System Identification Procedure Research Articles

Design and verification of a parallel elastic robotic leg

This paper presents the design and experimental verification of a parallel elastic robotic leg mechanism that aims to capture the dynamics of the linear mass-spring-damper model. The mechanism utilizes a wrapping cam mechanism to linearize the non-linear force resulting from the elongation of the parallel elastic element. Firstly, we explain the desired dynamics of the mass-spring-damper model, including the impact transitions, and the design of the wrapping cam mechanism. We then introduce a system identification procedure to estimate the parameters of the leg mechanism corresponding to the dynamic model. The estimated parameters are tested with a cross-validation approach to evaluate the mechanism’s performance in tracking the desired model. The experimental results show that the passive dynamics of the mechanism resemble the linear model as intended. Thus, the robot provides a basis for using parallel elastic actuation while using model-based controllers that benefit the analytic solutions of the linear model.

Experimental Investigation of a Hybrid Device Combining a Wave Energy Converter and a Floating Breakwater in a Wave Flume Equipped with a Controllable Actuator

This paper presents a hydrodynamic investigation carried out on the “Wave Attenuator” device, which is a new type of floating breakwater anchored with piles and equipped with a linear Power Take Off (PTO) mechanism, which is typical for wave energy converters. The device is tested in the wave flume, under regular waves, in slightly non-linear conditions. The PTO mechanism, that restrains one of the two degrees of freedom, is simulated through an actuator and a programmable logic controller with preassigned strategy. The paper presents the system identification procedure followed in the laboratory, supported by a numerical investigation essential to set up a credible control strategy aiming at maximizing the wave energy harvesting. The maximum power conversion efficiency under the optimal PTO control strategy is found: it is of order 50–70% when the incident wave frequency is lower than the resonance one, and only of order 20% for higher frequencies. This type of experimental investigation is essential to evaluate the actual efficiency limitations imposed by device geometry.

Nonlinear-Control-Oriented Modeling of the Multi-Variable Underground Coal Gasification Process for UCG Project Thar: A Machine Learning Perspective

The Underground Coal Gasification (UCG) process is a complex and multi-physics phenomenon, thus making it difficult to develop a mathematical model that encapsulates all dynamical aspects. In this regard, data-driven modeling techniques offer a reliable alternative for prediction, control, and optimization of dynamical systems, but their application in UCG is still in the early stages. This work aims to bridge this gap by implementing three cutting-edge nonlinear identification structures: Non-linear Autoregressive with Exogenous Inputs (NARX), Hammerstein–Wiener (HW), and State-Space Neural Networks (SSNN) on the UCG process to obtain a multivariable control-oriented model. The contributions include synthesizing an excitation signal for data acquisition, outlining the non-linear system identification procedure, and comparing predictive capabilities using statistical tools. The simulation results demonstrate a rigorous comparison of various techniques for the heating value and flowrate of the syngas, which are the outputs of the UCG process. The results of the analysis show that NARX outperforms other structures in statistical metrics, with MAE, RMSE, and Best fit values of 1.51,1.9, and 0.9, respectively, for the heating value; and 0.25,0.31, and 0.94, respectively, for the flowrate. Consequently, the outputs of the NARX model are compared with the experimental data obtained from the UCG project Thar, which show a good match for both outputs.

Modeling of Magnetoelectric Microresonator Using Numerical Method and Simulated Annealing Algorithm.

A comprehensive understanding of the linear/nonlinear dynamic behavior of wireless microresonators is essential for micro-electromechanical systems (MEMS) design optimization. This study investigates the dynamic behaviour of a magnetoelectric (ME) microresonator, using a finite element method (FEM) and machine learning algorithm. First, the linear/nonlinear behaviour of a fabricated thin-film ME microactuator is assessed in both the time domain and frequency spectrum. Next, a data driven system identification (DDSI) procedure and simulated annealing (SA) method are implemented to reconstruct differential equations from measured datasets. The Duffing equation is employed to replicate the dynamic behavior of the ME microactuator. The Duffing coefficients such as mass, stiffness, damping, force amplitude, and excitation frequency are considered as input parameters. Meanwhile, the microactuator displacement is taken as the output parameter, which is measured experimentally via a laser Doppler vibrometer (LDV) device. To determine the optimal range and step size for input parameters, the sensitivity analysis is conducted using Latin hypercube sampling (LHS). The peak index matching (PIM) and correlation coefficient (CC) are considered assessment criteria for the objective function. The data-driven developed models are subsequently employed to reconstruct/predict mode shapes and the vibration amplitude over the time domain. The effect of driving signal nonlinearity and total harmonic distortion (THD) is explored experimentally under resonance and sub-resonance conditions. The vibration measurements reveal that as excitation levels increase, hysteresis variations become more noticeable, which may result in a higher prediction error in the Duffing array model. The verification test indicates that the first bending mode reconstructs reasonably with a prediction accuracy of about 92 percent. This proof-of-concept study demonstrates that the simulated annealing approach is a promising tool for modeling the dynamic behavior of MEMS systems, making it a strong candidate for real-world applications.

Experimental modal analysis of a single-link flexible robotic manipulator with curved geometry using applied system identification methods

In this paper, the principal time-domain system identification methods are studied and used to carry out the experimental modal analysis of a single-link flexible manipulator with curved geometry in a comparative fashion. The identification process carried out in this study is aimed at deriving first-order state-space dynamical models and second-order configuration-space dynamical models of the single-link flexible manipulator by using an array of fundamental system identification procedures, which includes the ARX (AutoRegressive eXogenous method), SSEST (State-Space ESTimation method), N4SID (Numerical Algorithm for Subspace State-Space System Identification), ERA/OKID (Eigensystem Realization Algorithm combined with the Observer/Kalman Filter Identification method), and TFEST (Transfer Function ESTimation method) methods. The main goal of this paper is, therefore, to perform a comparative study between the most fundamental system identification procedures applied to the numerical and experimental analysis of the structural vibrations of a flexible manipulator having a curved geometric shape. First, this paper poses the theoretical foundations for the development of the numerical study and the experimental testing to be performed for the case study. Subsequently, the flexible manipulator analyzed in this work is modeled with various levels of complexity, which range from a simple lumped parameter model to a linear finite element model developed by integrating the interconnections between the SOLIDWORKS and ANSYS software. By doing so, the computational procedures applied to the time-domain experimental measurements of the dynamic behavior of the flexible manipulator allow for reconstructing first-order and second-order mechanical models of the structural system of interest in the MATLAB simulation environment. The numerical results and the experimental tests reported in this investigation demonstrate the effectiveness of all the time-domain system identification approaches considered in the paper.

Axial-piston pump optimal multivariable PID controller tunning

The aim of the present work is the synthesis and optimal tunning of a PID controller designed to control the displacement volume of an axial-piston pump intended for hydraulic systems with open circulation. The pump is controlled in real-time through a system developed by the authors based on an electro-hydraulic proportional valve (replacing the conventional hydro-mechanical controller) and an industrial controller. The experimental system was initially used to obtain a data set that is used in a system identification procedure to obtain a model. The obtained state space model was used for the synthesis of the PID controller. The optimal tunning of controller parameters is performed using three modern methods: genetic algorithm, simulated annealing and pattern search. The resulting three PID controllers with different settings depending on the used methods are compared in simulation and experimental conditions. Based on the results, an analysis of the control performance was carried out.

APPLICATION OF SPLINE FUNCTIONS AND WALSH FUNCTIONS IN PROBLEMS OF PARAMETRIC IDENTIFICATION OF LINEAR NONSTATIONARY SYSTEMS

Context. In this article, a generalized parametric identification procedure for linear nonstationary systems is proposed, which uses spline functions and orthogonal expansion in a series according to the Walsh function system, which makes it possible to find estimates of the desired parameters by minimizing the integral quadratic criterion of discrepancy based on solving a system of linear algebraic equations for a wide class of linear dynamical systems. The accuracy of parameter estimation is ensured by constructing a spline with a given accuracy and choosing the number of terms of the Walsh series expansion when solving systems of linear algebraic equations by the A. N. Tikhonov regularization method. To improve the accuracy of the assessment, an algorithm for adaptive partitioning of the observation interval is proposed. The partitioning criterion is the weighted square of the discrepancy between the state variables of the control object and the state variables of the model. The choice of the number of terms of the expansion into the Walsh series is carried out on the basis of adaptive approximation of non-stationary parameters in the observation interval, based on the specified accuracy of their estimates. The quality of the management of objects with variable parameters is largely determined by the accuracy of the evaluation of their parameters. Hence, obtaining reliable information about the actual nature of parameter changes is undoubtedly an urgent task.
 Objective. Improving the accuracy of parameter estimation of a wide class of linear dynamical systems through the joint use of spline functions and Walsh functions.
 Method. A generalized parametric identification procedure for a wide class of linear dynamical systems is proposed. The choice of the number of terms of the expansion into the Walsh series is made on the basis of the proposed algorithm for adaptive partitioning of the observation interval.
 Results. The results of modeling of specific linear non-stationary systems confirm the effectiveness of using the proposed approaches to estimating non-stationary parameters.
 Conclusions. The joint use of spline functions and Walsh functions makes it possible, based on the proposed generalized parametric identification procedure, to obtain analytically estimated parameters, which is very convenient for subsequent use in the synthesis of optimal controls of real technical objects. This procedure is applicable to a wide class of linear dynamical systems with concentrated and distributed parameters.

Full Bayesian identification of linear dynamic systems using stable kernels

System identification learns mathematical models of dynamic systems starting from input-output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examples arise in biology and industry, e.g., in the study of brain dynamics or sensor networks. In the last years, regularized kernel-based identification, with inspiration from machine learning, has emerged as an interesting alternative to the classical approach commonly adopted in the literature. In the linear setting, it uses the class of stable kernels to include fundamental features of physical dynamical systems, e.g., smooth exponential decay of impulse responses. Such class includes also unknown continuous parameters, called hyperparameters, which play a similar role as the model discrete order in controlling complexity. In this paper, we develop a linear system identification procedure by casting stable kernels in a full Bayesian framework. Our models incorporate hyperparameters uncertainty and consist of a mixture of dynamic systems over a continuum spectrum of dimensions. They are obtained by overcoming drawbacks related to classical Markov chain Monte Carlo schemes that, when applied to stable kernels, are proved to become nearly reducible (i.e., unable to reconstruct posteriors of interest in reasonable time). Numerical experiments show that full Bayes frequently outperforms the state-of-the-art results on typical benchmark problems. Two real applications related to brain dynamics (neural activity) and sensor networks are also included.

Tracking Distributed Parameters System Dynamics with Recursive Dynamic Mode Decomposition with Control

The goal of this work is to introduce a new online data driven modeling solution for tracking the dynamics of systems, the behavior of which is governed by (nonlinear) partial differential equations (PDEs). In order to reach this goal, this paper introduces a recursive algorithm for black box time varying model identification along with an online algorithm for reducing the order of the identified model. The resulting system model is a linear time varying low order state space representation usable, e.g., for controller design or prediction. The model reduction step relies on the recursive determination of the orthonormal basis of a specific data based proper orthogonal decomposition. The system identification procedure is initialized with the dynamic mode decomposition with control and updated recursively via the introduction of a specific recursive least squares algorithm. In both steps, a forgetting factor is used to focus on the most recent variations of the system. As case studies, a linear heat diffusion equation with a time varying diffusion parameter is first considered. The Burgers equation, a nonlinear hyperbolic PDE, is then utilized to assess the introduced methods applicability with nonlinear systems. Identification results based on simulation show the high accuracy of this new approach.

Intrinsic thermo-acoustic instability criteria based on frequency response of flame transfer function

The study of Intrinsic Thermo-Acoustic (ITA) instability behavior of flames anchored to a burner deck is performed by introducing a mapping between the Flame Transfer Function, FTF(s), defined in the complex (Laplace) domain and experimentally measured frequency response, FTF(iω). The conventional approach requires a system identification procedure to obtain the FTF(s) from the FTF(iω); next, root-finding techniques are applied to define the complex eigenfrequencies. The purpose of the present work is to establish instability criteria which are directly applicable in the frequency domain. The particular case is considered when the acoustic boundary conditions at both sides of the flame are anechoic. At first place, the causality of the measured FTF(iω) is checked. Then, the criteria of the ITA mode instability applicable to the FTF(iω) phase and magnitude, are derived. Cauchy's theorem and the path-independence Lemma are used to find the scaling factor of the mapping which allows to determine bounds of the unstable frequency and the maximum value of the linear growth rate. The proposed method is applied to study the behavior of burners with premixed burner-stabilized Bunsen-type flames. The comparison of the measured oscillation frequencies and the growth rates of observed unstable oscillations with that obtained from the derived bounds reveal good correspondence.

A Bayesian Method for Material Identification of Composite Plates via Dispersion Curves

Ultrasonic guided waves offer a convenient and practical approach to structural health monitoring and non-destructive evaluation. A key property of guided waves is the fully defined relationship between central frequency and propagation characteristics (phase velocity, group velocity and wavenumber)-which is described using dispersion curves. For many guided wave-based strategies, accurate dispersion curve information is invaluable, such as group velocity for localisation. From experimental observations of dispersion curves, a system identification procedure can be used to determine the governing material properties. As well as returning an estimated value, it is useful to determine the distribution of these properties based on measured data. A method of simulating samples from these distributions is to use the iterative Markov-Chain Monte Carlo (MCMC) procedure, which allows for freedom in the shape of the posterior. In this work, a scanning-laser Doppler vibrometer is used to record the propagation of Lamb waves in a unidirectional-glass-fibre composite plate, and dispersion curve data for various propagation angles are extracted. Using these measured dispersion curve data, the MCMC sampling procedure is performed to provide a Bayesian approach to determining the dispersion curve information for an arbitrary plate. The distribution of the material properties at each angle is discussed, including the inferred confidence in the predicted parameters. The percentage errors of the estimated values for the parameters were 10-15 points larger when using the most likely estimates, as opposed to calculating from the posterior distributions, highlighting the advantages of using a probabilistic approach.

A metaheuristic-based methodology for efficient system identification of the Proton Exchange Membrane Fuel Cell stacks

In this study, a new procedure for optimum and effective system identification of Proton Exchange Membrane Fuel Cell (PEMFC) stacks is introduced. The present study proposes a method to obtain the optimum amount of the uncertain parameters of the PEMFC design to deliver the uppermost confirmation with the real output voltage value. To do so, the integral of the absolute error (IAE) between the real and model outputted voltage values is considered an objective function. To minimize this function, a modified design of the emperor penguin optimizer has been suggested. The method has been then investigated by performing two real case study models and its achievements are put in comparison with several latest techniques to show the method's productivity. The achievements show that the suggested technique has a higher ability for parameter estimation of the PEMFC models.

Design of a NARX-ANN-Based SP Controller for Control of an Irrigation Main Canal Pool

The management of irrigation main canals are studied in this research. One way of improving this is designing an efficient automatic control system of the water that flows through the canal pools, which is usually carried out by PI controllers. However, since canal pools are systems with large time delays and nonlinear hydrodynamics, these PIs are tuned in a very conservative way so that the closed-loop instability that may appear depending on the chosen operation regime is avoided. These controllers are inefficient because they have slow time responses. In order to obtain faster responses that remain stable independently of the operation regime, a control system that combines a Smith predictor, which is appropriate to control linear systems with large time delays, with a NARX artificial neural network (ANN), that models the nonlinear dynamics of the pools, is proposed. By applying system identification procedures, two nonlinear NARX-ANN-based models and a linear mathematical model of a real canal pool were obtained. These models were applied to implement a modified NARX-ANN-based SP controller and a conventional linear SP controller. Experimental results on our real canal pool showed that our modified NARX-ANN-based SP controller overcomes conventional linear SP controllers in both setpoint tracking and load disturbance rejection.

Model tests of a hydroelastic truncated floating bridge

Literature on tank tests of floating bridges is extremely rare, while a very limited number of publications covering tests of other types of very large floating structures exist. Here, the authors share their experience in designing and carrying out a model test campaign aimed at providing empirical data to aid the process of validating and calibrating a numerically based design of a generic floating bridge. The tested model represents a truncated segment of a full straight bridge at a fjord crossing supported by floating pontoons with 4 mooring clusters providing additional lateral stiffness. The tested environmental conditions comprise combinations of regular and irregular waves, current and wind, including a spectral amplitude inhomogeneous condition realization. The setup of the objectives, strategy adopted for the truncation, experimental setup and relevant system identification and control procedures carried out, are explained thoroughly. Noteworthy is a novel approach for carrying out static pull-outs and decays using a set of actuator winches, also used for applying prescribed wind forces on the model, allowing for inhomogeneous dynamic prescribed forces to be accurately applied.A dataset of time series and selected video recordings is publicly shared for selected measurements and test runs. It is expected that this paper and the accompanying dataset become a valuable resource for researchers and engineers addressing model testing or experimental validation of numerical models of floating bridges within the functional design process of these structures. Specifically, the dataset should provide important empirical data for benchmarking numerical predictions of hydrodynamic interaction, and hydroelasticity models in general. Recommendations for testing of floating bridges in a basin are also given, based on the experience gathered in the project.

Uncertainty Analysis and Experimental Validation of Identifying the Governing Equation of an Oscillator Using Sparse Regression

In recent years, the rapid growth of computing technology has enabled identifying mathematical models for vibration systems using measurement data instead of domain knowledge. Within this category, the method Sparse Identification of Nonlinear Dynamical Systems (SINDy) shows potential for interpretable identification. Therefore, in this work, a procedure of system identification based on the SINDy framework is developed and validated on a single-mass oscillator. To estimate the parameters in the SINDy model, two sparse regression methods are discussed. Compared with the Least Squares method with Sequential Threshold (LSST), which is the original estimation method from SINDy, the Least Squares method Post-LASSO (LSPL) shows better performance in numerical Monte Carlo Simulations (MCSs) of a single-mass oscillator in terms of sparseness, convergence, identified eigenfrequency, and coefficient of determination. Furthermore, the developed method SINDy-LSPL was successfully implemented with real measurement data of a single-mass oscillator with known theoretical parameters. The identified parameters using a sweep signal as excitation are more consistent and accurate than those identified using impulse excitation. In both cases, there exists a dependency of the identified parameter on the excitation amplitude that should be investigated in further research.

Ultrasonic Bubble Imaging in Molten Salt Using a Multi-Mode Waveguide and Time Reversal

Direct ultrasound imaging of technical processes in harsh environments, such as high-temperature melts, is not possible beyond the destruction limits of ultrasound transducers. A waveguide between the measured medium and the sensitive ultrasound transducer allows acoustic access to the former while protecting the latter. State-of-the-art single-mode waveguides allow for acoustical coupling between a transducer and the measured medium but are unsuited for real-time imaging since mechanical scanning is necessary. In contrast, multimode waveguides can transmit complex 2-D signals to an imaged region. While multimode waveguides require adaptive wavefront correction to compensate for the complex propagation inside, they allow the reduction of mechanical complexity with the application of the time-reversal virtual array (TRVA) method. This calibration method takes advantage of the time invariance of sound propagation in linear media to identify and compensate for the propagation inside the waveguide. This work proposes a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> calibration procedure for system identification based on a traversing passive point scatterer. We characterize the imaging capacity of such a TRVA inside a molten nitrate salt at about 300 °C, exceeding the array’s operating temperature by 250 °C. By real-time imaging rising gas bubbles in the melt for the first time, we demonstrate the method’s potential for monitoring dynamic processes, such as metallurgical bubble column reactors with hot and opaque melts.

Gradient Methods for Fixed Structure Controller Synthesis and System Identification of Decomposable Systems

In this letter we are considering the problem of fixed structure controller synthesis and system identification for large scale systems. The systems considered are referred to as decomposable systems and can be seen as resulting from the interconnection of a large number of identical subsystems. Combining recent results from nonsmooth controller synthesis with the special structure of decomposable systems, we show that the computational complexity of the controller synthesis and system identification procedure scale linearly with the size of the system. Employing results from robust control, the computational complexity of the controller synthesis can be reduced further, however, at the cost of additional conservatism. Using numerical examples we demonstrate that the proposed method can reduce the conservatism compared to existing LMI methods for full order decomposable controllers.

Model Identification and Model Predictive Control of Biopharmaceutical and Biomedical Systems

This paper demonstrates the use of model predictive control (MPC) formulations for uncertain time-varying biopharmaceutical and biomedical systems implemented using measured data without prior knowledge of an accurate model. Furthermore, we demonstrate how prior knowledge can be incorporated in the identification of the model either through constraints or as regularization of the system identification procedure. We demonstrate the use of system identification to develop a model of the fed-batch Chinese hamster ovary mammalian cell bioreactor process and the implementation of model-based control to maximize therapeutic product yields. We also use a time-varying nonlinear biomedical system to demonstrate improvements due to incorporating prior information in the learning of the models and reidentification of the models when prediction accuracy deteriorates. We propose a new partial least squares algorithm that incorporates regularization from prior knowledge and can handle missing data in the independent covariates. Simulation case studies involving a biopharmaceutical production process and automated drug delivery demonstrate the capabilities of the proposed techniques.

Design and testing of a free floating dual flap wave energy converter

With a wide variety of wave energy device archetypes currently under consideration, it is a major challenge to ensure that research findings and methods are broadly applicable. In particular, the design and testing of wave energy control systems, a process which includes experimental design, empirical modeling, control design, and performance evaluation, is of interest. This goal motivated the redesign and testing of a floating dual flap wave energy converter. As summarized in this paper, the steps taken in the design, testing, and analysis of the device mirrored those previously demonstrated on a three-degree of freedom point absorber device. The method proposed does not require locking WEC degrees of freedom to develop an excitation model, and presents a more attainable system identification procedure for at-sea deployments. The results show that the methods employed work well for this dual flap device, lending additional support for the broad applicability of the design and testing methods applied here. The aim of this paper is to demonstrate that these models are particularly useful for deducing areas of device design or controller implementation that can be reasonably improved to increase device power capture.

Structural damage identification through sensitivity-based finite element model updating and wavelet packet transform component energy

Civil infrastructures deteriorate due to aging, adverse environmental conditions, and inadequate maintenance. Thus, to ensure both safety and serviceability of the structures as well as to mitigate economic losses, it is essential to employ a comprehensive structural health monitoring (SHM) system and appropriate damage identification procedure. Finite element (FE) model updating is one of the most common approaches of damage detection in civil engineering. The most widely used techniques for FE model updating have been developed based on data in the time, time–frequency, and modal domains. In this study, a novel damage identification technique is proposed based on wavelet packet transform component energy (WPTCE). The discrepancy between WPTCE of intact and damaged states of the structure was considered as a residual in the sensitivity-based FE model updating procedure. Two numerical examples, namely a two-dimensional truss bridge and a double layer diamatic dome was used to illustrate the efficiency and applicability of the proposed method in structural damage identification. Sensitivity analysis showed that the WPTCE is a highly sensitive response to structural damages. Further, the results revealed that the proposed method leads to accurate detection of damage, though the measured signals are contaminated by noise.