State-space Identification Research Articles

Transonic Aerodynamic–Structural Coupling Characteristics Predicted by Nonlinear Data-Driven Modeling Approach

Accurate prediction of nonlinear aerodynamics is essential for the transonic aeroelastic analysis of flight vehicles. Though reduced-order aerodynamic models are cheap and reasonable tools, it is still a tough problem to accurately evaluate the unsteady pressure distributions on the surface of an elastic structure. This paper presents a nonlinear data-driven modeling approach based on the high-fidelity simulations in the following three steps. The first step is to compute the dominant modes of unsteady pressure distributions through the proper orthogonal decomposition. The pressure snapshots used for the feature extraction are sampled under a multilevel sine-sweep excitation. The second step is to obtain the low-dimensional temporal dynamics of the coefficients of these modes via polynomial nonlinear state-space identification. The linear estimation implemented by employing the dynamic mode decomposition with control algorithm serves as the initialization of the nonlinear optimization. The third step is to reconstruct the unsteady pressure distributions under arbitrary structural excitation from the temporal coefficients. The paper validates the approach via two numerical examples of the transonic aerodynamic–structural coupling problem. One is an NACA0012 airfoil, and the other is an AGARD 445.6 wing. The examples show that the proposed approach exhibits both accurate and robust performance in the prediction of unsteady pressure distributions, aerodynamic forces, and aeroelastic responses. In particular, the approach well predicts the physical features at the fluid–structure coupling interface, previously neglected in the system identification of aerodynamic systems. Therefore, the approach serves as a promising tool for data-driven aeroelastic analysis.

Comparison of Subspace Identification Methods for Modal Estimation of Bladed Disks

Abstract Bladed disks are critical parts of aeronautic turbojet engines requiring numerous dynamic analysis tests to fully achieve their design process. This work presents subspace state-space identification techniques for estimation of modal parameters of bladed disks using realistic although numerically generated test case data. Indeed, modal testing of bladed disks can exhibit high modal density leading to modal estimation issues. This study focuses on subspace state-space identification framework as it is an efficient way to process vector valued time series and thus to estimate modal parameters in a context of high modal density. In order to evaluate the techniques of interest, a versatile modal model has been specifically implemented to simulate data representative of full scale rotating aeronautic fan modal tests. This model is easily adjustable allowing to evaluate the identification methods in a more or less severe estimation context. The performance of the investigated methods is discussed and compared with the prescribed parameters of the model. Moreover, different techniques to estimate the order of the associated state-space model are reviewed and tested over several simulated configurations. Finally, a method to evaluate the uncertainties over the model parameters using covariance of estimator results and pseudospectrum computation is proposed and discussed over the investigated test cases.

Reliability Measurement of Control and Instrumentation Systems of Nuclear Power Plants

Control and instrumentation (C&I) systems are used to measure the critical parameters to take decisions and, hence, such systems do have high reliability target. Therefore, it is essential to measure the reliability of such systems with high accuracy. Petri net (PN) is a mathematical tool that can model the stochastic behavior of the systems. The research work is devoted to propose a framework to measure the reliability of these systems using PN. The proposed framework contains three phases: 1) state-space identification, 2) probability of a system being in each state, and 3) reliability measurement. The proposed approach has been applied to 21 C&I systems of nuclear power plant (NPP) and is demonstrated on a case study of NPP to prove its effectiveness.

Initialization Approach for Nonlinear State-Space Identification via the Subspace Encoder Approach

The SUBNET neural network architecture has been developed to identify nonlinear state-space models from input-output data. To achieve this, it combines the rolled-out nonlinear state-space equations and a state encoder function, both parameterised as neural networks The encoder function is introduced to reconstruct the current state from past input-output data. Hence, it enables the forward simulation of the rolled-out state-space model. While this approach has shown to provide high-accuracy and consistent model estimation, its convergence can be significantly improved by efficient initialization of the training process. This paper focuses on such an initialisation of the subspace encoder approach using the Best Linear Approximation (BLA). Using the BLA provided state-space matrices and its associated reconstructability map, both the state-transition part of the network and the encoder are initialized. The performance of the improved initialisation scheme is evaluated on a Wiener-Hammerstein simulation example and a benchmark dataset. The results show that for a weakly nonlinear system, the proposed initialisation based on the linear reconstructability map results in a faster convergence and a better model quality.

Design and experiment of a double-wing wave energy converter

Considering the prospect to use marine energy to power ocean platforms, a double-wing wave energy converter suitable for power supply for them is proposed. Based on the mechanical structure and hydrodynamic parameters of the system, the frequency-domain dynamic model is established. According to the Cummins equation and the state space identification of the convolution term of the radiation force, the time-domain simulation of the system excited by wave is built. In addition, a 1:10 scaled prototype is manufactured and a tank experiment is carried out to study its performance. The accuracy of the simulation model is verified with the comparison between experimental and simulation results. The experimental results show that the power output of the prototype reaches 0.74 W under the regular wave with a period of 2.0 s and a wave height of 16 cm. Finally, adopting the similarity theory, the power output of the full-size system is calculated to be 2340.09 W. This study provides new ideas for solving the energy supply problem of ocean platforms.

Enhanced nonlinear state–space identification for efficient transonic aeroelastic predictions

Transonic aerodynamic systems exhibit strong nonlinearities due to various factors such as flow separations and shock wave oscillations. Thus, transonic aerodynamic modeling methods based on system identifications have attracted increasing attention. However, the dimensions of the models constructed via the current system identification methods are so high that it is difficult to predict transonic flutters and limit cycle oscillations simultaneously. This paper proposes an enhanced nonlinear state–space modeling method to identify a two-dimensional aerodynamic system in the transonic region. At first, the parsimonious linear model with modified inputs is identified by using the eigensystem realization algorithm. The model order is reduced by substituting the generalized displacement of the first-order mode (dominated by plunge) with its generalized velocity in the inputs. The polynomial functions are then used to represent the nonlinearities in the transonic aerodynamic systems. The polynomial functions do not contribute to the system linearization around the equilibrium such that the linear and nonlinear modeling stages are independent. The coefficients of these nonlinear terms are determined via nonlinear optimization. Finally, a nonlinear aerodynamic model is established and applied to aeroelastic applications. To demonstrate the accuracy and efficiency of this method, a two-dimensional, transonic aeroelastic wing with an NACA0012 profile is investigated. The simulation results show that the nonlinear state–space model with modified inputs improves the efficiency and accuracy of transonic aerodynamic nonlinear modeling. Moreover, the aerodynamic model coupled with the structural model can accurately predict the transonic flutter boundary and limit cycle oscillations.

An iterative state-space identification method with data correlation for MIMO systems with measurement noise

This work presents an iterative concept of the State-space Realization Algorithm with Data Correlation (SSRA-DC) to identify MIMO systems with measurement noise and subjected to a reduced number of samples acquired from the process. The measurement noise is characterized as a random signal with properties of white noise and having up to 1% of the output signal amplitude. The proposed technique is based on the Markov parameters matrix’s feedback in an iterative algorithm supported by the SSRA-DC method. A gain factor takes part in the closed-loop to update the Markov parameters matrix, reducing their residues at each iteration. A fixed value for the gain is applied all over the iterations. The Gaussian White Noise (GWN) is employed as the input excitation signal in simulated experiments of mass-damper-springer models with 50 and 100 degrees of freedom. For some algorithm settings, one hundred simulations, each holding more than 100 iterations, are performed to statistically demonstrate the iterative algorithm’s effectiveness compared to the conventional SSRA-DC. Further comparative analysis is accomplished between the iterative method with the ARMAX and N4SID algorithms.

Ekstremum Arama Temelli Hata Tahmini ile Esnek Bağlantılı Robot Kolunun Çıkış Geri Besleme Kontrolü

In this paper, an extremum seeking fault estimation based output feedback controller is proposed for the control of flexible-joint robot manipulator. First, using the approximate nonlinear robot model, a extremum seeking controller is designed to minimize the tracking error via output feedback. Then, in order to prevent the effects of faults, disturbances or unknown dynamics, an extremum seeking based fault estimator is proposed. In order to show that the advantage of the proposed configuration, a flexible-joint manipulator with unknown fault is controlled both in a numerical simulation and real-time experiment. An artificial payload is applied to the end-effector in a simulation environment. But, in the real-time experiment, an additional payload attached to the end effector when it is continuing the process. The approximate model of the robot manipulator is obtained by the state-space identification. As a result using the proposed estimation and controller, acceptable tracking and estimation results are obtained both in numerical and real-time experiments for future applications.

Identification of Aircraft Models

State space identification of aircraft flight models is carried out in this work. The identification results in estimation of derivatives of stability and control matrices and also biases of sensors. The identification procedure is based on likelihood function minimization based on Kalman filter and stochastic approximation. The least square method determines initial values for unknown parameter of state space models which are important for identification of models. The results obtained for models are presented. The decoupled longitudinal and lateral models of a small six seat aircraft are utilized in this work.

Non-linear State-space Model Identification from Video Data using Deep Encoders

Abstract Identifying systems with high-dimensional inputs and outputs, such as systems measured by video streams, is a challenging problem with numerous applications in robotics, autonomous vehicles and medical imaging. In this paper, we propose a novel non-linear state-space identification method starting from high-dimensional input and output data. Multiple computational and conceptual advances are combined to handle the high-dimensional nature of the data. An encoder function, represented by a neural network, is introduced to learn a reconstructability map to estimate the model states from past inputs and outputs. This encoder function is jointly learned with the dynamics. Furthermore, multiple computational improvements, such as an improved reformulation of multiple shooting and batch optimization, are proposed to keep the computational time under control when dealing with high-dimensional and large datasets. We apply the proposed method to a video stream of a simulated environment of a controllable ball in a unit box. The study shows low simulation error with excellent long term prediction capability of the model obtained using the proposed method.

Adaptive Robust Control Based on System Identification in Microgrid Considering Converter Controlled-Based Generator Modes

Microgrids with installation of converter controlled-based generations (CCGs), i.e. renewable energy source (RES) and battery energy storage system (BESS), may lead to a lack of system inertia. Moreover, CCG modes dominated by the CCGs may result in new control issues. Accordingly, optimal-fixed controllers designed at an operating point may not be sufficient to deal with the nonlinearity of such microgrids. This paper presents an adaptive robust control strategy of a future microgrid considering the CCG modes. Without requiring any microgrid parameters, the proposed control using a subspace-based state-space identification is used to 1) monitor microgrid changes along with moving window, 2) identify microgrid model, 3) assess stability indices, and 4) robustly design controllers of RES and BESS. Characteristic and sensitivity of the new CCG modes are analyzed. Effectiveness of the proposed control method is verified in a microgrid with 100% CCGs under various RES outputs and load patterns.

Fuzzy-driven strategy for fully automated modal analysis: Application to the SMART2013 shaking-table test campaign

A crucial step when identifying the modal signature of systems using growing order parametric methods consists in discriminating spurious modes from physical modes. In this paper, a three-stages clustering strategy is presented in a fuzzy framework for automating this selection process in the context of Input/Output and Output-Only identification. The novelty and strong point of the approach lies in the first stage where, after computation of single mode validation indicators, a modified fuzzy c-means clustering procedure is developed for performing a first partition. It is shown how the membership function obtained for the cluster of physical modes can be interpreted as a new synthetic modal indicator and helps with pole-splitting detection, outlier rejection and generally improves the final modal parameters estimation. The developed methodology does not involve any user-specified threshold and can be used for discriminating modes produced by any methodology consisting in fitting a growing order model to experimental data of any type. In this paper, accelerations measured during the SMART2013 shaking-table test campaign are processed using data-driven state-space identification algorithms. The automated selection process is used for tracking the modal signature of a trapezoidal shaped reinforced-concrete specimen using in turn stochastic and combined deterministic-stochastic algorithms, defining for the latter the movement of the shaking table as input. Variations in the modal signature are then correlated to the damage actually observed on the specimen and a comparison between Output-Only and Input/Output results is made in order to estimate the interaction between the specimen and the whole shaking table device.

Modal systems identification of an eleven-span concrete motorway off-ramp bridge using various excitations

This paper addresses and evaluates the influence of different types of dynamic excitation sources on identifiability and reliability of modal parameter identification of an eleven-span, post-tensioned, curved concrete motorway off-ramp bridge. The excitation sources included ground vibration waves generated by traffic on nearby motorways, people jumping on the bridge deck, broad-band linear chirp excitation induced by two light electro-dynamic shakers, and stepped sinusoidal sweeping forcing induced by a rotating eccentric mass shaker. Experimental modal analysis, operational modal analysis (OMA) and OMA with exogenous input system identification by a subspace state-space identification algorithm were carried out to extract the modal characteristics of the bridge. Numerical frequencies and mode shapes were also calculated from a detailed shell-element bridge model with the purpose of serving for the corroboration of the experimental modal properties. Through comprehensive cross-comparisons, it was revealed that the natural frequency discrepancies across different excitation methods were small (within ±1.5% relative difference), whist the consistency of the estimated damping ratios was poorer (up to 1.4% absolute difference). Eccentric mass shaker testing enabled identification of all modes predicted by the numerical model but used very heavy equipment. On the other hand, in ambient testing about one-third of the modes were missed, including the fundamental lateral mode. Electrodynamic shaker testing proved attractive as it only missed one mode and achieved its good performance with shakers that could be moved on site with relative ease.

Dynamic Characterization of Structures from Limited Measurements Using a Subspace System Identification Method

In this study, we investigate a subspace-system identification method that estimates the modal characteristics and damping ratio of structures using a small number of sensor measurement responses. With this method, a Kalman state vector is first constructed from the input and measurement data, and then the state-space system matrix is optimized from it. For this purpose, a block Hankel matrix is constructed using the input data of the load applied to the structure and the measurement data of the response, and then the matrix is decomposed through QR factorization. Then, singular value decomposition is used to obtain the extended observability matrix and state-space system order $$n$$ , and the state-space system matrix constituting the Kalman state vector is obtained via least-squares optimization. The natural frequency and damping ratio of the structural system are calculated from the eigenvalue of the obtained system matrix. To verify the effectiveness of this subspace state-space system identification method, the natural frequency and mode shape of a simply supported beam and cantilever beam were calculated using a limited number of measurement data, and the results were compared with an exact solution to evaluate the accuracy of the estimation results of the dynamic characteristics. Furthermore, the modal characteristics and damping ratio of a real bridge were estimated from acceleration data. The stability chart calculated from the example shows that the subspace state-space system identification method discussed in this study can accurately identify the modal characteristics of structures using only a small number of measurement data.

Smart process analytics for predictive modeling

While data analytics tools are changing how manufacturers make critical decisions and designs, the selection of the best method requires a substantial level of expertise. In practice, methods are chosen based on familiarity or on cross-validation results from a large candidate model pool which over-fits data. A Smart Process Analytics framework is presented which empowers the users to focus on goals rather than on methods and automatically transforms manufacturing data into intelligence. The method selection is based on domain knowledge, the specific data characteristics, and nested cross-validation procedures. The approach is demonstrated in case studies for experimental datasets from a variety of process systems. For a four-stage evaporator, a state-space identification method is selected that has half the long-term prediction error than a recurrent neural network. For a combined cycle power plant, machine learning methods are selected that have up to 30% lower mean-squared error than partial least squares.

Polynomial nonlinear state space identification of an aero-engine structure

Most nonlinear identification problems often require prior knowledge or an initial assumption of the mathematical law (model structure) and data processing to estimate the nonlinear parameters present in a system, i.e. they require the functional form or depend on a proposition that the measured data obey a certain nonlinear function. However, obtaining prior knowledge or performing nonlinear characterisation can be difficult or impossible for certain identification problems due to the individualistic nature of practical nonlinearities. For example, joints between substructures of large aerospace design frequently feature complex physics at local regions of the structure, making a physically motivated identification in terms of nonlinear stiffness and damping impossible. As a result, black-box models which use no prior knowledge can be regarded as an effective method. This paper explores the pragmatism of a black-box approach based on Polynomial Nonlinear State Space (PNLSS) models to identify the nonlinear dynamics observed in a large aerospace component. As a first step, the Best Linear Approximation (BLA), noise and nonlinear distortion levels are estimated over different amplitudes of excitation using the Local Polynomial Method (LPM). Next, a linear state space model is estimated on the non-parametric BLA using the frequency domain subspace identification method. Nonlinear model terms are then constructed in the form of multivariate polynomials in the state variables while the parameters are estimated through a nonlinear optimisation routine. Further analyses were also conducted to determine the most suitable monomial degree and type required for the nonlinear identification procedure. Practical application is carried out on an Aero-Engine casing assembly with multiple joints, while model estimation and validation is achieved using measured sine-sweep and broadband data obtained from the experimental campaign.

Modeling and state-space identification of deformable mirrors.

To develop high-performance controllers for adaptive optics (AO) systems, it is essential to first derive sufficiently accurate state-space models of deformable mirrors (DMs). However, it is often challenging to develop realistic large-scale finite element (FE) state-space models that take into account the system damping, actuator dynamics, boundary conditions, and multi-physics phenomena affecting the system dynamics. Furthermore, it is challenging to establish a modeling framework capable of the automated and quick derivation of state-space models for different actuator configurations and system geometries. On the other hand, for accurate model-based control and system monitoring, it is often necessary to estimate state-space models from the experimental data. However, this is a challenging problem since the DM dynamics is inherently infinite-dimensional and it is characterized by a large number of eigenmodes and eigenfrequencies. In this paper, we provide modeling and estimation frameworks that address these challenges. We develop an FE state-space model of a faceplate DM that incorporates damping and actuator dynamics. We investigate the frequency and time domain responses for different model parameters. The state-space modeling process is completely automated using the LiveLink for MATLAB toolbox that is incorporated into the COMSOL Multiphysics software package. The developed state-space model is used to generate the estimation data. This data, together with a subspace identification algorithm, is used to estimate reduced-order DM models. We address the model-order selection and model validation problems. The results of this paper provide essential modeling and estimation tools to broad AO and mechatronics scientific communities. The developed Python, MATLAB, and COMSOL Multiphysics codes are available online.

Model-Free Predictive Current Control of a Voltage Source Inverter

Conventional model predictive control (MPC) of power converter has been widely applied to power inverters achieving high performance, fast dynamic response, and accurate transient control of power converter. However, the MPC strategy is highly reliant on the accuracy of the inverter model used for the controlled system. Consequently, a parameter or model mismatch between the plant and the controller leads to a sub-optimal performance of MPC. In this paper, a new strategy called model-free predictive control (MF-PC) is proposed to improve such problems. The presented approach is based on a recursive least squares algorithm to identify the parameters of an auto-regressive with exogenous input (ARX) model. The proposed method provides an accurate prediction of the controlled variables without requiring detailed knowledge of the physical system. This new approach and is realized by employing a novel state space identification algorithm into the predictive control structure. The performance of the proposed model-free predictive control method is compared with conventional MPC. The simulation and experimental results show that the proposed method is totally robust against parameters and model changes compared with the conventional model based solutions.

State-Space Kernelized Closed-Loop Identification of Nonlinear Systems

In this paper, we propose a non-parametric state-space identification approach for open-loop and closed-loop discrete-time nonlinear systems with multiple inputs and multiple outputs. Employing a least squares support vector machine (LS-SVM) approach in a reproducing kernel Hilbert space framework, a nonlinear auto-regressive model with exogenous terms is identified to provide a non-parametric estimate of the innovation noise sequence. Subsequently, this estimate is used to obtain a compatible non-parametric estimate of the state sequence in an unknown basis using kernel canonical correlation analysis. Finally, the estimate of the state sequence is used together with the estimated innovation noise sequence to find a non-parametric state-space model, again using a LS-SVM approach. The performance of the approach is analyzed in a simulation study with a nonlinear system operating both in open loop and closed loop. The identification approach can be viewed as a nonlinear counterpart of consistent subspace identification techniques for linear time-invariant systems operating in closed loop.

State-Space System Identification Without a Hold Device by Lagrange Interpolation

This paper presents a solution to the state-space system identification problem from discrete-time data without a hold device on the input. We consider the case where the inter-sampled input is approximated by 4-point Lagrange interpolation. The resultant discrete-time state-space model becomes non-standard and non-causal, but a mathematically equivalent discrete-time model is found so that standard system identification can be adapted to identify it. From the identified equivalent model, a continuous-time state-space model of the system is recovered. Results for the special case of 2-point linear interpolation are also provided.