Effect Of Modeling Errors Research Articles

Robust Driving Control Design for Precise Positional Motions of Permanent Magnet Synchronous Motor Driven Rotary Machines with Position-Dependent Periodic Disturbances

Position-dependent periodic disturbances often limit the accuracy and smoothness of the positional motion of permanent magnet synchronous motor (PMSM)-driven rotary machines. Because the period of these disturbances varies with the motion velocity of the rotary machine, spatial domain control methods such as spatial iterative learning control (SILC) and spatial repetitive control (SRC) have been proposed and applied to improve rotary machine motion control designs. However, problems with learning period convergence and rotary machine dynamics significantly affect transient motion, further constraining the overall motion performance. To address these challenges, this study developed a robust driving control (RDC) that integrates a robust control design with position-dependent periodic disturbance feedforward compensation, rotary machine dynamics compensation, and proportional–proportional integral feedback control. A position-dependent periodic disturbance model was developed using multiple position–sinusoidal signals and identified using a spatial fast Fourier transform. RDC compensates for disturbances and dynamics and considers the effects of model parameter uncertainty and modeling error on the stability of the control system. Several motion control experiments were conducted on a PMSM test bench to compare the RDC, SILC, and SRC. The experimental results demonstrated that although both SILC and SRC can effectively suppress position-dependent periodic disturbances, SILC provides slower position error convergence owing to the learning process, and SILC and SRC result in significant position errors because of the influence of the PMSM-driven rotary machine dynamics. RDC not only suppresses position-dependent periodic disturbances, but also significantly reduces position errors with a reduction rate of 90%. Therefore, the RDC developed in this study effectively suppressed position-dependent periodic disturbances and significantly improved both the transient-state and steady-state position-tracking performances of the PMSM-driven rotary machine.

Assessing the effect of offline topography on electrical resistivity measurements: insights from flood embankments

Summary Electrical resistivity tomography (ERT), a geophysical imaging method, is commonly used on flood embankments (dykes or levees) to characterise their internal structure and look for defects. These surveys often use a single line of electrodes to enable 2D imaging through the embankment crest, an approach that enables rapid and efficient surveying compared to 3D surveys. However, offline variations in topography can introduce artefacts into these 2D images, by affecting the measured resistivity data. Such topographic effects have only been explored on a site-specific basis. If the topographic effects can be assessed for a distribution of embankment geometries (e.g. slope angle and crest width) and resistivity variations, it would allow for targeted correction procedures and improved survey design. To investigate topographic effects on ERT measurements, we forward-modelled embankments with different trapezoidal cross-sections sat atop a flat foundation layer with contrasting resistivity values. Each was compared to a corresponding flat model with the same vertical resistivity distribution. The modelling workflow was designed to minimise the effect of forward modelling errors on the calculation of topographic effect. We ran 1872 unique embankment forward models, representing 144 geometries, each with 13 different resistivity contrasts. Modelling results show that offline topography affects the tested array types (Wenner-Schlumberger, Dipole-Dipole, and Multiple-Gradient) in slightly different ways, but the magnitudes are similar, so all are equally suitable for embankment surveys. Three separate mechanisms are found to cause topographic effects. The dominant mechanism is caused by the offline topography confining the electrical current flow, increasing the measured transfer resistance from the embankment model. The two other mechanisms, previously unidentified, decrease the measured transfer resistances from the embankment model compared to a layered half-space but only affect embankments with specific geometries and resistivity distributions. Overall, we found that for typical embankment geometries and resistivity distributions, the resistivity distribution has a greater control on the magnitude of the topographic effect than the exact embankment geometry: the subsurface resistivity distribution cannot be neglected. 2D inversions are suitable when both the embankment is more resistive than the foundations and when the embankment's cross-sectional area is greater than 4 m2/m2 (area scaled to an embankment with a height of 1 m). Topographic corrections, 3D data acquisition or 3D forward models are required when these conditions are not met. These are demonstrated using field data from an embankment at Hexham, Northumberland, UK. Improving the accuracy of the resistivity values in ERT models will enable more accurate ground models, better integration of resistivity data with geotechnical datasets, and will improve the translation of resistivity values into geotechnical properties. Such developments will contribute to a better characterised and safer flood defence network.

Rejection of parametric model errors in a recursive Kalman filter for virtual sensing applications

The performance of the Kalman filter is often hindered by the discrepancies between a model used to realize the filter and the true model of the data-generating system. While some methods to account for those errors exists, the majority is restricted to Luenberger's observers. The objective of this work is to develop a Kalman filter where the effect of parametric model errors is rejected from the state and observation equations before the development of the state estimate, and without the explicit knowledge of the error terms. For this purpose, errors in a physical parameter of a parametrized mechanical system are modelled as additive terms in the state and observation equations by means of first-order perturbation analysis. The rejection step is achieved with an injection of a shaped output nullifying the effect of the added terms. A state observer is then derived under the assumption that the injected shaped outputs and the system states are uncorrelated. The performance of the proposed approach is illustrated on an experimental data of a plate system.

Active suspension hierarchical control with parameter uncertainty and external disturbance of electro-hydraulic actuators

In order to improve the ride comfort and handling stability of the electro-hydraulic active suspension system, a hierarchical control strategy is proposed. For the active suspension system with body mass uncertainty and safety constraints, an enhanced constraint adaptive backstepping controller is designed to generate the target force of body vertical motion. When dealing with constraints, nonlinear filters are introduced, backstepping technology and quadratic Lyapunov function are used to combine the control target and domain constraints, and the vertical displacement of the body and the suspension deflection control index are synthesized into a single controlled variable, so that the control variable converging to zero meets the suspension dynamic displacement limit. The ride comfort and safety of the active suspension system are improved. Secondly, stability analysis is conducted on the zero dynamic error system to ensure that all safety performance indicators are bounded. The effects of external disturbances, parameter uncertainties and modelling errors on the force tracking accuracy of asymmetric cylinder electrohydraulic systems are addressed. A backstepping dynamic surface control method based on a nonlinear perturbation observer is proposed, which estimates the composite perturbation terms such as modelling error and external perturbation, and uses the estimated value of the nonlinear observer to design a feedforward compensating control term to offset the effect of the composite perturbation on the system performance. In addition, the dynamic surface control method is used to calculate the derivative of the target force input, which avoids the derivative explosion phenomenon and reduces the computational complexity of the system. Simulation test results show that this method reduces the computational complexity of the system and improves the control performance. And under random and bumpy road conditions, the root-mean-square value of sprung mass acceleration performance index is reduced by 48.354 % and 72.677 % compared with passive suspension, which improves the ride comfort of the vehicle.

Process Damping Identification Using Bayesian Learning and Time Domain Simulation

Abstract Process damping can provide improved machining productivity by increasing the stability limit at low spindle speeds. While the phenomenon is well known, experimental identification of process damping model parameters can limit pre-process parameter selection that leverages the potential increases in material removal rates. This paper proposes a physics-informed Bayesian method that can identify the cutting force and process damping model coefficients from a limited set of test cuts without requiring direct measurements of cutting force or vibration. The method uses time-domain simulation to incorporate process damping and provide a basis for test selection. New strategies for efficient sampling and dimensionality reduction are applied to lower computation time and minimize the effect of model error. The proposed method is demonstrated, and the identified cutting and damping force coefficients are compared to values obtained using machining tests and least-squares fitting.

Extended State Observer Based Robust Feedback Linearization Control Applied to an Industrial CSTR

In the chemical and petrochemical industries, the Continuous Stirred Tank Reactor (CSTR) is, without doubt, one of the most popular processes. From a control point of view, the mathematical model describing the temporal evolution of the CSTR has a strongly nonlinear cross-coupled character. Moreover, modeling errors such as external disturbances, neglected dynamics, and parameter variations or uncertainties make its control task a very difficult challenge. This problem has been the subject of a wide number of control strategies. This article attempts to propose a viable, robust nonlinear decoupling control scheme. The idea behind the proposed approach lies in the design of two nested control loops. The inner loop is responsible for the compensation of the nominal model's nonlinear cross-coupled terms via a static nonlinear feedback; while the outer loop, designed around an Extended State Observer (ESO), which the additional state gathers the global effect of modeling errors, is charged with instantaneously estimating and then compensating the ESO extended state. This way, the CSTR complex dynamics are reduced to a series of decoupled linear subsystems easily controllable using a simple Proportional-Integral (PI) linear control to ensure the robust pursuit of reference signals respecting the desired performance. The presented control validation was performed numerically by an objective comparison to a classical PID controller.

A novel dynamic load identification method based on improved basis functions and implicit Newmark-[formula omitted] for continuous system with unknown initial conditions

For structural design and optimization, precise knowledge of dynamic load on structures is essential. However, load identification can be sensitive to the initial conditions, and even small variations can lead to inaccurate results. The existing load identification methods always assume that the structure’s initial condition is zero, which is not the case in real engineering problems where structures are already in a state of vibration before load identification implementation. In this work, we propose a novel dynamic load identification method that takes into account unknown initial conditions of structures which is based on the improved basis functions and implicit Newmark-β method. The real vibration response is decomposed into forced vibration caused by dynamic load and free vibration caused by initial condition, which are characterized by the coefficients of undetermined orthogonal polynomials. Moreover, to overcome the ill-posedness problem arising from factors such as response noise and model error, we introduce the L1 regularization method. To validate the performance of the proposed method, numerical simulations and tests of load identification are conducted on simply supported beam. The effects of noise and model error on the load identification results are analyzed. Finally, we discuss the impact of modal truncation order and the effect of measurement points on load identification.

A study on the implementation of nonlinear Kalman filter applying MMG model

Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.

Assessing the effects of head modelling errors and measurement noise on EEG source localization accuracy in preterm newborns: A single-subject study.

The accuracy of electroencephalogram (EEG) source localization is compromised because of head modelling errors. In this study, we investigated the effect of inaccuracy in the conductivity of head tissues and head model structural deficiencies on the accuracy of EEG source analysis in premature neonates. A series of EEG forward and inverse simulations was performed by introducing structural deficiencies into the reference head models to generate test models, which were then used to investigate head modelling errors caused by cerebrospinal fluid (CSF) exclusion, lack of grey matter (GM)-white matter (WM) distinction, fontanel exclusion and inaccuracy in skull conductivity. The modelling errors were computed between forward and inverse solutions obtained using the reference and test models generated for each deficiency. Our results showed that the exclusion of CSF from the head model had a strong widespread effect on the accuracy of the EEG source localization with position errors lower than 4.17 mm. The GM and WM distinction also caused strong localization errors (up to 3.5mm). The exclusion of fontanels from the head model also strongly affected the accuracy of the EEG source localization for sources located beneath the fontanels with a maximum localization error of 4.37 mm. Similarly, inaccuracies in the skull conductivity caused errors in EEG forward and inverse modelling in sources beneath cranial bones. Our results indicate that the accuracy of EEG source imaging in premature neonates can be largely improved by using head models, which include not only the brain, skull and scalp but also the CSF, GM, WM and fontanels.

Cubature Kalman Filters Model Predictive Static Programming Guidance Method with Impact Time and Angle Constraints Considering Modeling Errors

This paper proposes a CKF-MPSP guidance method for hitting stationary targets with impact time and angle constraints for missiles in the presence of modeling errors. This innovative guidance scheme is composed of three parts: First, the model predictive static programming (MPSP) algorithm is used to design a nominal guidance method that simultaneously satisfies impact time and angle constraints. Second, the cubature Kalman filter (CKF) is introduced to estimate values of the influence of the inevitable modeling errors. Finally, a one-step compensation scheme is proposed to eliminate the modeling errors’ influence. The proposed method uses a real missile dynamics model, instead of a simplified one with a constant-velocity assumption, and eliminates the effects of modeling errors with the compensation scheme; thus, it is more practical. Simulations in the presence of modeling errors are conducted, and the results illustrate that the CKF-MPSP guidance method can reach the target with a high accuracy of impact time and angles, which demonstrates the high precision and strong robustness of the method.

Series reversion for electrical impedance tomography with modeling errors *

This work extends the results of Garde and Hyvönen (2022 Math. Comput. 91 1925–1953) on series reversion for Calderón’s problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and the contact admittivity at the electrode-object interfaces treated as unknowns. The forward operator, sending the internal and contact admittivities to the linear electrode current-to-potential map, is first proven to be analytic. A reversion of the corresponding Taylor series yields a family of numerical methods of different orders for solving the inverse problem of electrical impedance tomography, with the possibility to employ different parametrizations for the unknown internal and boundary admittivities. The functionality and convergence of the methods is established only if the employed finite-dimensional parametrization of the unknowns allows the Fréchet derivative of the forward map to be injective, but we also heuristically extend the methods to more general settings by resorting to regularization motivated by Bayesian inversion. The performance of this regularized approach is tested via three-dimensional numerical examples based on simulated data. The effect of modeling errors related to electrode shapes and contact admittances is a focal point of the numerical studies.

Effects of head modeling errors on the spatial frequency representation of MEG

Objectives. We aim to investigate the effects of head model inaccuracies on signal and source reconstruction accuracies for various sensor array distances to the head. This allows for the assessment of the importance of head modeling for next-generation magnetoencephalography (MEG) sensors, optically-pumped magnetometers (OPM). Approach. A 1-shell boundary element method (BEM) spherical head model with 642 vertices of radius 9 cm and conductivity of 0.33 S m−1 was defined. The vertices were then randomly perturbed radially up to 2%, 4%, 6%, 8% and 10% of the radius. For each head perturbation case, the forward signal was calculated for dipolar sources located at 2 cm, 4 cm, 6 cm and 8 cm from the origin (center of the sphere), and for a 324 sensor array located at 10 cm to 15 cm from the origin. Equivalent current dipole (ECD) source localization was performed for each of these forward signals. The signal for each perturbed spherical head case was then analyzed in the spatial frequency domain, and the signal and ECD errors were quantified relative to the unperturbed case. Main results. In the noiseless and high signal-to-noise ratio (SNR) case of approximately ≥6 dB, inaccuracies in our spherical BEM head conductor models lead to increased signal and ECD inaccuracies when sensor arrays are placed closer to the head. This is true especially in the case of deep and superficial sources. In the noisy case however, the higher SNR for closer sensor arrays allows for an improved ECD fit and outweighs the effects of head geometry inaccuracies. Significance. OPMs may be placed directly on the head, as opposed to the more commonly used superconducting quantum interference device sensors which must be placed a few centimeters away from the head. OPMs thus allow for signals of higher spatial resolution to be captured, resulting in potentially more accurate source localizations. Our results suggest that an increased emphasis on accurate head modeling for OPMs may be necessary to fully realize its improved source localization potential.

Robust TS-ANFIS MPC of an Autonomous Racing Electrical Vehicle Considering the Battery State of Charge

In this work, the trajectory tracking problem of an autonomous racing electrical vehicle is addressed. Accordingly, a two-layer control scheme is developed, such that stability, recursive feasibility, and constraint satisfaction are guaranteed. The outer layer includes a zonotopic tube-based predictive control to ensure trajectory tracking while minimizing energy consumption considering the state of charge of the vehicle's battery. Meanwhile, the inner layer combines a linear quadratic zonotopic controller with a zonotopic Kalman filter to reduce the effect of exogenous disturbances and modeling errors. Moreover, for control and estimation purposes, a data-driven Takagi–Sugeno (TS) model trained by an adaptive neuro-fuzzy inference system (ANFIS) is employed. To illustrate the performance of the proposed control scheme, a simulated 1/10 Scale RC car is used.

Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework

In this paper, the periodic solutions of nonlinear mechanical systems are studied starting from the nonlinear state-space model estimated using the nonlinear subspace identification (NSI) technique. In its standard form, NSI needs the input–output data from a nonlinear structure undergoing broadband excitation and requires the prior knowledge of the locations and kind of nonlinearities to be estimated. The method allows the estimation of the nonlinear features of the system and the indirect study of its periodic solutions using a single broadband excitation, without the need of feedback control loops. To this end, the nonlinear frequency response curves of the system are estimated merging the harmonic balance method with the NSI technique and using a continuation approach. Then, a monodromy-based stability analysis is developed in the nonlinear state-space framework to study the stability of the periodic solutions of the system and to track its bifurcations. The method is validated considering conservative nonlinearities on two numerical examples and one experimental application, the latter comprising a double-well oscillator with period-doubling phenomena. The effects of noise and nonlinear modeling errors are also evaluated.

A Two-Step FE Model Updating Approach for System and Damage Identification of Prestressed Bridge Girders

This study presents a two-step FE model updating approach for health monitoring and damage identification of prestressed concrete girder bridges. To reduce the effects of modeling error in the model updating process, in the first step, modal-based model updating is used to estimate linear model parameters mainly related to the stiffness of boundary conditions and material properties. In the second step, a time-domain model updating is carried out using acceleration data to refine parameters accounting for the nonlinear response behavior of the bridge. In this step, boundary conditions are fixed at their final estimates using modal-based model updating. To prevent the convergence of updating algorithm to local solutions, the initial estimates for nonlinear material properties are selected based on the first-step model updating results. To validate the applicability of the two-step FE model updating approach, a series of forced-vibration experiments are designed and carried out on a pair of full-scale decommissioned and deteriorated prestressed bridge I-girders. In the first step, parameters related to boundary conditions, including stiffness of supports and coupling beams, as well as material properties, including initial stiffness of concrete material, are estimated. In the second step, concrete compressive strength and damping properties are updated. The final estimates of the concrete compressive strength are used to infer the extent of damage in the girders. The obtained results agree with the literature regarding the extent of reduction in concrete compressive strength in deteriorated concrete structures.

Reconstructing action potential and ionic current dynamics of a mammalian ventricular cell using data assimilation.

The dynamics of the cardiac ventricular myocyte action potential (AP) is regulated by intricate and nonlinear interactions between the cell transmembrane potential, and ionic currents and concentrations. Present technology limits the ability to simultaneously measuring multiple ionic currents and concentration during an AP in in vitro single cell experiments, which limits the scope of experimental data to provide a complete snapshot of the cardiac myocyte system state. This limitation presents an obstacle for understanding how cellular perturbations can trigger arrhythmogenic conditions. In this study, we applied a data assimilation approach, which combines limited noisy observations with predictions from a computational model, paired with a parameter estimation to minimize the effects of parameter uncertainty and model error. We performed a series of in silico experiments, in which a forecasting system was tasked with reconstructing AP dynamics of a virtual ventricular myocyte in the presence varying degrees of parameter and model error. With appropriate protocol design, we find that a data assimilation approach can successfully reconstruct and predict the dynamics of not only the directly observed state variables (such as the transmembrane potential and a selected ionic current), but also unobserved state variables, such as unmeasured ionic currents and concentrations. As an extension of the results of these series of in silico experiments, we generated simulations to assess which ionic currents, when measured, offer greater predictive ability using the data assimilation algorithm. This can offer valuable information for the design of single cardiac in vitro experiments, as it is not feasible to measure all ionic currents and concentrations across time within the same cell during an AP. Future work will investigate the longer-term accuracy of this approach predicting potentially pro-arrhythmic perturbations for arrhythmia risk assessment.

Mitigation of model error effects in neural network-based structural damage detection

This paper proposes a damage detection procedure based on neural networks that is able to account for the model error in the network training. Vibration-based damage detection procedures relied on machine learning techniques hold great promises for the identification of structural damage thanks to their efficiency even in presence of noise-corrupted data. However, it is rarely possible in the context of civil engineering to have large amount of data related to the damaged condition of a structure to train a neural network. Numerical models are then necessary to simulate damaged scenarios. However, even if a finite element model is accurately calibrated, experimental results and model predictions will never exactly match and their difference represents the model error. Being the neural network tested and trained with respect to the data generated from the numerical model, the model error can significantly compromise the effectiveness of the damage detection procedure. The paper presents a procedure aimed at mitigating the effect of model errors when using models associated to the neural network. The proposed procedure is applied to two case studies, namely a numerical case represented by a steel railway bridge and a real structure. The real case study is a steel braced frame widely adopted as a benchmark structure for structural health monitoring purposes. Although in the first case the procedure is carried out considering simulated data, we have taken into account some key aspects to make results representative of real applications, namely the stochastic modelling of measurement errors and the use of two different numerical models to account for the model error. Different networks are investigated that stand out for the preprocessing of the dynamic features given as input. Results show the importance of accounting for the model error in the network calibration to efficiently identify damage.

The effect of model errors in ensemble sequential assimilation of geomagnetic field

Earth’s magnetic field is generated in the fluid outer core through the dynamo process. Over the last decade, data assimilation has been used to retrieve the core dynamics and predict the evolution of the geomagnetic field. The presence of model errors in the geomagnetic data assimilation is inevitable because current numerical geodynamo models are still far from realistic core dynamics. In this paper, we investigate the effect of model errors in geomagnetic data assimilation based on ensemble Kalman filter (EnKF). We construct two dynamo models with different control parameters but exhibiting similar force balance and magnetic morphology at the core surface. We then use one dynamo model to generate synthetic observations and the other as the forward model in EnKF. Our test experiments show that the EnKF approach with the pre-setting model errors can nevertheless recover large-scale core surface flow and make a rough short-term (5-year) prediction. However, the data assimilation in the presence of model errors cannot keep improving the core state even though new observations are available. Motivated by the planned Macau Science Satellite-1, which is expected to provide improved internal geomagnetic field model, we also perform a test experiment using synthetic observations up to spherical harmonic degree <inline-formula><tex-math id="M1">\begin{document}$\ell=18$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-lijinfeng_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-lijinfeng_M1.png"/></alternatives></inline-formula>. Our results indicate that high-resolution observations are crucial in reconstructing small scale flow.

Optimal Data-Driven Difference-Inversion-Based Iterative Control: High-Speed Nanopositioning Tracking Example

In this article, an optimal data-driven difference-inversion-based iterative control (ODDD-IIC) method is proposed for high-speed precision tracking in the presence of dynamics changes and random disturbances. Iterative learning control (ILC) has been shown to be advantageous over feedback and feedforward control for repetitive operations. Challenges, however, still exist to achieve high accuracy and fast convergence in ILCs as the bandwidth, i.e., the frequency range for guaranteed convergence, can be limited by adverse effects of modeling error and random disturbances. The aim of the proposed method is to compensate for these adverse effects through a data-driven approach without a modeling process. A frequency- and iteration-dependent iteration gain is introduced in the control law to enhance both the tracking performance and the robustness. The technique is illustrated in an output tracking experiment on a piezoelectric actuator, with comparison to two existing ILC methods.

Run-to-Run Adaptive Nonlinear Feedforward Control of Electromechanical Switching Devices

Feedforward control can greatly improve the response time and control accuracy of any mechatronic system. However, in order to compensate for the effects of modeling errors or disturbances, it is imperative that this type of control works in conjunction with some form of feedback. In this paper, we present a new adaptive feedforward control scheme for electromechanical systems in which real-time measurements or estimates of the position and its derivatives are not technically or economically feasible. This is the case, for example, of commercial electromechanical switching devices such as solenoid actuators. Our proposal consists of two blocks: on the one hand, a feedforward controller based on differential flatness theory; on the other, an iterative adaptation law that exploits the repetitive operation of these devices to modify the controller parameters cycle by cycle. As shown, this law can be fed with any available measurement of the system, with the only requirement that it can be processed and converted into an indicator of the performance of any given operation. Simulated and experimental results show that our proposal is effective in dealing with a long-standing control problem in electromechanics: the soft-landing control of electromechanical switching devices.