System Identification Framework Research Articles

A data‐driven identification method for impedance stability analysis of inverter‐based resources

AbstractObtaining inverter controller information may be a premise for seeking its dynamic behaviour. But accurate knowledge of such information would be unrealistic for real functioning inverter‐interfaced generators (IIGs), which hinders the stability analysis of the IIG. A new data‐driven impedance identification method is proposed for stability analysis, which involves an improved sparse identification algorithm as an ancillary function within the system identification framework. It contains mainly two design stages. First, the transform basis matrix (TBM) is devised systematically as a prior knowledge library to contain the possibly existing control structures. In the second stage, a sparse identification algorithm is reformulated in order to extract the relevant structures in TBM while obtaining controller parameters. The authors demonstrate that the sparse vector between the TBM and output signal is closely related to the controller structure. The effectiveness of the proposed method is verified on grid‐connected inverters based on droop control and virtual synchronous machine control.

A bias-compensated NLMS algorithm based on arctangent framework for system identification

A bias-compensated NLMS algorithm based on arctangent framework for system identification

System Identification Framework for Modeling of Static Creep and Dynamic Creep Behavior of Dense-Graded Asphalt Mixtures

The response of two dense-graded asphalt concrete (AC) mixtures under static and dynamic creep tests conducted in compression is modeled using the principles of the system identification framework in this study. The AC materials under static and dynamic creep loading conditions exhibit complex behavior patterns such as history dependency, plasticity, and temperature dependency. It is desired to formulate a constitutive model describing these complex phenomena. The empirical approach is outside the scope of this study. A viscoelastic continuum damage model requires individual experimentation to characterize linear and damage behavior. A viscoplastic model requires incremental deviator stress for plastic deformation. Both static and dynamic creep tests do not satisfy this condition. Therefore, the “system identification” approach is used in this study. Two methods of system identification approach—that is, black box and grey box modeling—are adopted to characterize static and dynamic creep behavior of AC. Of these two models under consideration, the black box models were versatile in modeling complex loading situations with a high degree of accuracy but lacked physical interpretation. While the grey box models have a physical interpretation, they are not as versatile as black box models.

A Markov chain Monte Carlo-based Bayesian framework for system identification and uncertainty estimation of full-scale structures

Identifying modal parameters and updating finite element models (FEMs) of real structures through ambient tests is essential in Structural Health Monitoring (SHM). However, efficiently solving the high-dimensional identification problem for full-scale structures and rigorously quantifying the uncertainties remain challenging. To address these two difficulties, a novel Bayesian framework based on Markov chain Monte Carlo (MCMC) is developed. The basic idea is to identify the high-dimensional posterior probability density functions (PDFs) in both modal analysis and model updating through constructing Markov chains by sampling in the important region of the parameter spaces. The sampling is done by Bayes-Mode-ID and the adaptive sequential Monte Carlo (ASMC) for modal analysis and model updating, respectively. A new formulation is developed to link the results from modal analysis, model updating and model class selection using the Markov chain samples. Thus, the propagation of the posterior uncertainties from the identified modal parameters to the updated model parameters can be quantified. Furthermore, the original ASMC method, which was developed by the authors, is extended for model class selection based on the set of generated Markov chain samples. To demonstrate the effectiveness of the proposed framework, multi-setup ambient vibration tests on a busy footbridge were conducted for measuring the accelerations at some pre-selected measurement points. The most probable modal and model parameters of the footbridge were identified together with the associated uncertainties by the proposed framework.

A filter proportionate LMS algorithm based on the arctangent framework for sparse system identification

A filter proportionate LMS algorithm based on the arctangent framework for sparse system identification

Do-mpc: Towards FAIR nonlinear and robust model predictive control

Over the last decades, model predictive control (MPC) has shown outstanding performance for control tasks from various domains. This performance has further improved in recent years with advanced MPC schemes for nonlinear systems under uncertainty including economic control objectives. These recent improvements often fail to bridge the gap between MPC researchers and control practitioners in academia and industry, where classical control approaches and traditional linear MPC still dominate most applications. This is despite the fact that advanced MPC controllers can lead to significant energy savings, yield improvements, safer operation and other benefits.In this work, we identify four main obstacles hindering the widespread adoption of advanced MPC methods. These are the unavailability of models, the challenges associated with deploying complex controllers on physical systems, the scarcity of rapid prototyping tools for advanced methods and the limited reproducibility and reusability of advanced MPC controllers and their results. We find that the FAIR principles (findable, accessible, interoperable, reusable) for scientific data-management and research software can play an important role in tackling these obstacles. Following these guidelines, we discuss FAIR solutions and present the open-source software do-mpc as a concrete implementation. The presented solutions include interoperability with neural network toolboxes to simplify nonlinear system identification, interoperability with the OPC UA communication protocol for deployment, and a reproducible data-sampling framework for transparent controller validation, system identification and approximate MPC. The potential of the proposed solutions is illustrated with several simulation studies.

A numerically efficient output-only system-identification framework for stochastically forced self-sustained oscillators

Self-sustained oscillations are ubiquitous in nature and engineering. In this paper, we propose a novel output-only system-identification framework for identifying the system parameters of a self-sustained oscillator affected by Gaussian white noise. A Langevin model that characterizes the self-sustained oscillator is postulated, and the corresponding Fokker–Planck equation is derived from stochastic averaging. From the drift and diffusion terms of the Fokker–Planck equation, unknown parameters of the system are identified. We develop a numerically efficient algorithm for enhancing the accuracy of parameter identification. In particular, a modified Levenberg–Marquardt optimization algorithm tailored to output-only system identification is introduced. The proposed framework is demonstrated on both numerical and experimental oscillators with varying system parameters that develop into self-sustained oscillations. The results show that the computational cost required for performing the system identification is dramatically reduced by using the proposed framework. Also, system parameters that were difficult to be extracted with the existing method could be efficiently computed with the system identification method developed in this study. Pertaining to the robustness and computational efficiency of the presented framework, this study can contribute to an accurate and fast diagnosis of dynamical systems under stochastic forcing.

System identification for high‐performance UAV control in wind

SummaryThis article describes and experimentally evaluates a comprehensive system identification framework for high‐performance UAV control in wind. The framework incorporates both linear offline and nonlinear online methods to estimate model parameters in support of a nonlinear model‐based control implementation. Inertial parameters of the UAV are estimated using a frequency‐domain linear system identification program by incorporating control data obtained from motor‐speed sensing along with state estimates from an automated frequency sweep maneuver. The drag‐force coefficients and external wind are estimated recursively in flight with a square‐root unscented Kalman filter. A custom flight controller is developed to handle the computational demand of the online estimation and control. Flight experiments illustrate the nonlinear controller's tracking performance and enhanced gust rejection capability.

Preserving transfer-behavior in Model Order Reduction for thermoacoustic stability analysis

Thermoacoustic systems are often modeled with a hybrid approach that combines separate models for acoustic propagation and flame dynamics. Model Order Reduction (MOR) may be applied to the acoustic subdomains to reduce the computational cost of parametric studies and robust stability analysis. In the present study, a frequency-weighted pseudo-optimal rational Krylov algorithm is used in combination with frequency-domain System Identification and cumulative reduction framework to perform MOR by preserving the transfer-behavior of the full-order subdomain. The reduced-order subdomain is then coupled with other acoustic subdomains and a flame model to yield a reduced-order thermoacoustic system. Results show that the thermoacoustic modes of the full-order system can be reproduced by the reduced-order model with good accuracy.

Automated slip system identification and strain analysis framework using high-resolution digital image correlation data: Application to a bimodal Ti-6Al-4V alloy

Statistical analysis of slip system identification and quantitative study on local plasticity is crucial to understand the collective deformation by the sub-grain-scale slip activities in polycrystalline metallic materials. In this study, an automated framework for identifying slip system and assessing strain localization of slip bands termed ASSISL (automated Slip System Identification and Strain Localization analysis of slip bands) is introduced, using the results from high resolution digital image correlation (HR-DIC), and is demonstrated on 1591 primary α grains of a bimodal Ti-6Al-4V alloy under tensile loading. The framework includes: (1) alignment of electron backscattered diffraction (EBSD) maps with strain field maps from HR-DIC through treatment of EBSD distortion, (2) slip band orientations identification from strain field map of each grain through a Radon-transform-based algorithm, (3) slip system assignment with combined Schmid factor and critical resolved shear stress analysis, (4) quantification of plasticity by slip activities which provides information on the numbers, positions and mean strain of slip bands in each grain. The confidence of ASSISL is validated through comparing current statistical results with existing literature, as well as examining reasons for grains assigned with wrong slip systems, which accounts for 9.6 percent (153 out of 1591) of the primary α grains. A comparison between ASSISL and other HR-DIC-based slip identification methods is also conducted. This framework provides a method for analyzing slip activities in a large number of grains of polycrystalline metals in a time-saving and automated fashion.

Adaptive event-triggered mechanism-based online system identification framework for marine craft

Online dynamic model identification is a promising technology for designing the model-based controller of marine crafts. This study confronts the online model identification and maneuvering prediction for marine crafts with an adaptive event-triggered mechanism. In particular, the least square-twin support vector machines algorithm is exploited to identify the dynamic model accurately. Meanwhile, an online adaptive event-triggered identification and prediction framework is proposed to deal with the issue of when to update the dynamic model. Finally, a comparative analysis of the identification and prediction performance between the proposed framework and the non-updated model method is performed. The former superiority is highlighted by experiments based on a marine craft, which shows that it reduces the root mean square error of the yaw rate by up to 45.9%. Thereby, the proposed online identification framework offers great potential for future practical applications of marine crafts.

Data-Driven Link Prediction Over Graphical Models

The positive link prediction problem is formulated in a system identification framework: We consider dynamic graphical models for autoregressive moving-average (ARMA) Gaussian random processes. For the identification of the parameters, we model our network on two different time scales: A quicker one, over which we assume that the process representing the dynamics of the agents can be considered to be stationary, and a slower one in which the model parameters may vary. The latter accounts for the possible appearance of new edges. The identification problem is cast into an optimization framework which can be seen as a generalization of the existing methods for the identification of ARMA graphical models. We prove the existence and uniqueness of the solution of such an optimization problem and we propose a procedure to compute numerically this solution. Simulations testing the performances of our method are provided.

Predicting Nonlinear Modal Properties by Measuring Free Vibration Responses

AbstractIdentifying dynamical system models from measurements is a central challenge in the structural dynamics community. Nonlinear system identification, in particular, is a big challenge as there are many possible combinations of model structures, which requires expert knowledge to construct an appropriate model. Furthermore, traditional nonlinear system identification methods require a steady excitation input that is not always available in many practical applications. Recently, a technique referred to as the sparse identification of nonlinear dynamics (SINDy) algorithm was developed to discover mathematical models of general nonlinear systems. The SINDy method finds a generalized linear state-space model for an autonomous nonlinear system by analyzing the collected response data. In this work, the SINDy method is adapted and combined with the shooting method and the numerical continuation technique to form a system identification framework that can predict the nonlinear modal properties of mechanical oscillators. The proposed framework predicts the nonlinear normal modes (NNMs) of these systems by processing the noised data of the systems' free vibration response. In addition, the NNMs and the internal resonance of nonlinear systems at a high energy level can be captured using the proposed framework by processing the response data at a lower energy level. The proposed method is numerically demonstrated on a 2-degree-of-freedom mechanical oscillator. Furthermore, the effects of the measurement error and the excitation condition on NNM prediction are investigated. The NNM prediction framework presented in this paper is fairly general and is applicable to a variety of nonlinear systems.

Novel Physics-Informed Artificial Neural Network Architectures for System and Input Identification of Structural Dynamics PDEs

Herein, two novel Physics Informed Neural Network (PINN) architectures are proposed for output-only system identification and input estimation of dynamic systems. Using merely sparse output-only measurements, the proposed PINNs architectures furnish a novel approach to input, state, and parameter estimation of linear and nonlinear systems with multiple degrees of freedom. These architectures are comprised of parallel and sequential PINNs that act upon a set of ordinary differential equations (ODEs) obtained from spatial discretization of the partial differential equation (PDE). The performance of this framework for dynamic system identification and input estimation was ascertained by extensive numerical experiments on linear and nonlinear systems. The advantage of the proposed approach, when compared with system identification, lies in its computational efficiency. When compared with traditional Artificial Neural Networks (ANNs), this approach requires substantially smaller training data and does not suffer from generalizability issues. In this regard, the states, inputs, and parameters of dynamic state-space equations of motion were estimated using simulated experiments with “noisy” data. The proposed framework for PINN showed excellent great generalizability for various types of applications. Furthermore, it was found that the proposed architectures significantly outperformed ANNs in generalizability and estimation accuracy.

A data-driven approach for analyzing Hall thruster discharge instability leading to plasma blowoff

The Hall-effect thruster is a prominent space propulsion system, providing a high specific impulse and thrust-to-power ratio. However, detrimental phenomena occurring in Hall thrusters, such as plasma instability and blowoff, are less understood. In this study, we employ a data-driven approach for analyzing the blowoff phenomenon of the Hall-effect propulsion system. From a 600-W class Hall thruster, we observe the oscillatory behavior of the anode current with a frequency of 34–38 kHz, which sometimes leads to plasma blowoff. We employ an output-only system identification framework that uses the noise-induced dynamics at this frequency, extracting linear and nonlinear coefficients of the low-order system model. The computed coefficients suggest that the plasma blowoff is characterized by large linear and small nonlinear parameters of the stochastic Van der Pol equation. From the obtained results, we conclude that this framework can be exploited either to identify a reliable operating condition with a low possibility of plasma blowoff or to diagnose the blowoff susceptibility of the thruster. This research constitutes the first application of stochastic system identification to the Hall-effect thruster, opening new possibilities for avoiding unwanted oscillations and blowoff phenomena in electric propulsion systems.

Nonlinear UGV Identification Methods via the Gaussian Process Regression Model for Control System Design

In this paper, two identification methods are proposed for a ground robotic system. A Gaussian process regression (GPR) model is presented and adopted for a system identification framework. Its performance and features were compared with a wavelet-based nonlinear autoregressive exogenous (NARX) model. Both algorithms were compared and experimentally validated for a small ground robot. Moreover, data were collected throughout the onboard sensors. The results show better prediction performance in the case of the GPR method, as an estimation algorithm and in providing a measure of uncertainty.

Automated identification of slip system activity fields from digital image correlation data

Crystallographic slip system identification methods are widely employed to characterize the fine scale deformation of metals. While powerful, they usually rely on the occurrence of discrete slip bands with clear slip traces and can struggle when complex mechanisms such as cross-slip, curved slip, diffuse slip and/or intersecting slip occur. This paper proposes a novel slip system identification framework, termed SSLIP (for Slip Systems based Local Identification of Plasticity), in which the measured displacement gradient fields (from Digital Image Correlation) are locally matched to the kinematics of one or multiple combined theoretical slip systems, based on the measured crystal orientations. To identify the amount of slip that conforms to the measured kinematics, an optimization problem is solved for every datapoint individually, resulting in a slip activity field for every considered slip system. The identification framework is demonstrated and validated on an HCP virtual experiment, for discrete and diffuse slip, incorporating 24 slip systems. Experimental case studies on FCC and BCC metals show how full-field identification of discrete slip, diffuse slip and cross-slip becomes feasible, even when considering 48 slip systems for BCC. Moreover, the methodology is extended into a dedicated cross-slip identification method, which directly yields the orientation of the local slip plane trace orientation, purely based on the measured kinematics and on one or two chosen slip directions. For even more challenging cases revealing a persistent uncertainty in the slip identification, a two-step identification approach can be employed, as is demonstrated on a highly challenging HCP virtual experiment.

Physics-informed recurrent neural networks for linear and nonlinear flame dynamics

This paper demonstrates the ability of recurrent neural networks (RNNs) to predict the linear and the nonlinear response of a premixed laminar flame to incoming velocity perturbations. We develop data-driven models, which require the velocity and heat release rate fluctuations as input data. Both time series are obtained from Direct Numerical Simulations (DNS) of a laminar flame. The length of the signals, and, hence, the cost of the simulation, is comparable to those used in the linear framework of System Identification. A more robust type of RNNs, namely long short term memory (LSTM), is employed to reduce the dependency on large datasets. The LSTM framework is modeled as a time series regression problem and four models are trained with decreasing data set lengths. All purely data-driven models accurately predict the unsteady time series of the heat release rate and, hence, the Flame Transfer Functions (FTFs). We further improve the model accuracy by incorporating a physical constraint, namely the low-frequency limit for perfectly-premixed flames, into the LSTM model. This step reduces the required data length compared to the purely data-driven approach. The proposed model, called PI-LSTM, is able to reproduce the linear and the nonlinear FTFs for amplitudes up to 50% of the laminar flame based on one numerical simulation, where the length of the time series is 100 ms.

A hybrid time-frequency method for robust drive-by modal identification of bridges

Indirect bridge health monitoring (iBHM) has gained significant attention in recent years as an alternative to direct bridge monitoring techniques. iBHM leverages the use of a vehicle traveling over a bridge as a sensing device as well as an actuator. The resulting data acquired from the vehicle contains dynamic information about the bridge, vehicle suspension, engine noise, ambient traffic noise, road roughness, etc. Due to the presence of sensor-vehicle-bridge interactions in vehicle measurement, a powerful decoupling framework of system identification is required to extract useful information about the bridge and delineate the effect of vehicle and driving frequencies. This paper proposes a hybrid time-frequency method capable of decoupling vehicle-bridge interactions of vehicle measurement and performing a robust bridge modal identification under various operational challenges. In the proposed research, wavelet packet transformation (WPT) is first used to decompose the vehicle measurement into various WPT coefficients. Then, the modal frequencies of the bridge are extracted from the resulting WPT coefficients using Synchro-Extracting Transform (SET) and are separated from the vehicle and driving frequencies. The proposed method is validated using numerical and laboratory studies as well as a full-scale study comprising of a 220 m long box-girder bridge. The results provide strong evidence that the proposed hybrid time-frequency method can serve as a promising iBHM method.

Nonlinear system identification framework of folding fins with freeplay using backbone curves

Due to wear and manufacturing tolerance, the freeplay is unavoidable in the hinges of folding fins, which exerts significant effects on the aerodynamic characteristics. This paper proposes a backbone-curve-based framework for the dynamical identification of folding fins containing the freeplay nonlinearity. With no need to measure the input force signal and the response signals of nonlinear related Degrees of Freedom (DOFs), the proposed method is more direct and elegant than most existing nonlinear identification approaches, and it contains three steps: Firstly, the underlying linear model of the folding fin structure is obtained through the modal test on its linear sub-parts, and then, the harmonic approximation solves the analytical expressions of the backbone curves of measurable DOFs. Secondly, response data measured from the sine-sweep test are used to extract the fitting points of backbone curves for these DOFs. Finally, the curve fitting approach is applied to identify the freeplay parameters. A series of numerical experiments verify the effectiveness of the proposed method. A real-life folding fin structure is also employed to illustrate how the method can be applied. These examples demonstrate that the identification framework can give an accurate dynamic model of the folding fin structure.