Identification Of Linear Models Research Articles

A comprehensive approach to sparse identification of linear parameter-varying models for lithium-ion batteries using improved experimental design

This paper proposes a comprehensive approach to the identification of battery models in the linear parameter-varying (LPV) framework inspired by the equivalent-circuit model structures. The proposed LPV model structure is formulated using the input–output representation, wherein the model parameters are considered to depend on the state-of-charge, the current magnitude, and the current direction. The aforementioned dependence is explained using a suitable set of basis functions motivated with appropriate physical insight. Furthermore, the optimal experimental design problem is discussed to propose an improved input design for the model identification procedure. Subsequently, the Least Absolute Shrinkage and Selection Operator (LASSO) along with the ridge regression are employed for the selection of significant model terms and parameter estimation to yield a sparse model with adequate simulation capabilities. Finally, several battery models with varying model order and basis-function complexity are identified, which are subsequently validated and compared using a real drive-cycle dataset. The corresponding voltage simulation results yield the root-mean-squared error (RMSE) value for the best-performing model to be around 24.5 mV when a 1 A h NMC battery gets discharged with the lower voltage cutoff as low as 2.5 V.

Statistical analysis of identification of linear viscoelastic models

Statistical analysis of identification of linear viscoelastic models

Finite-Sample Identification of Linear Regression Models With Residual-Permuted Sums

Finite-Sample Identification of Linear Regression Models With Residual-Permuted Sums

An industrial case study on the combined identification and offset-free control of a chemical process

For three decades, model predictive control (MPC) has been the flagship advanced control method in the chemical process industries. However, most implementations still use heuristic methods for designing MPC estimators, especially for offset-free MPC implementations. In this paper, we present a recently developed maximum likelihood-based method for the identification of linear augmented disturbance models for use in offset-free MPC. This method provides noise covariances that are used to derive Kalman filters and moving horizon estimators, forgoing the need for manual design and tuning of the estimator. The method is extended to handle closed-loop plant data. The proposed identification method and estimator design are evaluated in industrial-scale, real-world case study of a process at Eastman Chemical’s Kingsport plant. Using this identified model, we reduced the mean stage cost by 38% compared to the performance of the existing, hand-tuned MPC model.

Adaptive predictive control of a fan-ventilated tunnel greenhouse with evaporative cooling

In the present work, micro-climate control of a fan-ventilated tunnel greenhouse with evaporative cooling is investigated via simulation study. For this purpose, the adaptive generalized predictive control (AGPC) strategy is adopted to control temperature, relative humidity, and CO2 concentration in the greenhouse on extremely hot summer days. A dynamic model which integrates a distributed model of greenhouse micro-climate with a crop growth model is used for numerical simulation of the tunnel greenhouse. The controller performance is analyzed via numerical simulation. The relative gain array analysis confirms that greenhouse micro-climatic parameters are highly interactive. However, simulation results showed that AGPC can efficiently handle variables interaction and follow set-points despite actuator limitations and high outside temperature. Besides, by considering output constraints in applying AGPC, the control system can keep the humidity of the greenhouse in a specific range instead of in a particular set point. The calculation burden for the AGPC strategy is kept low without increasing prediction error by employing a linear model and on-line adaptive identification. The applied strategy can handle the uncertainty of the design model due to the model mismatch by on-line identification of model parameters using the recursive least square method.

Equivalent Linear Model Identification and Periodic Control of a Mono-Wing Aerial Vehicle

Equivalent Linear Model Identification and Periodic Control of a Mono-Wing Aerial Vehicle

Data-driven modeling for damping and positioning control of gantry crane

Flexible structural vibrations of large gantry cranes are a well-known issue. Several control strategies were proposed for this problem, which require a detailed dynamical model. Since the modeling of large-scaled structures, as well as of significant nonlinear friction effects is complicated and time consuming, a direct data-driven dynamic reconstruction based on the Koopman operator theory is proposed. Such identification results in a higher order linear state-space model, which reflects the nonlinear behavior in the broad dynamical range of the system and does not depend on a specific operating point. In this paper, a data-driven linear model identification is investigated for a simulation model, as well as for an experimental laboratory crane. The damping and positioning control dynamics based on the identified model were studied and it was shown, that the resulting performance is comparable to model-based nonlinear approaches.

Linear Time-Invariant Model Identification Algorithm for Mechatronic Systems Based on MIMO Frequency Response Data

This article describes a new frequency- domain multi-input multioutput linear time-invariant (LTI) system identification algorithm for accurate model construction suitable for motion control systems. The proposed method can capture the effects of time-delay, lightly damped poles (structural resonances), as well as highly damped complex or real poles, and direct or derivative-like terms. The effectiveness of the algorithm has been validated using experimental frequency response measurements obtained from different types of motion control mechanisms. The proposed algorithm has also been compared with “ <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tfest</monospace> ” and “ <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modalfit</monospace> ” functions in MATLAB. Over these methods, nearly two orders of magnitude improvement is observed in the closeness of the model prediction, in terms of root mean square of the frequencywise modeling error.

A Continuous Time Domain Direct Identification Method for Unsteady Fluid Dynamic Model in Incompressible Flow

To identify the unsteady fluid dynamic model for a solid moving in the fluid, a new identification method that operates in the continuous time domain is proposed. It is illustrated that this new identification method is more accurate and appropriate for identifying unsteady fluid dynamic model in incompressible flow in comparison with the classical frequency domain or discrete domain method. This new method is applied to identify the unsteady fluid dynamic models of a NACA0012 airfoil and the effect of the fluid viscosity on the model parameter is analyzed. The result shows that the added mass in viscous flow is dependent on the input signal frequency and is exactly the added mass in inviscid flow when the frequency approaches infinity. Based on this discovery, the long controversy on the relationship of added mass between viscous and inviscid flow is solved. Then, the enlightenment of this discovery on the identification of both linear and nonlinear unsteady aerodynamic model in incompressible flow is illustrated. At last, the advantage of the new acquired unsteady fluid dynamic model is discussed in comparison with the classical quasi-steady aerodynamic model.

Linear Identification of Linear Rational-Expectations Models by Exogenous Variables Reconciles Lucas and Sims

Linear Identification of Linear Rational-Expectations Models by Exogenous Variables Reconciles Lucas and Sims

Identification and Validation of Linear Friction Models Using ANOVA and Stepwise Regression

For wet disk clutches, the energy input is strongly influenced by its friction behavior. However, the friction behavior cannot be simulated and therefore is mostly derived from experimental data for specific clutch systems. This paper presents a new approach for the identification and validation of linear friction models using analysis of variance (ANOVA) and stepwise regression. Therefore, we use experimental data of three different friction systems with paper- and carbon-based friction lining. The designed experiments support an efficient parameter-based analysis of the friction behavior. The obtained models can be used as an input for thermal simulations, for example, but can also support a better understanding of the main influencing factors and are applicable to various friction systems. For validation, the obtained models are applied to measured data. A good correspondence between the simulated and measured friction behavior can be shown for speeds in the investigated operating range. The presented procedure can be easily adapted, for different factors and operation modes, as well as other applications.

A Piece-Wise Linear Model-Based Algorithm for the Identification of Nonlinear Models in Real-World Applications

In this work, a data-driven approach for the identification of a piece-wise linear model for nitrogen oxide daily concentration simulation is presented and applied. The model has been identified by using daily measured concentrations, meteorological variables, and emission levels estimated starting from the results contained in suitable emission databases. We propose an innovative methodology that jointly optimizes clustering and parameter identification. The procedure has been applied considering data from the Milan (Italy) metropolitan area. The methodology has been compared with two state-of-the-art approaches based on a two-step, cluster-based algorithm and on Hammerstein–Wiener models. The results show how, in the presented application, the devised approach ensures better performance with respect to the two literature methods, both in terms of statistical indexes (correlation, normalized mean absolute error) and in terms of problem-specific metrics (hit ratio, false alarm). For this reason, the approach can be considered suitable to be used in the definition of optimal emission control strategies.

Pairwise and higher-order measures of brain-heart interactions in children with temporal lobe epilepsy

Objective. While it is well-known that epilepsy has a clear impact on the activity of both the central nervous system (CNS) and the autonomic nervous system (ANS), its role on the complex interplay between CNS and ANS has not been fully elucidated yet. In this work, pairwise and higher-order predictability measures based on the concepts of Granger Causality (GC) and partial information decomposition (PID) were applied on time series of electroencephalographic (EEG) brain wave amplitude and heart rate variability (HRV) in order to investigate directed brain-heart interactions associated with the occurrence of focal epilepsy. Approach. HRV and the envelopes of δ and α EEG activity recorded from ipsilateral (ipsi-EEG) and contralateral (contra-EEG) scalp regions were analyzed in 18 children suffering from temporal lobe epilepsy monitored during pre-ictal, ictal and post-ictal periods. After linear parametric model identification, we compared pairwise GC measures computed between HRV and a single EEG component with PID measures quantifying the unique, redundant and synergistic information transferred from ipsi-EEG and contra-EEG to HRV. Main results. The analysis of GC revealed a dominance of the information transfer from EEG to HRV and negligible transfer from HRV to EEG, suggesting that CNS activities drive the ANS modulation of the heart rhythm, but did not evidence clear differences between δ and α rhythms, ipsi-EEG and contra-EEG, or pre- and post-ictal periods. On the contrary, PID revealed that epileptic seizures induce a reorganization of the interactions from brain to heart, as the unique predictability of HRV originated from the ipsi-EEG for the δ waves and from the contra-EEG for the α waves in the pre-ictal phase, while these patterns were reversed after the seizure. Significance. These results highlight the importance of considering higher-order interactions elicited by PID for the study of the neuro-autonomic effects of focal epilepsy, and may have neurophysiological and clinical implications.

Identification of Linear Latent Variable Model with Arbitrary Distribution

An important problem across multiple disciplines is to infer and understand meaningful latent variables. One strategy commonly used is to model the measured variables in terms of the latent variables under suitable assumptions on the connectivity from the latents to the measured (known as measurement model). Furthermore, it might be even more interesting to discover the causal relations among the latent variables (known as structural model). Recently, some methods have been proposed to estimate the structural model by assuming that the noise terms in the measured and latent variables are non-Gaussian. However, they are not suitable when some of the noise terms become Gaussian. To bridge this gap, we investigate the problem of identification of the structural model with arbitrary noise distributions. We provide necessary and sufficient condition under which the structural model is identifiable: it is identifiable iff for each pair of adjacent latent variables Lx, Ly, (1) at least one of Lx and Ly has non-Gaussian noise, or (2) at least one of them has a non-Gaussian ancestor and is not d-separated from the non-Gaussian component of this ancestor by the common causes of Lx and Ly. This identifiability result relaxes the non-Gaussianity requirements to only a (hopefully small) subset of variables, and accordingly elegantly extends the application scope of the structural model. Based on the above identifiability result, we further propose a practical algorithm to learn the structural model. We verify the correctness of the identifiability result and the effectiveness of the proposed method through empirical studies.

Multi-objective evolutionary spatio-temporal forecasting of air pollution

Nowadays, air pollution forecasting modeling is vital to achieve an increase in air quality, allowing an improvement of ecosystems and human health. It is important to consider the spatial characteristics of the data, as they allow us to infer predictions in those areas for which no information is available. In the current literature, there are a large number of proposals for spatio-temporal air pollution forecasting. In this paper we propose a novel spatio-temporal approach based on multi-objective evolutionary algorithms for the identification of multiple non-dominated linear regression models and their combination in an ensemble learning model for air pollution forecasting. The ability of multi-objective evolutionary algorithms to find a Pareto front of solutions is used to build multiple forecast models geographically distributed in the area of interest. The proposed method has been applied for one-week NO2 prediction in southeastern Spain and has obtained promising results in statistical comparison with other approaches such as the union of datasets or the interpolation of the predictions for each monitoring station. The validity of the proposed spatio-temporal approach is thus demonstrated, opening up a new field in air pollution engineering.

Gravitational Base Parameters Identification for a Knee Rehabilitation Parallel Robot

New robotic technology is emerging nowadays to tackle lower limb rehabilitation issues. However, the commercial robots available for lower limb rehabilitation are usually oversize and expensive. Knee rehabilitation is generally aided by a professional therapist, making this clinical procedure an interesting scope for robotics. Parallel robots are suitable candidates for knee rehabilitation due to their high load capacity, stiffness, and accuracy compared to serial ones. In contrast, this robot has singular configurations inside its workspace, and its dynamic model is generally complex. For these reasons, a parallel robot for knee rehabilitation needs an advanced control unit to solve complex mathematical problems that ensure patient security. This study proposes the base parameters identification of a compact gravitational linear model of a 3UPS+RPU parallel robot using singular value decomposition. This paper recommends adding a statistical method focused on condition number minimization to the singular value decomposition process. This statistical method reduces the computational resources taken searching for the best inertial parameters combination at the beginning of the base parameter identification. The gravitational base parameters identified have a physical meaning and low complexity. This fact makes the results of this research the basis of an adaptative control applied to 3UPS+RPU parallel robot. This study shows that the gravitational term is the most influential for knee rehabilitation tasks, compared with the inertial, Coriolis, and centrifugal components, regarding the dynamic behavior of the parallel robot.

A robust whiteness test for the identification of discrete-time linear models: Use of orthonormal transfer functions

A novel whiteness test of residuals is proposed, which makes use of generalized bases of orthonormal transfer functions. It can be viewed as a robustified version of the classical whiteness test in the sense that it reduces the risk of type II errors, by introducing a frequency weighting in the assessment of the flatness in the residual power spectrum density. This frequency weighting, which depends on the basis poles, can be employed for the validation of reduced order models, when the flatness of the residual power spectrum density is evaluated over a limited frequency band.

Linear Model Identification for Personalized Prediction and Control in Diabetes.

Type-1 diabetes (T1D) is a disease characterized by impaired blood glucose (BG) regulation, forcing patients to multiple daily therapeutic actions, including insulin administration. T1D management could considerably benefit of accurate BG predictions and automated insulin delivery. For both tasks, the large inter- and intra-individual variability in glucose response represents a major challenge. This work investigates different techniques to learn individualized linear models of glucose response to insulin and meal, suitable for model-based prediction and control. We focus on data-driven techniques for linear model-learning and compare the state-of-art parametric pipeline with a novel non-parametric approach based on Gaussian regression and Stable-Spline kernel. On data collected by 11 T1D individuals, the effectiveness of different models was evaluated by measuring root mean squared error (RMSE), coefficient of determination (COD), and time gain associated with BG predictors. Among the tested approaches, the non-parametric technique results in the best prediction performance: median RMSE = 29.8 mg/dL, and median COD = 57.4%, for a prediction horizon (PH) of 60 min. With respect to the state-of-the-art parametric techniques, the non-parametric approach grants a COD improvement of about 2%, 7%, 21%, and 41% for PH = 30, 60, 90, and 120 min (paired-sample t-test p ≤ 0.001, p = 0.003, p = 0.03, and p = 0.07 respectively). Non-parametric linear model-learning grants statistically significant improvement with respect to the state-of-art parametric approach. The higher PH, the more pronounced the improvement. The use of a linear non-parametric model-learning approach for model-based prediction and control could bring to a more prompt, safe and effective T1D management.

Control-Oriented Modeling using Koopman Operator: An application to the Cahn-Hilliard Coarsening Problem

In this paper, we present results for the data-driven control oriented modeling of complex dynamics that arise in phase separation of multi-phase immiscible system. This phase separation phenomena is modeled using a complicated nonlinear partial differential equations which are not suitable for control. We use simulation data generated from a detailed physics-based model for the data-driven modeling. We employ Koopman-based lifting for the identification of linear models from the data both under controlled and uncontrolled setting. Spectral analysis of Koopman and its adjoint Perron-Frobenius operator helps us identify invariant structure and dominant modes for the reduced-order representation from the data. Simulation results are presented for the reconstruction and validation of the controlled dynamical model.

Adaptive System Identification with Regularized FIR Models

Recent developments propose regularized FIR models as superior to other linear model identification methods. Different kernels exist to incorporate prior knowledge in form of regularization. In this work, we use the impulse response preserving (IRP) kernel which applies prior knowledge of the process pole(s) to the model estimation, yielding a gray-box approach. This concept is extended to deal with time-variant systems in an online manner. Leaky recursive least squares (LRLS), leaky least mean squares (LLMS) and non-fading regularized recursive least squares (NFRA-RLS) are used for this purpose. To increase the interpretability of the regularization strength a new scaling factor is proposed including knowledge about the effective number of data points. A simulation study of a linear time-variant process shows that only the LRLS and LLMS algorithm are able to perform the intended gray-box approach.