Model Identification Procedure 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.

Electro-mechanical modeling and identification of the UR5 e-series robot

Abstract Collaborative robotics is a field of growing industrial interest, within which understanding the energetic behavior of manipulators is essential. In this work, we present the electro-mechanical modeling of the UR5 e-series robot through the identification of its dynamics and electrical parameters. By means of the identified robot model, it is then possible to compute and optimize the energy consumption of the robot during prescribed trajectories. The proposed model is derived from data acquired from the robot controller during bespoke experimental tests, using model identification procedures and datasheet provided by manipulator, motors, and gearbox manufacturers. The entire procedure does not require the use of any additional sensor, so it can be easily replicated with an off-the-shelf manipulator, and applied to other robots of the same family.

Data-driven moving horizon state estimation of nonlinear processes using Koopman operator

In this paper, a data-driven constrained state estimation method is proposed for nonlinear processes. Within the Koopman operator framework, we propose a data-driven model identification procedure for state estimation based on the algorithm of extended dynamic mode decomposition, which seeks an optimal approximation of the Koopman operator for a nonlinear process in a higher-dimensional space that correlates with the original process state-space via a prescribed nonlinear coordinate transformation. By implementing the proposed procedure, a linear state-space model can be established based on historic process data to describe the dynamics of a nonlinear process and the nonlinear dependence of the sensor measurements on process states. Based on the identified Koopman operator, a linear moving horizon estimation (MHE) algorithm that explicitly addresses constraints on the original process states is formulated to efficiently estimate the states in the higher-dimensional space. The states of the treated nonlinear process are recovered based on the state estimates provided by the MHE estimator designed in the higher-dimensional space. Two process examples are utilized to demonstrate the effectiveness and superiority of the proposed framework.

Regulation of Uncertain Markov Jump Linear Systems With Application on Automotive Powertrain Control

Modeling and control of dynamic systems that experience abrupt changes are challenging and fundamental tasks in applications of different areas of engineering. Among these, control synthesis for autonomous heavy-duty vehicles has the potential to highly benefit transportation systems. That said, we propose a robust recursive regulator for discrete-time Markov jump linear systems with polytopic uncertain data. We assume the uncertainties affect the state-space parameters as well as the transition probability matrix. We formulate an optimization problem using the penalty function method and design a recursive solution, whereby we attain the robust state feedback gains. We impose no restrictions on how fast the uncertainties can change between two consecutive iterations. Conditions for convergence and mean-square stability are well defined in terms of Riccati recursive equations. We also set up a procedure for powertrain polytopic model identification based on CAN bus data of an autonomous heavy-duty ground vehicle. We provide two numerical examples to verify the effectiveness of the robust recursive regulator. Moreover, in a third example, we validate the obtained powertrain model on a trajectory tracking problem and compute acceleration and braking inputs using the robust regulator.

A hybrid orthosis combining functional electrical stimulation and soft robotics for improved assistance of drop-foot

Drop-foot is characterised by an inability to lift the foot, and affects an estimated 3 million people worldwide. Current treatment methods include rigid splints, electromechanical systems, and functional electrical stimulation (FES). However, these all have limitations, with electromechanical systems being bulky and FES leading to muscle fatigue. This paper addresses the limitations with current treatments by developing a novel orthosis combining FES with a pneumatic artificial muscle (PAM). It is the first system to combine FES and soft robotics for application to the lower limb, as well as the first to employ a model of their interaction within the control scheme. The system embeds a hybrid controller based on model predictive control (MPC), which combines FES and PAM components to optimally balance gait cycle tracking, fatigue reduction and pressure demands. Model parameters are found using a clinically feasible model identification procedure. Experimental evaluation using the system with three healthy subjects demonstrated a reduction in fatigue compared with the case of only using FES, which is supported by numerical simulation results.

Identification and validation of constitutive parameters of a Hencky-type discrete model via experiments on millimetric pantographic unit cells

Pantographic metamaterial design benefits from model identification procedures starting from what can be considered as the elementary unit cell of larger pantographic structures. Results from a tensile experiment and digital image correlation are utilized to identify the constitutive parameters of a discrete Hencky-type model for a millimetric pantographic cell. In the performed calibration, two different cost functions are formulated. First, the cost function is based upon measured resultant forces on the specimen boundaries. Then, the second cost function is based upon the measured pivot displacements in addition to reaction forces. The second cost functions thus exploits the pivot kinematics, which is a key feature of the deformation of pantographic structures. The identified model is further validated by predicting the reaction forces and pivot displacements of the same specimen subjected to compression. It is shown that the identification with the cost function incorporating pivot displacements is superior. It is also noted that the calibrated parameters deviate considerably from their initial guess derived from the linear Saint Venant problem, thereby indicating microscale nonlinear affects in otherwise linear reaction force-prescribed displacement responses at the macroscale.

Grey-box model and neural network disturbance predictor identification for economic MPC in building energy systems

This paper presents a novel model identification procedure to treat the occupancy induced unmeasured heat disturbance in the building model identification step for a model predictive control (MPC) implementation. First, we present a grey-box identification framework to estimate a dynamic building model that systematically accounts for the large unmeasured disturbance in the training data. Then, we discuss an approach to compute the confidence intervals (CIs) on the parameters estimated in the building model. Next, we develop a framework to identify a neural network (NN) using historical operational data to give the feedforward predictions of the heat disturbance in the MPC optimization problem. Further, we discuss the application of the composite building model and the NN disturbance predictor for energy cost optimization using an economic MPC formulation. We present case studies using a simple two time scale based building model, and demonstrate the effectiveness of the proposed grey-box model and the NN disturbance predictor identification procedures. We perform closed-loop simulations to highlight that additional energy cost savings of up to 4–5% are provided by including the feedforward NN disturbance predictions in the MPC controller. Finally, we also demonstrate the suitability of the proposed two-step model identification procedure to estimate accurate and reliable models using an industrial data set collected from a real office building.

Data-Driven Model Identification and Control of the Inertial Systems

In the synthesis of the control algorithm for complex systems, we are often faced with imprecise or unknown mathematical models of the dynamical systems, or even with problems in finding a mathematical model of the system in the open loop. To tackle these difficulties, an approach of data-driven model identification and control algorithm design based on the maximum stability degree criterion is proposed in this paper. The data-driven model identification procedure supposes the finding of the mathematical model of the system based on the undamped transient response of the closed-loop system. The system is approximated with the inertial model, where the coefficients are calculated based on the values of the critical transfer coefficient, oscillation amplitude and period of the underdamped response of the closed-loop system. The data driven control design supposes that the tuning parameters of the controller are calculated based on the parameters obtained from the previous step of system identification and there are presented the expressions for the calculation of the tuning parameters. The obtained results of data-driven model identification and algorithm for synthesis the controller were verified by computer simulation.

Data-driven identification of lithium-ion batteries: A nonlinear equivalent circuit model with diffusion dynamics

An accurate battery model is essential for battery management system (BMS) applications. However, existing models either do not describe battery physics or are too computationally intensive for practical applications. This paper presents a non-linear equivalent circuit model with diffusion dynamics (NLECM-diff) which phenomenologically describes the main electrochemical behaviours, such as ohmic, charge-transfer kinetics, and solid-phase diffusion. A multisine approach is applied to identify the elements for high frequency dynamics, as well as a distributed SoC dependent diffusion model block is optimized to account for long time dynamics. The model identification procedure is conducted on a three-electrode experimental cell, such that NLECM-diff models are developed for each electrode to then obtain the full cell voltage. Results imply that the NLECM-diff reduces the voltage root mean square error (RMSE) by 49.6% compared to a conventional ECM in the long duration discharge and has comparable accuracy to a parameterized SPMe in the NEDC driving cycle. Additionally, the variation of diffusion-related characteristics of the negative electrode under different currents is determined as the primary reason of the battery models’ large low-SoC-range error. Furthermore, the diffusion process is determined as the dominant voltage loss contributor in the long duration discharge and the ohmic voltage loss is identified as the dominant dynamic under NEDC driving profile.

A comparison of ship manoeuvrability models to approximate ship navigation trajectories

ABSTRACT It is essential to describe a ship’s manoeuvrability for various applications, e.g. optimal control of unmanned surface vehicles (USVs). In this study, the capability of two recognised manoeuvrability models to predict ships’ trajectories is investigated based on both simulation and open-water experiment test data. The parameters of these models are estimated by a statistical learning method. The goodness of the two estimated models for describing a merchant ship’s manoeuvrability is first studied using her manoeuvring simulation data. Then, experimental manoeuvring tests to use a USV in open water with wind and drifting effects are used to check the conventional model identification procedures. Finally, some modifications and adjustments are proposed to improve the conventional procedures. It shows that the proposed procedures can accurately derive the ship’s manoeuvrability based on experimental data.

Robustness analysis of Adaptive Model Predictive Control for uncertain non-linear dynamic systems using s-gap metric concepts

Robustness analysis of adaptive control systems, when operating in a certain domain, has been a gulf during the past decades. This problem is more complicated in the case of non-linear dynamic systems including un-modelled dynamics as unstructured uncertainty. To find a clear solution for this famous and interesting problem, limitations and effects of controller operation on performance of on-line model identification procedure (and vice versa) must be determined. In this paper, as the main novelty, we show that it needs some developments and new concepts in robust control theory as the s-gap metric, generalized stability margin (GSM) and modifications on the gain bound calculation. These achievements help us to present an on-line identification method with its convergence proof in sense of the s-gap metric and a relation between GSM and identifier convergence area. Therefore, consideration of GSM in Adaptive Model Predictive Control (AMPC) cost function concludes a systematic solution relating controller robustness and adaptivity, clearly. To this aim, a linear matrix inequality (LMI) representation for GSM constraint is suggested. Also, the stability of AMPC on a certain operating domain is guaranteed in sense of the s-gap metric and GSM. All of these help to determine the attraction area of closed loop system and we show that there exists a trade-off between each two cases of the attraction area size, convergence area size and robustness of closed loop control system. Finally, simulations and experimental results imply on correctness of the proposed method.

CONCRETE DAMAGE PLASTICITY MATERIAL MODEL PARAMETERS IDENTIFICATION

The procedure for identifying concrete damage plasticity material model parameters is presented in this paper. Concrete damage plasticity material model represents a constitutive model which is based on a combination of theory of plasticity and theory of damage mechanics. This material model is often used in solving geotechnical problems due to its realistic description of mechanical behavior of concrete material. Theoretical basis of concrete damage plasticity material model and material parameters identification procedure are presented in this paper. Proposed identification procedure is applied on experimental data from uniaxial compression and tension load-unload tests taken from literature. By applying experimental data, stress-strain curve is created. Based on stress-strain load-unload curve, stress-plastic strain and stress-degradation dependences are created which are necessary for material parameters identification. Using these dependences material parameters are determined. Verification of estimated parameters is performed in PAK software package using concrete damage plasticity material model. Finite element model is created for numerical simulations of uniaxial compression and tension tests. Numerical simulation results are compared with experimental data. By comparing numerical simulation results and experimental data it can be concluded that this procedure is effective for determining concrete damage plasticity model parameters.

КОМПЕНСАЦИЯ ВЛИЯНИЯ ТЕМПЕРАТУРЫ В АВИАЦИОННЫХ ПЬЕЗОРЕЗИСТИВНЫХ ДАТЧИКАХ ДАВЛЕНИЯ

Currently, piezoresistive pressure sensors (PDS) find expanded applications in various microelectronicdevices used in aviation technology. The behavior of the electrical signal of suchPDS mainly depends on the ambient temperature. It is known that the temperature drift of the PDSoutput signal is influenced by various factors: the temperature effect, the dependence of the resistanceof the sensitive element on the concentration of impurities, the dependence of the Young'smodulus of the sensor membrane and substrate materials on temperature, etc. It was found that thepreviously developed analytical calibration model of the sensor output signal, which takes intoaccount the models describing individual temperature effects, does not allow the pressure to bemeasured with the required accuracy in the temperature range characteristic of aviation equipmentfrom –60 C to 140 C. Therefore, conventional polynomial mathematical models are used todescribe the dependence of the PDS output signal on the measured pressure and temperature.The work uses a traditional approach, when the dependence of the output voltage on pressure is represented using a polynomial of relatively low order, and the dependences of the coefficients ofthis polynomial on temperature are also specified by the corresponding polynomials. Unfortunately,the temperature dependences of the coefficients are adequately described only by high-orderpolynomials (at least 7), which complicates the model identification procedure and leads to computationerrors. Therefore, the authors proposed to look for the dependence of the coefficients ontemperature in the form of cubic splines. The paper describes in detail the identification techniqueof the polynomial model under consideration and obtains expressions for correcting the PDS readingswhen measuring pressure in wide temperature ranges. In order to experimentally confirm theefficiency of the proposed method, an intelligent industrial automated system for the calibration oftraffic rules, described in the work, was used. It is shown how it can be used to take experimentaldata to calibrate the sensor readings over a wide temperature range, and the procedure for identifyingthe mathematical model of the pressure sensor required to minimize the cost of its certificationis described. The results of experimental studies of specific pressure sensors used in aviationtechnology are presented.

Parameters’ Identification of Vessel Based on Ant Colony Optimization Algorithm

In this paper, the ant colony optimization (ACO) method is used to identify the parameters of a 3-DOF nonlinear vessel model. Identifying the parameters is abstracted as a nonlinear optimization problem to solve through the ant colony optimization algorithm. The identification procedure is divided into two parts. The first part of the identification procedure is to identify the parameters related to surge motion. The second part of the identification procedure is to identify the rest parameters of the vessel’s kinetics model. In the surge model identification procedure, the transient motor speed is used to generate the training data, and in the sway and yaw motion identification procedure, the zigzag maneuvering with different motor speeds is used to generate the training data. All the parameters are identified by the ACO method and the least-square (LS) method based on the training data and then validated on the validation data. The prediction performance of parameters identified by different methods is compared in the simulation to demonstrate the effectiveness of the ACO algorithm.

Theoretical and experimental investigation of driver noncooperative-game steering control behavior

This paper investigates two noncooperative-game strategies which may be used to represent a human driver's steering control behavior in response to vehicle automated steering intervention. The first strategy, namely the Nash strategy is derived based on the assumption that a Nash equilibrium is reached in a noncooperative game of vehicle path-following control involving a driver and a vehicle automated steering controller. The second one, namely the Stackelberg strategy is derived based on the assumption that a Stackelberg equilibrium is reached in a similar context. A simulation study is performed to study the differences between the two proposed noncooperative-game strategies. An experiment using a fixed-base driving simulator is carried out to measure six test driver's steering behavior in response to vehicle automated steering intervention. The Nash strategy is then fitted to measured driver steering wheel angles following a model identification procedure. Control weight parameters involved in the Nash strategy are identified. It is found that the proposed Nash strategy with the identified control weights is capable of representing the trend of measured driver steering behavior and vehicle lateral responses. It is also found that the proposed Nash strategy is superior to the classic driver steering control strategy which has widely been used for modeling driver steering control over the past. A discussion on improving automated steering control using the gained knowledge of driver noncooperative-game steering control behavior was made.

Piecewise linear model predictive control of a rapid pressure swing adsorption system

AbstractRapid pressure swing adsorption (RPSA) is a gas separation technology used in the small‐scale oxygen concentrator devices. These devices are commonly used to produce high purity (~90%) oxygen from air for oxygen rehabilitation therapy, but can also produce a much wider range of oxygen purities for other applications. RPSA is a complex, cyclic, nonlinear switched logic process resulting from the coupling of gas adsorption, heat transfer, flow reversal effects, and process logic switches. For RPSA devices to operate satisfactorily, feedback control is critical but challenging due to their inherent complexity. In this article, we present a piecewise linear model predictive control framework for operation and control of a single‐bed RPSA system. A set of coupled, nonlinear partial differential equations with flow switching conditions is used as a plant model for the RPSA process. Subspace system identification with pseudo‐random binary sequence signals applied to this plant model at multiple operating points is used to generate a family of piecewise linear models for use in the model predictive controller algorithm. Detailed descriptions of the RPSA plant model, the multiple linear model identification procedure, the controller formulation and model switching logic are presented. The closed‐loop system is evaluated in simulation using several realistic set point tracking and disturbance rejection cases.

Accelerated Re-Design of Antenna Structures Using Sensitivity-Based Inverse Surrogates

The paper proposes a novel framework for accelerated re-design (dimension scaling) of antenna structures using inverse surrogates. The major contribution of the work is a sensitivity-based model identification procedure, which permits a significant reduction of the number of reference designs required to render the surrogate. Rigorous formulation of the approach is supplemented by its comprehensive numerical validation using a triple-band uniplanar dipole antenna and a dual-band monopole antenna re-designed with respect to operating frequencies as well as the substrate parameters (thickness and dielectric permittivity). It is demonstrated that-for the considered test cases-the reliable inverse model can be set up using a significantly smaller (by a factor of three) number of reference points as compared to the original version of the method, whereas the dimension scaling process itself requires up to four EM simulations of the antenna structure.

Aerodynamic Model Identification of a Quadrotor Subjected to Rotor Failures in the High-Speed Flight Regime

This letter presents a high-fidelity aerodynamic model of a quadrotor in the high-speed flight, with the normal configuration, or subjected to rotor failures. A novel experimental setup, data processing, and model identification procedure are developed. The main idea is that by first establishing the thrust and torque model from static wind tunnel tests as the benchmark of the aerodynamic model, and then identifying the in-plane forces, pitch and roll moments of each rotor from the free flight data obtained in a large-scale open-jet wind tunnel. The validation results show a decent model performance in predicting forces/moments, lateral forces effects, and the quadrotor trimming curve, by comparing with the benchmark model.

Prior-knowledge-based subspace identification for batch processes

In this paper, a prior-knowledge-based subspace identification method (SIM) is proposed for batch processes subject to repeatable disturbances. The proposed method is a two-step procedure for state-space model identification: in the first step, the extended observability and triangular Toeplitz matrices are estimated simultaneously from a parity space of the experimental data and, based on which, the corresponding system matrices are retrieved in the second step. More specifically, A and C are retrieved from the estimated extended observability matrix, while B and D are retrieved from the estimated triangular Toeplitz matrix. The proposed method shows several superiorities in the following aspects. Firstly, it is able to provide unbiased parameter estimation in the presence of repeatable disturbances, thanks to the proposed difference operator which eliminates the disturbance effect. Secondly, it shows better robustness to measurement noise compared with the existing SIMs using parity space, due to the inherent instrumental variable mechanism and the new technique to build the instrument, which greatly enhance the estimated model efficiency/accuracy. Lastly, by taking the auxiliary static-gain information into account in the identification procedure, the variance properties of the parameters can be improved, especially for the system matrices B and D. All the above-mentioned developments are analyzed with strict mathematical proofs, along with two illustrative examples to confirm the effectiveness and merits.

Adaptivity in Bayesian Inverse Finite Element Problems: Learning and Simultaneous Control of Discretisation and Sampling Errors.

The local size of computational grids used in partial differential equation (PDE)-based probabilistic inverse problems can have a tremendous impact on the numerical results. As a consequence, numerical model identification procedures used in structural or material engineering may yield erroneous, mesh-dependent result. In this work, we attempt to connect the field of adaptive methods for deterministic and forward probabilistic finite-element (FE) simulations and the field of FE-based Bayesian inference. In particular, our target setting is that of exact inference, whereby complex posterior distributions are to be sampled using advanced Markov Chain Monte Carlo (MCMC) algorithms. Our proposal is for the mesh refinement to be performed in a goal-oriented manner. We assume that we are interested in a finite subset of quantities of interest (QoI) such as a combination of latent uncertain parameters and/or quantities to be drawn from the posterior predictive distribution. Next, we evaluate the quality of an approximate inversion with respect to these quantities. This is done by running two chains in parallel: (i) the approximate chain and (ii) an enhanced chain whereby the approximate likelihood function is corrected using an efficient deterministic error estimate of the error introduced by the spatial discretisation of the PDE of interest. One particularly interesting feature of the proposed approach is that no user-defined tolerance is required for the quality of the QoIs, as opposed to the deterministic error estimation setting. This is because our trust in the model, and therefore a good measure for our requirement in terms of accuracy, is fully encoded in the prior. We merely need to ensure that the finite element approximation does not impact the posterior distributions of QoIs by a prohibitively large amount. We will also propose a technique to control the error introduced by the MCMC sampler, and demonstrate the validity of the combined mesh and algorithmic quality control strategy.