Constrained Unscented Kalman Filter Research Articles

Application of model updating to a large‐scale hybrid simulation

AbstractModel updating can enhance hybrid simulation by utilizing the experimental data from the physically tested substructure to update the parameters of like‐components in the numerical substructure throughout the test, improving the overall accuracy and reducing the extent of the experimental setup. Identifying and updating parameters can be challenging, especially when coupling between degrees of freedom (DOF) must be considered or the specimen experiences loading scenarios which result in newly observed behavior. To explore the performance of model updating under these challenging conditions, a large‐scale hybrid simulation was conducted using a model of a major toll bridge with seismic isolation lead rubber bearings (LRB). One LRB is physically tested considering axial, shear, and rotational loading, while the remainder of the bearings are simulated and updated with a phenomenological model within the numerical substructure. A weighted adaptive constrained unscented Kalman filter is applied as the online model updating algorithm. The study explored the effect of learning over different loading patterns, the selection of initial model parameters, and the selection of the physically tested substructure. The improvement of numerical model hysteresis performance accuracy of the force prediction demonstrates the benefits of model updating in large‐scale hybrid simulation.

Application of constrained unscented Kalman filter (CUKF) for system identification of coupled hysteresis under bidirectional excitation

Application of constrained unscented Kalman filter (CUKF) for system identification of coupled hysteresis under bidirectional excitation

Constrained unscented Kalman filter for parameter identification of structural systems

The unscented Kalman filter (UKF) can be used to identify model parameters of structural systems from the measurement data. However, the standard UKF may provide unreliable and nonphysical estimates, since no parameter constraints are incorporated in the identification process. This paper discusses and compares several constrained UKF (CUKF) methods for parameter identification of structural systems. The effectiveness and robustness of the methods are evaluated through numerical simulation on a Bouc–Wen hysteretic system. The results demonstrate that with properly handling of the constraints, the identification accuracy can be improved. The proposed CUKF method is further validated using experimental data collected from a full-scale reinforced concrete structure. Based on the identified model parameters, the updated models can achieve more accurate simulation responses than the initial model.

Estimation of the instantaneous friction coefficients of sliding isolators subjected to bi-directional orbits through a nonlinear state observer

One of the most challenging task for earthquake engineers is the accurate prediction of the dynamic response of structures implementing sliding seismic isolators, like the curved surface sliders. Indeed, the force–displacement behaviour of these devices strictly depends on the coefficiens of friction developed at the two sliding surfaces whose values vary instantaneously depending on variable compression load, sliding velocity, and contact temperature developed during the seismic motion. However, only the overall (or effective) friction coefficient of the isolator can be estimated, as weighted average of the values at the two sliding surfaces, through tipycal displacement controlled prototype experimental tests. This information is not suitable for the calibration of predictive isolator models (e.g. FEM analyses) or to characterize the tribological behaviour of potentially different friction pads at the two sliding surfaces. In this paper, an estimation approach, based on a Constrained Unscented Kalman Filter (CUKF) integrated with a Random Walk Model technique (RWM), that is capable to identify the two distinct friction coefficients, and their time-variations during displacement-controlled test is presented. The proposed tool allows the identification of the distinct frictional properties without any a-priori knowledge about the design properties at the two sliding surfaces that can widely differ in terms of adopted sliding materials, presence of lubrificant, and radius of curvature. The developed tool is firstly validated through the comparison with the results of FEM analyses and then applied on experimental tests carried out on a full-scale isolator prototype demonstrating its suitability for the assessment of the actual friction coefficients.

Nonlinear finite element model updating using constrained unscented Kalman filter for condition assessment of reinforced concrete structures

Nonlinear finite element model updating using constrained unscented Kalman filter for condition assessment of reinforced concrete structures

Performance of unscented Kalman filter for model updating with experimental data

AbstractThe unscented Kalman filter (UKF) is one of the most widely used algorithms for identifying and updating numerical model parameters. When updating from experimental data, the UKF performs well but it is sensitive to the selection of the initial algorithm variables and vulnerable to the influence of measurement noise. Furthermore, the ability to capture new behavioral features, such as hardening at large displacements, is a challenge. To achieve a more robust algorithm that can learn new features, techniques from the constrained UKF and the adaptive UKF are combined with an additional weighting on learning based on the magnitude of the input. The weighted adaptive constrained unscented Kalman filter (WACUKF) updates the numerical model with adaptive calculation of measurement noise and assigns a different learning rate for measurement data through the weighting function. To confine parameter values in the ranges with physical sense, the WACUKF adopts the sigma points projecting strategy for constrained parameters. Data from two experiments conducted on different structural components, in different laboratories, with different setups are used to validate the effectiveness of the WACUKF and compare against the performance of the UKF. The results demonstrate that the WACUKF can capture and preserve new features during model updating and is more robust and accurate than the UKF.

Tire–road friction coefficient estimation based on designed braking pressure pulse

Knowledge of tire–road friction coefficient (TRFC) is valuable for autonomous vehicle control and design of active safety systems. This paper investigates TRFC estimation on the basis of longitudinal vehicle dynamics. A two-stage TRFC estimation scheme is proposed that limits the disturbances to the vehicle motion. A sequence of braking pressure pulses is designed in the first stage to identify desired minimal pulse pressure for reliable estimation of TRFC with minimal interference with the vehicle motion. This stage also provides a qualitative estimate of TRFC. In the second stage, tire normal force and slip ratio are directly calculated from the measured signals, a modified force observer based on the wheel rotational dynamics is developed for estimating the tire braking force. A constrained unscented Kalman filter (CUKF) algorithm is subsequently proposed to identify the TRFC for achieving rapid convergence and enhanced estimation accuracy. The effectiveness of the proposed methodology is evaluated through CarSim™-MATLAB/Simulink™ co-simulations considering vehicle motions on high-, medium-, and low-friction roads at different speeds. The results suggest that the proposed two-stage methodology can yield an accurate estimation of the road friction with a relatively lower effect on the vehicle speed.

Monitoring of hysteretic friction degradation of curved surface sliders through a nonlinear constrained estimator

The lack of validated physical models concerning the degradation of the coefficient of friction of sliding isolators induced from the heating of the sliding surfaces during the seismic motion hampers the interpretation of experimental data and the formulation of accurate numerical models. An estimator based on a Constrained Unscented Kalman Filter (CUKF), suitable for real-time monitoring, combined with a Random Walk Model approach (RWM) which identifies the friction degradation function without the a priori knowledge of a physical model and ensuing analytical law has been developed in the study. Both numerical analyses and experimental tests of a 2 DOF shear-type physical model are employed to demonstrate the validity of the technique. The proposed estimator is able to provide an accurate estimation of the state of the system, by predicting the structural displacement histories, and to identify the hysteretic degradation function in different friction conditions, from low to high friction.

Constrained Unscented Kalman Filter for Structural Identification of Bouc–Wen Hysteretic System

The Bouc–Wen hysteresis model has been extensively used to identify earthquake damage on civil structures where hysteretic behavior is expected. One of the challenging problems in the identification of Bouc–Wen parameters is overfitting, which is caused by too many nonphysical model parameters. Limit on the search domain of parameters helps to solve the problem. The unscented Kalman filter (UKF) is widely developed to find Bouc–Wen parameters. In order to improve the accuracy and convergence speed of conventional UKF, this study developed a constrained UKF (CUKF) which can be used for the simultaneous identification of the Bouc–Wen hysteretic model. The proposed CUKF is very helpful when certain parameters can be constrained in a physical sense. We compare the proposed CUKF with conventional UKF to validate its robustness and efficacy in identifying Bouc–Wen parameters.

Loss of Excitation Detection in Synchronous Generators Based on Dynamic State Estimation

In this article, we present a new approach to the detection of Loss-Of-Excitation (LOE), a typical failure of synchronous generators. Unlike most of the algorithms proposed in the literature, which only use the information available at the point of connection, we also take advantage of prior knowledge of the generator model. To track the field voltage and the other state variables, we have chosen the Constrained Unscented Kalman Filter (CUKF) as the core estimation technique, with phasor measurements as the input for this filtering algorithm. Detection of LOE is then performed by using the Faulty Modes Detection and Diagnosis (FMDD) algorithm, which combines the normal operation and a LOE-based model to decide in real-time whether an LOE has occurred or not. Results of simulations using a small two-area power system and the IEEE 39-bus system show that LOE detection times can be significantly reduced as compared to conventional and state-of-the-art approaches. Moreover, we observe that the new fault detection signal used to trip the generator can avoid short-term voltage stability problems.

Constrained Kalman Filter for Identification of Semiphysical Building Thermal Models

Model-based energy management of buildings through a model predictive control framework proved to be the promising solution for improving the energy efficiency of the building sector. The keystone for further improvements and real implementation is to have reliable and accurate mathematical models that are simple enough to be used in real-time control. In the work presented, a general identification framework for acquiring a control-oriented semiphysical thermal model of a building based on a modified constrained unscented Kalman filter algorithm is proposed. Experiments performed on a living-lab skyscraper building show that the adopted algorithm applied to short-term operation data outperforms the standard Kalman filter forms, both in convergence rate and numerical stability. The proposed method thus paves the way to the fast deployment of model-based energy management strategies in buildings.

Nonlinear estimation of the Bouc-Wen model with parameter boundaries: Application to seismic isolators

The Bouc-Wen model is one of the most widely used parametric models of hysteresis. The exactness of the Bouc-Wen model depends on the correctness of the model parameters that are subjected to bound constraints in accordance with their physical meaning. Constraints and nonlinearities of the model introduce a complexity for the parameter estimation. In this paper, a constrained unscented Kalman filter (CUKF) is proposed in order to identify the hysteresis model parameters in a robust and reliable way. The adopted parameter estimator has been compared with the well-known extended Kalman filter (EKF) that is often used for nonlinear system identification. The effectiveness of the proposed approach has been verified by numerical simulations and experimental tests. In particular, for the experimental verification of the CUKF, the Bouc-Wen model has been adopted to describe the hysteretic shear behaviour of a seismic isolator. The results show that the CUKF provides better parameter identification than the EKF also taking into account parameter boundaries.

Constrained nonlinear filter for vehicle sideslip angle estimation withno a priori knowledge of tyre characteristics

The vehicle sideslip angle is one of the most functional feedbacks for the actual control systems of vehicle dynamics. The measurement of the sideslip angle is expensive and unsuitable for common vehicles. Consequently, its estimation is nowadays an important task.This paper focuses on the vehicle sideslip angle estimation adopting a constrained unscented Kalman filter (CUKF) that takes into account state constrains during the estimation process. State boundaries are useful in real-world applications to prevent unphysical results and to improve the estimator robustness. The proposed technique fully takes into account the measurement noise and nonlinearities. A vehicle model with single track has been adopted for the design of the estimator. Simulations have been carried out and comparisons with the unscented Kalman filter (UKF) are illustrated. Performance of the estimators have been checked through the application to experimental data. The results show the goodness of the CUKF, able to give an estimate fully in accordance with the measurement. Moreover, the results show that the CUKF, due to the presence of the boundaries, outperforms the UKF.

Blind adaptive constrained constant modulus algorithms based on unscented Kalman filter for beamforming

This work proposes constrained constant modulus unscented Kalman filter (CCM-UKF) algorithm and its low-complexity version called reduced-rank constrained constant modulus unscented Kalman filter (RR-CCM-UKF) algorithm for blind adaptive beamforming. In the generalized sidelobe canceller (GSC) structure, the proposed algorithms are devised according to the CCM criterion. Firstly, the cost function of the constrained optimization problem is transformed to suit the Kalman filter-style state space model. Then, the optimum weight vector of the beamformer can be estimated by using the recursive formulas of UKF. In addition, the a priori parameters of UKF (system and measurement noises) are processed adaptively in the implementation. Simulation results demonstrate that the proposed algorithms outperform the existing methods in terms of convergence speeds, output signal-tointerference- plus-noise ratios (SINRs), mean-square deviations (MSDs) and robustness against steering mismatch.

Identification of the non-linear dynamics and state of charge estimation of a LiFePO4 battery using constrained unscented Kalman filter

State of charge (SOC) estimation of a LiFePO4 battery exhibiting significant hysteresis is considered. The dynamics of the battery is modeled as a linear system in conjunction with a non-linear hysteresis block. The linear part is assumed to be of a second order equivalent circuit model along with an open circuit voltage (OCV) source Voc. The circuit model is descretised and the resulting parameters are modeled as a multivariate random walk with a diagonal noise covariance matrix. These parameters are estimated using a Kalman filter. The linear model is then validated using a hybrid pulse power characterisation (HPPC) current profile. The major loop of the non-linear hysteresis relating Voc and SOC is experimentally determined by charging and discharging the battery with low magnitude currents. Using Chebyshev polynomials, a model is fit for the hysteresis curves. Constrained unscented Kalman filter (CUKF) is used for estimating the minor loops of the hysteresis, and the SOC. The SOC estimation is then validated from a full electrochemical model simulation of the battery using COMSOL software.

Parameter Identification for Nonlinear Structures by a Constrained Kalman Filter with Limited Input Information

In this study, a new structural identification method is proposed to simultaneously evaluate the parameter and partial external excitation. The external excitation is decomposed as the linear combination of orthogonal bases, by which the problem of time-variant excitation identification is transformed into the identification of constant decomposition coefficients. A new constrained unscented Kalman filter (UKF) is proposed to identify the structural parameters and coefficients of excitation decomposition based only on measurement of the acceleration response. The proposed filter can retain the physical meaning of the structural parameters identified. A three-storey hysteretic nonlinear shear building is investigated numerically. The structural parameter and external force can be accurately identified with the proposed filter. The results of the simulation studies using the constrained UKF are compared with those from the conventional UKF. It is shown that some parameters identified by the conventional UKF may lose physical meaning, while the proposed constrained UKF can retain physical meaning. In the presence of measurement noise, the structural parameters and dynamic load can still be accurately identified using the proposed constrained UKF, which indicates the stability of the identification process.

Real time hybrid simulation with online model updating: An analysis of accuracy

In conventional hybrid simulation (HS) and real time hybrid simulation (RTHS) applications, the information exchanged between the experimental substructure and numerical substructure is typically restricted to the interface boundary conditions (force, displacement, acceleration, etc.). With additional demands being placed on RTHS and recent advances in recursive system identification techniques, an opportunity arises to improve the fidelity by extracting information from the experimental substructure. Online model updating algorithms enable the numerical model of components (herein named the target model), that are similar to the physical specimen to be modified accordingly. This manuscript demonstrates the power of integrating a model updating algorithm into RTHS (RTHSMU) and explores the possible challenges of this approach through a practical simulation. Two Bouc–Wen models with varying levels of complexity are used as target models to validate the concept and evaluate the performance of this approach. The constrained unscented Kalman filter (CUKF) is selected for using in the model updating algorithm. The accuracy of RTHSMU is evaluated through an estimation output error indicator, a model updating output error indicator, and a system identification error indicator. The results illustrate that, under applicable constraints, by integrating model updating into RTHS, the global response accuracy can be improved when the target model is unknown. A discussion on model updating parameter sensitivity to updating accuracy is also presented to provide guidance for potential users.

Model updating with constrained unscented Kalman filter for hybrid testing

The unscented Kalman filter (UKF) has been developed for nonlinear model parametric identification, and it assumes that the model parameters are symmetrically distributed about their mean values without any constrains. However, the parameters in many applications are confined within certain ranges to make sense physically. In this paper, a constrained unscented Kalman filter (CUKF) algorithm is proposed to improve accuracy of numerical substructure modeling in hybrid testing. During hybrid testing, the numerical models of numerical substructures which are assumed identical to the physical substructures are updated online with the CUKF approach based on the measurement data from physical substructures. The CUKF method adopts sigma points (i.e., sample points) projecting strategy, with which the positions and weights of sigma points violating constraints are modified. The effectiveness of the proposed hybrid testing method is verified by pure numerical simulation and real-time as well as slower hybrid tests with nonlinear specimens. The results show that the new method has better accuracy compared to conventional hybrid testing with fixed numerical model and hybrid testing based on model updating with UKF.

On the choice of importance distributions for unconstrained and constrained state estimation using particle filter

Recursive state estimation of constrained nonlinear dynamical system has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used (Arulampalam et al. [1]). As pointed out by Daum [2], particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approach for generating the proposal distribution based on a constrained Extended Kalman filter (C-EKF), Constrained Unscented Kalman filter (C-UKF) and constrained Ensemble Kalman filter (C-EnkF) has been proposed. The efficacy of the proposed state estimation algorithms using a particle filter is illustrated via a successful implementation on a simulated gas-phase reactor, involving constraints on estimated state variables and another example problem, which involves constraints on the process noise (Rao et al. [10]). We also propose a state estimation scheme for estimating state variables in an autonomous hybrid system using particle filter with Unscented Kalman filter as a proposal and unconstrained Ensemble Kalman filter (EnKF) as a proposal. The efficacy of the proposed state estimation scheme for an autonomous hybrid system is demonstrated by conducting simulation studies on a three-tank hybrid system. The simulation studies underline the crucial role played by the choice of proposal distribution in formulation of particle filters.

Constrained State Estimation Using Particle Filters

Abstract Recursive estimation of constrained nonlinear dynamical systems has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used. As pointed out by Daum (2005), particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approach for generating the proposal distribution based on a Constrained Unscented Kalman filter is proposed. The efficacy of the proposed constrained state estimation algorithm using a particle filter (CUPF) is illustrated via a successful implementation on a simulated gas-phase reactor.