article, an upper bound is established for the estimation error of a standard least squares (LS) algorithm used to identify a continuous-time model from filtered, sampled input–output data. It is found that the error has three constituent components due to the initial conditions, observation noise, and sample period. In particular, the initial condition bias is bounded by $O(1/[N\Delta t])$ , which requires sufficiently large $[N\Delta t]$ for accurate LS estimation. The theoretical results obtained are confirmed by simulation.

Continuous-time model identification: application on a behavioural (miLife) study

To develop efficient just-in-time personalised treatments, dynamical models are needed that provide a description of how an individual responds to treatment. However, available system identification approaches cannot effectively be applied to most behavioural datasets since, usually, the data collected is subjected to a large amount of noise and time sampling is not uniform. To be able to circumvent these issues, in this paper a new method is proposed for parsimonious system identification of continuous-time systems that does not require specially structured data. The developed algorithm provides an effective way to leverage these ‘non-standard’ datasets to identify continuous time dynamical models that are compatible with a-priori information available on the process. The algorithm developed is tested on data obtained from a behavioural study on adolescents and violence. The objective is to model the temporal dynamics of the association between violence exposure and mental health symptoms (depression and anxiety) in day-to-day life among a sample of adolescents at heightened risk for both substance use exposure and problem behaviour. The information extracted from individual models of behaviour such as the maximum burden and the time of fading away of depression/anxiety does differ substantially from person to person. This information has the potential to be useful to design personalised interventions that would have a better chance of succeeding.

Integrated Neural Networks for Nonlinear Continuous-Time System Identification

This letter introduces a novel neural network architecture, called Integrated Neural Network (INN), for direct identification of nonlinear continuous-time dynamical models in state-space representation. The proposed INN is used to approximate the continuous-time state map, and it consists of a feed-forward network followed by an integral block. The unknown parameters are estimated by minimizing a properly constructed dual-objective criterion. The effectiveness of the proposed methodology is assessed against the Cascaded Tanks System benchmark.

Identification of continuous-time models with slowly time-varying parameters

The off-line estimation of the parameters of continuous-time, linear, time-invariant transfer function models can be achieved straightforwardly using linear prefilters on the measured input and output of the system. The on-line estimation of continuous-time models with time-varying parameters is less straightforward because it requires the updating of the continuous-time prefilter parameters. This paper shows how such on-line estimation is possible by using recursive instrumental variable approaches. The proposed methods are presented in detail and also evaluated on a numerical example using both single experiment and Monte Carlo simulation analysis. In addition, the proposed recursive algorithms are tested using data from two real-life systems.

Benchmark problems for continuous-time model identification: Design aspects, results and perspectives

The problem of estimating continuous-time model parameters of linear dynamical systems using sampled time-domain input and output data has received considerable attention over the past decades and has been approached by various methods. The research topic also bears practical importance due to both its close relation to first principles modelling and equally to linear model-based control design techniques, most of them carried in continuous time. Nonetheless, as the performance of the existing algorithms for continuous-time model identification has seldom been assessed and, as thus far, it has not been considered in a comprehensive study, this practical potential of existing methods remains highly questionable. The goal of this brief paper is to bring forward a first study on this issue and to factually highlight the main aspects of interest. As such, an analysis is performed on a benchmark designed to be consistent both from a system identification viewpoint and from a control-theoretic one. It is concluded that robust initialization aspects require further research focus towards reliable algorithm development.

Recursive IV Identification of Continuous-Time Models With Time Delay From Sampled Data

This brief investigates recursive instrumental variable (IV) identification of time-delayed continuous-time (CT) models from the sampled input–output data. The refined IV method is extended for the first time to identify recursively both the parameters and time delay of a CT transfer function model. It is shown that the proposed method is able to yield consistent parameter estimation. Due to the nonlinear nature of the loss function to be optimized, time-delay estimation suffers from local minima. Thus, the global convergence performance relies on the quality of initial parameters. To increase the chance of converging to the global optimum, several guidelines are suggested to help the choice of starting values. The main results derived in this brief are confirmed by numerical examples and an experimental application.

Finite-horizon integration for continuous-time identification: bias analysis and application to variable stiffness actuators

ABSTRACT Direct identification of continuous-time dynamical models from sampled data is now a mature discipline, which is known to have many advantages with respect to indirect approaches based on the identification of discretised models. This paper faces the problem of continuous-time identification of linear time-invariant systems through finite-horizon numerical integration and least-square estimation. The bias in the least-squares estimator due to the noise corrupting the signal observations is quantified, and the benefits of numerical integration in the attenuation of this bias are discussed. An extension of the approach which combines numerical integration, least-squares estimation and particle swarm optimisation is proposed for the identification of nonlinear systems and nonlinear-in-the-parameter models, and then applied to the estimation of the torque-displacement characteristic of a commercial variable stiffness actuator driving a one-degree-of-freedom pendulum.

Frequency domain identification of continuous-time output-error models with time-delay from relay feedback tests

This paper is concerned with identification of continuous-time output-error models with time-delay from relay feedback tests. Conventional methods for solving this problem consist in deriving analytical limit cycle expressions and fitting them to measured shape factors. However, they may fail to handle different limit cycles uniformly, due to the structural differences in the analytical expressions. To overcome this problem, we consider a more general, data-based, parametric identification framework using sampled limit cycle data. A frequency domain method that minimizes the sum of squared output-errors is developed. The proposed method can be of high accuracy, thanks to the periodic input–output signals provided by sustained relay feedback oscillations, which can help to reduce leakage and aliasing errors. Besides, a distinctive merit of the proposed method is that identification of stable and unstable plants can be equally simple. The effectiveness and superiority of the proposed method are demonstrated by means of both theoretical analyses and simulation examples.

Issues in separable identification of continuous-time models with time-delay

This paper discusses several issues related to the identification of time-delayed continuous-time systems using the refined instrumental variable method. The proposed estimation procedure is iterative where, at each iteration, the rational system parameters and time-delay are estimated separately. The main contribution of this paper covers three aspects. Firstly, conditions for persistent excitation are established, which should be satisfied to guarantee the identifiability of the system parameters and time-delay. Secondly, existence of multiple minima in the loss function is investigated. Due to the nonlinear nature of the loss function to be optimized with respect to the time-delay, initialization is a particularly important issue for correct estimation of the time-delay. Lastly, to reliably initialize the identification algorithm, based on the previous analysis, some guidelines are proposed to facilitate the choice of reliable initial parameters. The main results derived in this paper are verified by means of both theoretical analyses and numerical simulations.

CONTSID: a Matlab toolbox for standard and advanced identification of black-box continuous-time models

The CONtinuous-Time System IDentification (CONTSID) toolbox provides Matlab functions for estimating continuous-time black-box models of dynamical systems from measured data without having to fully characterize the mathematics governing the system behavior. The toolbox includes tools for standard identification of linear continuous-time models such as simple process, transfer functions and state-space models. The toolbox also provides algorithms for more advanced identification such as errors-in-variable (EIV) and closed-loop model estimation or to capture nonlinear system dynamics. This paper presents an overview of the main features of the latest release of the CONTSID toolbox and outlines some recent developments for on-line parameter and time-delay system estimation.

A data-driven modeling approach to identify disease-specific multi-organ networks driving physiological dysregulation.

Multiple physiological systems interact throughout the development of a complex disease. Knowledge of the dynamics and connectivity of interactions across physiological systems could facilitate the prevention or mitigation of organ damage underlying complex diseases, many of which are currently refractory to available therapeutics (e.g., hypertension). We studied the regulatory interactions operating within and across organs throughout disease development by integrating in vivo analysis of gene expression dynamics with a reverse engineering approach to infer data-driven dynamic network models of multi-organ gene regulatory influences. We obtained experimental data on the expression of 22 genes across five organs, over a time span that encompassed the development of autonomic nervous system dysfunction and hypertension. We pursued a unique approach for identification of continuous-time models that jointly described the dynamics and structure of multi-organ networks by estimating a sparse subset of ∼12,000 possible gene regulatory interactions. Our analyses revealed that an autonomic dysfunction-specific multi-organ sequence of gene expression activation patterns was associated with a distinct gene regulatory network. We analyzed the model structures for adaptation motifs, and identified disease-specific network motifs involving genes that exhibited aberrant temporal dynamics. Bioinformatic analyses identified disease-specific single nucleotide variants within or near transcription factor binding sites upstream of key genes implicated in maintaining physiological homeostasis. Our approach illustrates a novel framework for investigating the pathogenesis through model-based analysis of multi-organ system dynamics and network properties. Our results yielded novel candidate molecular targets driving the development of cardiovascular disease, metabolic syndrome, and immune dysfunction.

Identification of Fractional Differential Models for Lithium-ion Polymer Battery Dynamics

This paper presents a non-integer order (fractional) derivative model for modeling lithium-ion (Li-ion) battery dynamics in which direct continuous-time (CT) model identification methods are used to estimate the battery model parameters. In particular, the CT least squares-based state-variable filter (lssvf) identification method is extended to be used in fractional differential model identification of a battery system. The model performance and validation accuracy are evaluated on the basis of experimental data of a Li-ion polymer (LiPo) battery. It is shown how the proposed lssvf identification method can accurately capture the fractional order battery dynamics and exhibit better performance than integer order differential models.

Closed-loop continuous-time model identification with noisy input-output

In this paper, system identification is proposed for closed-loop systems in input/output noisy context. Although instrumental variable techniques exist in the literature, the proposed filtering in input/ouput noisy context is not optimal. Also, three algorithms are proposed, and the closed-loop simplified refined instrumental variable for continuous-time system gives optimal results: estimates are consistent and with minimum variance. The main contributions relies on the filtering of the instruments and signals considered.