Presence Of Modeling Errors Research Articles

Generalization gap estimation for damage classification tasks when finite element simulated data is used for training: A numerical study and experimental validation on a steel truss

Labeled simulated structural responses by Finite Element (FE) methods may be used to construct training sets for monitoring the health state of structures. Such an approach appears to be an attractive way to avoid experimental costs. However, the main obstacle is the simulation error contained in such numerical responses. The error can contaminate the training data and lead to wrong conclusions when the learned features try to generalize on subsequent online experimental data. It is therefore very important to have an estimation of how good the available simulated data is for a given problem. The present work gives a novel methodology where classifiers trained by FE vibration response data are subjected to inputs of various perturbations, emulating in such way the generalization gap (classification errors) due to simulation errors. The response of the classifiers is gathered afterwards in a dataset which is used to construct a function that estimates the generalization gap based on the perturbed intact state response. Results are presented that show the behavior of the proposed gap estimation function for different binary damage classification scenarios. A numerical truss structure is used to test the concept. Convolutional Neural Networks (CNN) are applied for all data-driven related tasks, such as learning of health state features in vibration responses or evaluation of the gap function. The results show a promising methodology that can be used to estimate the reliability of numerically trained classifiers. In the final part of this study, the framework is tested on an experimental truss structure. The presented methodology contributes to the quantitative study of uncertainty when extrapolating from the numerical to the experimental domain in the presence of modeling errors.

Design and Development of Cartesian Coordinate Robot

Abstract: For precise motion control in Cartesian coordinates, essential for assembly tasks requiring both force and position control to ensure part integrity and smooth operation. Previous methods lacked the ability to maintain fast and accurate motion control in the presence of modeling errors and external disturbances. Our proposed scheme comprises both nonlinear and linear components in the control input. The nonlinear part stabilizes and decouples robot dynamics in Cartesian coordinates, while the linear part, drawing from servomechanism theory, mitigates modeling errors and disturbances.

Bayesian two-stage structural identification with equivalent formulation and EM algorithm

For structural model identification using a Bayesian two-stage approach, modal properties (e.g., natural frequencies) are first extracted from measured data in Stage I and then used for determining structural properties (e.g., stiffness) in Stage II. With sufficient data that allow the problem to be globally identifiable, the computational problem often reduces to optimizing a ‘measure-of-fit’ function to yield the ‘most probable value’ (MPV) that informs the ‘best estimate’, and determining the Hessian of the function to yield the posterior covariance matrix that informs the remaining uncertainty. Recent developments deal with the presence of model error, and the increasing complexity calls for proper computational strategy. In this spirit, assuming Gaussian model error, this work develops a hypothetical yet mathematically equivalent formulation for the two-stage problem, which facilitates development of effective algorithms for MPV using Expectation-Maximization techniques. By treating hypothetically the MPV of modal properties in Stage I as ‘data’ and model error as latent variables, the Q-function in the M−step can be expressed as a sum of two terms that can be optimized with respect to structural parameters and model error parameters. The optimization of structural parameters reduces to that of a Stage II problem without model error, for which existing algorithms can be applied. Analytical expressions are also derived for computing the posterior covariance matrix. The proposed methodology is investigated with synthetic data for model errors associated with sensor misalignment and model simplification, lab data for the effect of number of modes and measured degrees of freedom (DoFs), and field data for reality tests.

A meticulous covariance adaptive Kalman filter for satellite attitude estimation

Aiming at the problems of model errors, non-Gaussian noise and measurement anomaly in the spacecraft attitude estimation system, this article proposes an improved adaptive filtering method based on covariance matching, which solves the problems of simultaneous dynamics model error and measurement model error in the attitude estimation system, and at the same time, effectively reduces the effects of non-Gaussian noise and large outlier situations occurring in the vector measurement sensor. Firstly, an adaptive filtering algorithm based on the innovation sequence estimation covariance is investigated under the framework of multiplicative extended Kalman filter (MEKF), which is used to correct process noise covariance, then the Sage–Husa adaptive Kalman filtering (SHAKF) method is combined to correct the measurement noise covariance, and finally the meticulous covariance adaptive multiplicative extended Kalman filter is designed. The proposed algorithm uses both innovation and SHAKF methods to correct the two covariance matrices simultaneously. Several attitude estimation simulation scenarios are set up to simulate the proposed algorithm in the presence of model errors, non-Gaussian noise, and large outlier. The simulation results demonstrate that the proposed algorithm outperforms the conventional algorithms in terms of estimation accuracy and robustness.

A Hybrid Gain Analog Offline EnKF for Paleoclimate Data Assimilation

AbstractFor Paleoclimate data assimilation (PDA), a hybrid gain analog offline ensemble Kalman filter (HGAOEnKF) is proposed. It keeps the benefits of the analog offline ensemble Kalman filter (AOEnKF) that constructs analog ensembles from existing climate simulations with joint information of the proxies. The analog ensembles can provide more accurate prior ensemble mean and “flow‐dependent” error covariances than randomly sampled ensembles. HGAOEnKF further incorporates the benefits of static prior error covariances that better capture large‐scale error correlations and mitigate sampling errors than the sample prior error covariances, through a hybrid gain approach within an ensemble framework. Observing system simulation experiments are conducted for various data assimilation methods, using ensemble simulations from the Community Earth System Model‐Last Millennium Ensemble Project. Results show that using the static prior error covariances estimated from a sufficiently large sample set is beneficial for the traditional offline ensemble Kalman filter (OEnKF) and AOEnKF. HGAOEnKF method is superior to the OEnKF and AOEnKF with and without static prior error covariances, especially for the reconstruction of extreme events. The advantages of HGAOEnKF over OEnKF and AOEnKF with and without static prior error covariances are persistent with varying sample sizes and presence of model errors.

Design Procedure for Motion Profiles with Sinusoidal Jerk for Vibration Reduction

High-speed motions performed by industrial machines can induce severe vibrations that degrade the positioning accuracy and efficiency. To address this issue, this paper proposes a novel motion profile design method utilizing a sinusoidal jerk model to generate fast and smooth motions with low vibrations. The expressions for the acceleration, velocity, and displacement were obtained through successive integrations of the continuous jerk profile. A minimum-time solution with actuator limits was formulated based on an analysis of the critical constraint conditions. Differing from previous studies, the current study introduces an analytical optimization procedure for the profile parameters to minimize both the motion duration and excitation frequency contents corresponding to the system pole. By examining the correlation between the input motion profiles and system responses, the conditions for vibration elimination were identified, highlighting the significance of specific time intervals in controlling the vibration amplitude. Numerical and experimental studies were conducted to validate the effectiveness of the proposed method. The comparative results illustrate that this method outperforms existing baseline techniques in terms of smoothness and vibration attenuation. The residual-vibration level and settling time are significantly reduced with the optimized sinusoidal jerk profile, even in the presence of modeling errors, contributing to higher productivity.

Adaptive Anti-Disturbance Control of Dissolved Oxygen in Circulating Water Culture Systems

In the three-dimensional culture model, the breeding basket of the culture area is symmetrical and it is important to control the dissolved oxygen in the symmetrical region to improve the culture efficiency. Practical engineering issues, such as the influence of flow rate, pH, water temperature, and biological oxygen consumption on the dissolved oxygen content in the circulating water culture system, must be considered along with the presence of modeling errors in the control model. The authors propose an adaptive anti-disturbance control strategy for dissolved oxygen that combines nonlinear disturbance observation with an adaptive sliding model control. Initially, a dynamic model for controlling dissolved oxygen in a recirculating water aquaculture system was developed. The model considers external disturbances like artificial oxygenation, abrupt changes in system flow, and variations in culture oxygen consumption. Secondly, to enhance the robustness and accuracy of controlling dissolved oxygen concentration, the paper introduces a nonlinear adaptive disturbance observer for real-time estimation and observation of external disturbances and system uncertainties. This is accompanied by a sliding-mode control-based adaptive anti-disturbance strategy. Lastly, the simulation results demonstrate that the control strategy proposed in this paper shows resistance to system uncertainties and unknown external disturbances. Furthermore, it reduces the model accuracy requirements for the controller and proves to be suitable for accurately controlling dissolved oxygen in circulating water systems.

Deep reinforcement learning based voltage control revisited

AbstractDeep Reinforcement Learning (DRL) has shown promise for voltage control in power systems due to its speed and model‐free nature. However, learning optimal control policies through trial and error on a real grid is infeasible due to the mission‐critical nature of power systems. Instead, DRL agents are typically trained on a simulator, which may not accurately represent the real grid. This discrepancy can lead to suboptimal control policies and raises concerns for power system operators. In this paper, we revisit the problem of RL‐based voltage control and investigate how model inaccuracies affect the performance of the DRL agent. Extensive numerical experiments are conducted to quantify the impact of model inaccuracies on learning outcomes. Specifically, techniques that enable the DRL agent are focused on learning robust policies that can still perform well in the presence of model errors. Furthermore, the impact of the agent's decisions on the overall system loss are analyzed to provide additional insight into the control problem. This work aims to address the concerns of power system operators and make DRL‐based voltage control more practical and reliable.

Observer-Based Power Factor Control for Matrix Converters in Dynamic Applications

Matrix Converters provide an efficient, compact and reliable alternative to the traditional AC/DC/AC converters in various applications including mining. A typical requirement for a converter is to maintain the grid-side power factor close to unity. To address this requirement, a novel power factor control method is proposed, which optimizes the grid-side power factor over the full power/frequency ranges of the prospective applications. A major novelty of this method is utilization of observers to establish a closed-loop mechanism for maintaining the optimal power factor in the presence of modelling errors and load changes. The paper presents a background study, description of the system model and the control strategy, and a detailed derivation of the proposed algorithm. The proposed method is validated by simulation and experimental results.

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.

Modeling Model Misspecification in Structural Equation Models

Structural equation models constrain mean vectors and covariance matrices and are frequently applied in the social sciences. Frequently, the structural equation model is misspecified to some extent. In many cases, researchers nevertheless intend to work with a misspecified target model of interest. In this article, a simultaneous statistical inference for sampling errors and model misspecification errors is discussed. A modified formula for the variance matrix of the parameter estimate is obtained by imposing a stochastic model for model errors and applying M-estimation theory. The presence of model errors is quantified in increased standard errors in parameter estimates. The proposed inference is illustrated with several analytical examples and an empirical application.

L0 Regularization parameter for sparse DOA estimation of coherent signals with modeling errors

Sparse methods have been recently introduced in Direction-Of-Arrival (DOA) estimation as an alternative to subspace-based methods and Maximum Likelihood (ML) techniques. This paper proposes a low complexity sparse L0-regularized method for DOA estimation of coherent signals in multipath environment, a scenario in which subspace-based methods fail. The first eigenvector of the covariance matrix is used as an observation and its statistics in the presence of modeling errors are derived. Thanks to those statistics, we present a theoretical statistical analysis of an interval in which the regularization parameter, usually empirically tuned, should stand. For a regularization parameter in this interval, the global solution of the L0-regularized problem coincides with the solution of the deterministic ML. An off-line selection of the regularization parameter is therefore proposed. Simulations confirm the relevance of this interval and of the proposed method.

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.

Bayesian Actor-Critic Wave Energy Converter Control With Modeling Errors

This paper presents a comparison of a Reinforcement-Learning (RL) based wave energy conversion controller against standard reactive damping and model predictive control (MPC) approaches, in the presence of modeling errors. Wave energy converters (WECs) are under the influence of many non-linear hydrodynamic forces, yet for ease and expediency, it is common to formulate linear WEC models and control laws. Therefore it is expected that significant modeling errors may be present, which may degrade model-based control performance. Model-free RL approaches to control may offer a significant advantage in robustness to modeling errors, in that the model is learned by the controller by experience. It is shown that, for an annual average sea state, RL-based controllers can outperform model-based control – reactive control and MPC – by 19% and 16%, respectively, when significant modeling error is present. Furthermore, compared to similar studies of RL-based control, the proposed model can reduce the training time from 8.4 hr to 1.5 hr.

Linear Quadratic Regulator Weighting Matrices for Output Covariance Assignment in Nonlinear Systems

A time-varying output covariance assignment problem in the presence of a stochastic disturbance is solved using finite-horizon optimal control formulation. It is shown that an assignment of time-varying output error covariance is possible in the presence of model error by utilizing a time-varying linear quadratic regulator controller with a class of output and control weighting sequences. This paper develops a systematic algorithm to calculate the sequence of such time-varying output weights that are further shown to be the Lagrange multipliers associated with the covariance constraints. A short horizon attitude control problem with stringent covariance constraints and a more nonlinear example concerning a low-thrust interplanetary maneuver are solved to demonstrate the utility of the proposed approach. Numerical results offer a degree of optimism about the broad applicability of the time-varying covariance assignment approach to solve guidance and control problems associated with nonlinear dynamic systems.

Evaluation of machine learning techniques for forecast uncertainty quantification

AbstractEnsemble forecasting is, so far, the most successful approach to produce relevant forecasts with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture and quantify different sources of uncertainty, particularly those associated with model errors. In this article we perform toy‐model and state‐of‐the‐art model experiments to analyze to what extent artificial neural networks (ANNs) are able to model the different sources of uncertainty present in a forecast. In particular, those associated with the accuracy of the initial conditions and those introduced by the model error. We also compare different training strategies: one based on a direct training using the mean and spread of an ensemble forecast as target, and the other ones rely on an indirect training strategy using an analyzed state as target in which the uncertainty is implicitly learned from the data. Experiments using the Lorenz'96 model show that the ANNs are able to emulate some of the properties of ensemble forecasts like the filtering of the most unpredictable modes and a state‐dependent quantification of the forecast uncertainty. Moreover, ANNs provide a reliable estimation of the forecast uncertainty in the presence of model error. Preliminary experiments conducted with a state‐of‐the‐art forecasting system also confirm the ability of ANNs to produce a reliable quantification of the forecast uncertainty.

Exponential Control Lyapunov-Barrier Function Using a Filtering-Based Concurrent Learning Adaptive Approach

The state-of-the-art quadratic-program-based control Lyapunov-barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in an optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause violation or restriction of safety-critical constraints. This article presents an adaptive QP-CLBF approach for a class of nonlinear systems in the presence of parameter uncertainties with an unknown control coefficient. We begin by presenting a filtering-based concurrent learning (FCL) adaptive technique to guarantee simultaneous exponential convergence of system parameters and control coefficient. The proposed FCL extends and encompasses the baseline concurrent learning technique, which was developed to achieve exponential convergence of either system parameters exclusively or control coefficient while relying on the estimation of state derivatives using numerical smoothing. The proposed FCL adaptive method is then unified with a modified version of QP-CLBF to achieve exponential convergence of system parameters, control coefficient, and control Lyapunov and control barrier functions while establishing safety with the largest safe region. Under this unification, all results are exponential in the presence of modeling error without the need for numerical methods to estimate state derivatives. This is formally proven by employing a Lyapunov argument. Simulations are finally carried out to validate the theoretical results.

Sequential and batch data assimilation approaches to cope with groundwater model error: An empirical evaluation

Groundwater model data assimilation (DA) aims to reduce uncertainty in simulated outcomes of interest to resource management while minimizing the potential for predictive bias. Sequential DA, which can estimate model states along with properties and stresses dynamically in time, offers a potentially powerful alternative to batch DA (i.e., history matching) for reducing bias in decision-relevant predictions in the presence of incorrect model structure and/or processes. This study evaluates the ability of batch and sequential DA approaches to history match and forecast simulated quantities in the presence of model error using a novel ensemble-based paired complex–simple approach that enables the incorporation of stochastic uncertainty and a statistical evaluation of predictive bias. Our findings have implications for groundwater decision support modeling as they underscore the pitfalls of fixing parameters and forcing variables a priori and present a proof of concept for using adjustable model states to cope with model error.

Quantifying uncertainty for structural damage identification in the presence of model errors from a deterministic sensitivity-based regime

Structural damage identification is often recast as the procedure to find the damage parameters from the measured data and the prescribed structural model. However, noises are encountered inevitably in practical tests and this essentially introduces uncertainty into damage identification. Most of the existed damage identification methods are deterministic and unable to provide the uncertainty information. In this paper, the widely-used sensitivity approach, though being deterministic, is further explored and extended for uncertainty quantification. The key lies in the equivalence between Tikhonov regularization in the sensitivity approach and the prior distribution in Bayesian inference. Motivated by this equivalence, a new uncertainty quantification approach is proposed where the uncertainty information is directly drawn from the deterministic sensitivity-based regime. As is noteworthy, the proposed approach can quickly quantify the uncertainty even when the probabilistic information of the measurement noise and the prior distribution are unknown. Furthermore, considering the model errors, a measurement-changes-correction strategy is adopted where the measured data is simply corrected by pre-post measurement changes and by this way, uncertainty is quantified in the same sensitivity-based regime. Numerical examples and an experimental case are studied to verify the effectiveness of the proposed approach for uncertainty quantification in structural damage identification.

Three-dimensional nonlinear trajectory tracking control based on adaptive sliding mode

A novel three-dimensional adaptive sliding mode controller (ASMC) is proposed for the nonlinear three-dimensional trajectory tracking of missiles. Firstly, the three-dimensional trajectory tracking problem is decomposed into the pitch channel and the yaw channel, and the trajectory tracking control model of each channel is established, respectively. Secondly, in the design process of the controller, a fast non-singular terminal sliding mode with finite-time convergence characteristics that can avoid singularities and a novel adaptive reaching law that can avoid chattering and accelerate convergence are introduced into the two channels. Thirdly, the Lyapunov stability analysis shows that the adaptive sliding mode tracking controller proposed in this paper can guarantee the rapid convergence and stability of the closed-loop system in the presence of modeling errors. Finally, simulation results show that the controller can effectively complete trajectory tracking under the influence of the wind disturbance and mismatched disturbances.