Model Identification Framework Research Articles

An optimal experimental design framework for fast kinetic model identification based on artificial neural networks

The development of mathematical models to describe reaction kinetics is crucial in process design, control, and optimisation. However, distinguishing between different candidate kinetic models presents a non-trivial challenge. Recent works on this topic introduced an approach that employs artificial neural networks (ANNs) to identify kinetic models. In this paper, the ANNs-based model identification approach is expanded by introducing an optimal experimental design procedure. The performance of the method is evaluated through a case study related to the identification of kinetics in a batch reaction system, where different combinations of experimental design variables and noise level on the measurements are compared to assess their impact on kinetic model identification. The proposed experimental design methodology effectively reduces the number of required experiments while enhancing the artificial neural network's ability to accurately identify the appropriate set of equations defining the kinetic model structure.

Advancing Vehicle Classification: A Novel Framework for Type, Model, and Fuel Identification Using Nonvisual Sensor Systems for Seamless Data Sharing

Advancing Vehicle Classification: A Novel Framework for Type, Model, and Fuel Identification Using Nonvisual Sensor Systems for Seamless Data Sharing

Electronic nose algorithm design using classical system identification for odour intensity detection

The two elements considered crucial for constructing an efficient environmental odour intensity monitoring systems are sensors and algorithms typically addressed to as electronic nose sensor (e-nose). Due to operational complexity of biochemical sensors developed in human bodies algorithms based on computational methods of artificial intelligence are typically considered superior to classical model based approaches in development of e-nose algorithms. However, in this work authors proposed an approach to derive an algorithm for e-nose using a classical approach kept in model identification framework. The benefits of the proposed solution, apart of the structural correctness of the derived algorithm model, include improved generalisation capabilities in case of low training data volume is available. To that goal the algorithm structure is derived based on available knowledge on human senses reaction to odorants. Due to the algorithm structure a random search algorithm with heuristics (evolutionary algorithm) is used to search for the required parameters of the electronic nose e-nose to be able to explain the laboratory experiment data. The evolutionary algorithm is kept in a multi-objective optimisation framework. As such, two heuristic decision making mechanisms have been proposed to select parameters for the algorithm under development. A comparison of the resulting algorithm with the one developed based on artificial neural networks (ANNs) is provided.

Adaptive Bayesian Inference Framework for Joint Model and Noise Identification

Adaptive Bayesian Inference Framework for Joint Model and Noise Identification

The medium amplitude response of nonlinear Maxwell–Oldroyd type models in simple shear

A general framework for Maxwell-Oldroyd type differential constitutive models is examined, in which an unspecified nonlinear function of the stress and rate-of-deformation tensors is incorporated into the well-known corotational version of the Jeffreys model discussed by Oldroyd. For medium amplitude simple shear deformations, the recently developed mathematical framework of medium amplitude parallel superposition (MAPS) rheology reveals that this generalized nonlinear Maxwell model can produce only a limited number of distinct signatures, which combine linearly in a well-posed basis expansion for the third order complex viscosity. This basis expansion represents a library of MAPS signatures for distinct constitutive models that are contained within the generalized nonlinear Maxwell model. We describe a framework for quantitative model identification using this basis expansion, and discuss its limitations in distinguishing distinct nonlinear features of the underlying constitutive models from medium amplitude shear stress data. The leading order contributions to the normal stress differences are also considered, revealing that only the second normal stress difference provides distinct information about the weakly nonlinear response space of the model. After briefly considering the conditions for time-strain separability within the generalized nonlinear Maxwell model, we apply the basis expansion of the third order complex viscosity to derive the medium amplitude signatures of the model in specific shear deformation protocols. Finally, we use these signatures for estimation of model parameters from rheological data obtained by these different deformation protocols, revealing that three-tone oscillatory shear deformations produce data that is readily able to distinguish all features of the medium amplitude, simple shear response space of this generalized class of constitutive models.

Preserving the DAE structure in the Loewner model reduction and identification framework

We propose an extension of the Loewner framework to descriptor linear systems that preserves the DAE (differential algebraic equation) structure of the underlying system. More precisely, by means of post-processing the data, the behavior at infinity is matched. As it turns out, the conventional procedure constructs a reduced model by directly compressing the data and hence losing information at infinity. By transforming the matrix pencil composed of the E and A matrices into a generalized block diagonal form, we can separate the descriptor system into two subsystems; one corresponding to the polynomial part and the other to the strictly proper part of the transfer function. Different algorithms are implemented to transform the matrix pencil into block diagonal form. Furthermore, a data-driven splitting of the descriptor system can be achieved in the Loewner framework. Hence, the coefficients of the polynomial part can be estimated directly from data. Several numerical examples are presented to illustrate the theoretical discussion.

An Optimization-Based Framework for Nonlinear Model Selection and Identification

This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results.

Machine learning-based adaptive model identification of systems: Application to a chemical process

Many of the existing offline system identification methods cannot completely comprehend the dynamics of an evolving complex process without relying on impractically large data sets. As a solution to this, a systematic procedure capable of identifying and predicting the nonlinear dynamics on the fly promises to provide a useful representation of the process model. Motivated by this, an adaptive model identification framework that relies on the methods of sparse regression and feature selection is presented in this work. The proposed method is a three-step procedure: (1) identifying potential functions from a candidate library using recently developed Sparse Identification of Nonlinear Dynamics (SINDy), (2) updating coefficients of the identified model using ordinary least-squares regression, (3) selecting the most important features using stepwise regression. The proposed algorithm is implemented as follows. Initially, a baseline model is identified offline using SINDy, and as a new data becomes available, the subsequent online steps are triggered based on a pre-specified tolerance to further update the model. Such an adaptive identification scheme facilitates in perceiving the model structure using a less amount of data than its offline counterpart, SINDy. To highlight its significance, the dynamics of a continuous stirred tank reactor is identified using the proposed adaptive method and is compared with a model identified using SINDy alone.

Sparse model identification and learning for ultra-high-dimensional additive partially linear models

The additive partially linear model (APLM) combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the “curse of dimensionality”. A natural question raised in practice is the choice of structure in the nonparametric part, i.e., whether the continuous covariates enter into the model in linear or nonparametric form. In this paper, we present a comprehensive framework for simultaneous sparse model identification and learning for ultra-high-dimensional APLMs where both the linear and nonparametric components are possibly larger than the sample size. We propose a fast and efficient two-stage procedure. In the first stage, we decompose the nonparametric functions into a linear part and a nonlinear part. The nonlinear functions are approximated by constant spline bases, and a triple penalization procedure is proposed to select nonzero components using adaptive group LASSO. In the second stage, we refit data with selected covariates using higher order polynomial splines, and apply spline-backfitted local-linear smoothing to obtain asymptotic normality for the estimators. The procedure is shown to be consistent for model structure identification. It can identify zero, linear, and nonlinear components correctly and efficiently. Inference can be made on both linear coefficients and nonparametric functions. We conduct simulation studies to evaluate the performance of the method and apply the proposed method to a dataset on the Shoot Apical Meristem (SAM) of maize genotypes for illustration.

Nonlinear space–time varying parameter estimation using consensus-based in-network distributed strategy

In the present world, distributed signal processing plays a significant role in applications ranging from surveillance and tracking to exploration and monitoring. In this paper, an online distributed framework of spatio-temporal Wiener model is presented. A conventional Wiener model is extended to nonlinear distributed parameter systems (DPSs), which comprises of a linear time-invariant (LTI) system in series with a static nonlinear element. The standard Wiener model identification framework is reformulated as the minimization of multiple constrained optimization subtasks that get solved using alternating direction method of multipliers (ADMM) along with coordinate descent techniques. DPSs are significantly used in industrial processes e.g. thermal process, fluid process, etc. Almost all the real-time data contain non-linearity in them which is modeled using several methods: Wiener modeling is one of them. Adaptive as well as distributed implementation of such model is considered to take the advantages of both adaptive and distributed signal processing. The proposed method overcomes the limitations concerning fusion center (FC) and least-square (LS) based approaches. Unknown parameters of Wiener DPS are identified in an adaptive and distributed manner. To dignify the effectiveness of the proposed methodology, simulations on a catalytic rod (an example of a parabolic system) are illustrated.

Traveling Traders’ Exchange Problem: Stochastic Modeling Framework and Two-Layer Model Identification Strategy

The Traveling Traders’ Exchange Problem (TTEP) is formalized, aiming at studying the collision–exchange systems found in various research areas. As an example of the TTEP models, a 1-D model is developed and characterized in detail. The computational stochastic simulation of the 1-D TTEP model relies on a stochastic simulation algorithm implemented on the basis of the Monte Carlo method. A model identification framework is proposed where the money distribution in the system obtained from the stochastic model is characterized in terms of (a) standard deviation of the money redistribution; (b) its probability density function. Results indicate that the expressions of the estimated functions for terms (a) and (b) are tightly related to the system input conditions. The example of curve fitting on the probability density function shows how the variation of money redistribution in the system in time is driven by different values of the parameters describing the interaction mechanism.

Experimental Scheduling Functions for Global LPV Human Controller Modeling

In this paper, the Linear Parameter Varying (LPV) model identification framework is applied to estimating time-varying human controller (HC) dynamics in a single-loop tracking task. Given the inherently unknown time changes in HC behavior, a global LPV approach with experimentally determined Scheduling Functions (SFs) is needed for this application. In this paper, a methodology based on the Predictor-Based Subspace Identification (PBSID) algorithm is tested. Using Monte Carlo simulation data matching a recent experimental study, two experimental SFs derived from measured HC control inputs are tested for their LPV model identification performance. The results are compared with LPV models obtained using the true (analytical) SFs used for generating the simulation data. An experimental SF obtained from the double derivative of HCs’ control inputs using zero-phase low-pass filtering was found to yield time-varying HC model estimates of equivalent accuracy as obtained with the analytical SFs; a promising result for future application of this methodology to measured HC behavior.

A Feature Selection and Classification Algorithm Based on Randomized Extraction of Model Populations.

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection (FS) and classifier design tasks. The classifier is constructed as a polynomial expansion of the original features and a selection process is applied to find the relevant model terms. The selection method progressively refines a probability distribution defined on the model structure space, by extracting sample models from the current distribution and using the aggregate information obtained from the evaluation of the population of models to reinforce the probability of extracting the most important terms. To reduce the initial search space, distance correlation filtering is optionally applied as a preprocessing technique. The proposed method is compared to other well-known FS and classification methods on standard benchmark problems. Besides the favorable properties of the method regarding classification accuracy, the obtained models have a simple structure, easily amenable to interpretation and analysis.

Modeling and Compensation for the Distortion of Parametric Loudspeakers Using a One-Dimension Volterra Filter

Recently, the general Volterra filter (VF) has been adopted for the modeling of parametric loudspeakers. However, the computation complexity of the VF is too high for real-time implementation. In this paper, a one-dimension Volterra filter (ODVF) with much lower complexity is introduced to model and compensate for the nonlinearity of parametric loudspeakers. A theoretical framework for ODVF model identification is established and a method of measuring the ODVF kernels using the exponential swept-sine signal is provided. The validity of modeling the nonlinearity of the parametric loudspeaker using the ODVF is verified theoretically and experimentally. Based on the established ODVF model, an inverse filter is designed to compensate for the 2nd harmonic distortion of the parametric loudspeakers. To further reduce the 3rd harmonic distortion, an improved compensation method is also proposed. Experimental results show that the performance of the ODVF-based compensation is comparable to that of the Volterra-filter based compensation.

Generic model identification framework for thermodynamic engines for use in hybrid power stations control and simulation

Thermodynamic engines are focusing increasing attention in the context of solar-based electric power generation. Knowledge-based models of such engines are sometimes difficult to derive and when they are available, their simulation may be numerically a rather heavy task given the control updating period that may be needed. In the present work a generic nonlinear identification framework that enables the dynamics of the key quantities of a thermodynamic engine to be captured is proposed. Such a fast model can then be used in the simulation and the control design stage of the whole electric power generation station. The proposed identification framework is validated on a recently developed knowledge-based model of a beta-type Stirling engine with rhomic-drive mechanism.

State-dependent control of a hydraulically actuated nuclear decommissioning robot

This paper develops and evaluates state-dependent parameter (SDP) control systems for the hydraulically actuated dual-manipulators of a mobile nuclear decommissioning robot. A unified framework for calibration and SDP model identification is proposed, in which the state-dependent variable is a delayed voltage input associated with the time-varying system gain. Such nonlinearities can cause undesirable joint movements under automatic control. Hence, the present paper develops a nonlinear pole assignment algorithm for the SDP model. Closed-loop experimental data shows that the SDP design more closely follows the joint angle commands than an equivalent linear algorithm, offering improved resolved motion.

Wavelet neural networks: A practical guide

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of applications. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thoroughly examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey–Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications.

A novel hybrid mechanistic-data-driven model identification framework using NSGA-II

This paper describes a novel evolutionary data-driven model (DDM) identification framework using the NSGA-II multi-objective genetic algorithm. The central concept of this paper is the employment of evolutionary computation to search for model structures among a catalog of models, while honoring the physical principles and the constitutive theories commonly used to represent the system/processes being modeled. The presented framework provides high computational efficiency through connecting a series of NSGA-II runs which share results. Furthermore, the employment of a multi-objective optimization algorithm enables a unique way of incorporating different aspects of model goodness in the model selection process, and also, at the end of the search procedure, provides a number of potential optimal model structures, making it possible for the modeler to make a choice based on the goal of the modeling. As an illustration, the framework is used for modeling wash-off and build-up of suspended solids (TSS) in highway runoff. The performance of the discovered model confirms the potential of the proposed evolutionary DDM framework for modeling environmental processes.

Wavelet Neural Networks: A Practical Guide

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, methods to train a WN, initialization algorithms, variable significance and variable selection algorithms, a model selection method and finally methods to construct confidence and prediction intervals. Our proposed framework was tested in two simulated cases and in one real dataset consisting of daily temperatures in Berlin. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications.

Integrating point glacier mass balance observations into hydrologic model identification

Abstract. The hydrology of high mountainous catchments is often predicted with conceptual precipitation-discharge models that simulate the snow accumulation and ablation behavior of a very complex environment using as only input temperature and precipitation. It is hereby often assumed that some glacier-wide annual balance estimates, in addition to observed discharge, are sufficient to reliably calibrate such a model. Based on observed data from Rhonegletscher (Switzerland), we show in this paper that information on the seasonal mass balance is a pre-requisite for model calibration. And we present a simple, but promising methodology to include point mass balance observations into a systematic calibration process. The application of this methodology to the Rhonegletscher catchment illustrates that even small samples of point observations do contain extractable information for model calibration. The reproduction of these observed seasonal mass balance data requires, however, a model structure modification, in particular seasonal lapse rates and a separate snow accumulation and rainfall correction factor. This paper shows that a simple conceptual model can be a valuable tool to project the behavior of a glacier catchment but only if there is enough seasonal information to constrain the parameters that directly affect the water mass balance. The presented multi-signal model identification framework and the simple method to calibrate a semi-lumped model on point observations has potential for application in other modeling contexts.