Effect Of Modeling Errors Research Articles

Estimation of single plane unbalance parameters of a rotor-bearing system using Kalman filtering based force estimation technique

This paper proposes a model-based method to estimate single plane unbalance parameters (amplitude and phase angle) in a rotor using Kalman filter and recursive least square based input force estimation technique. Kalman filter based input force estimation technique requires state-space model and response measurements. A modified system equivalent reduction expansion process (SEREP) technique is employed to obtain a reduced-order model of the rotor system so that limited response measurements can be used. The method is demonstrated using numerical simulations on a rotor-disk-bearing system. Results are presented for different measurement sets including displacement, velocity, and rotational response. Effects of measurement noise level, filter parameters (process noise covariance and forgetting factor), and modeling error are also presented and it is observed that the unbalance parameter estimation is robust with respect to measurement noise.

Sensitivity-based damage identification method for structures exposed to ground excitation

The purpose of this paper is to present a sensitivity-based finite element model (FEM) updating method using earthquake displacement response in the frequency domain and the frequency response function of structure due to ground excitation. The obtained sensitivity equation is solved by linear least square method through defining constraints on the design variables. Numerical examples of a plane truss and a plane frame support the fact that the proposed method is capable of reliable damage detection. In order to assess the effects of measurement and mass modelling errors on achieved results, model updating is conducted by adding random errors to numerically extracted displacement response and assigned mass properties. The issue of underlying soil foundation influences on obtained results is discussed and the proposed formulation is extended to more accurately capture the soil–structure behaviour. Results indicate that the proposed method is capable of identifying damage properties under different soil conditions with acceptable precision.

A novel post-processing scheme for two-dimensional electrical impedance tomography based on artificial neural networks.

ObjectiveElectrical Impedance Tomography (EIT) is a powerful non-invasive technique for imaging applications. The goal is to estimate the electrical properties of living tissues by measuring the potential at the boundary of the domain. Being safe with respect to patient health, non-invasive, and having no known hazards, EIT is an attractive and promising technology. However, it suffers from a particular technical difficulty, which consists of solving a nonlinear inverse problem in real time. Several nonlinear approaches have been proposed as a replacement for the linear solver, but in practice very few are capable of stable, high-quality, and real-time EIT imaging because of their very low robustness to errors and inaccurate modeling, or because they require considerable computational effort.MethodsIn this paper, a post-processing technique based on an artificial neural network (ANN) is proposed to obtain a nonlinear solution to the inverse problem, starting from a linear solution. While common reconstruction methods based on ANNs estimate the solution directly from the measured data, the method proposed here enhances the solution obtained from a linear solver.ConclusionApplying a linear reconstruction algorithm before applying an ANN reduces the effects of noise and modeling errors. Hence, this approach significantly reduces the error associated with solving 2D inverse problems using machine-learning-based algorithms.SignificanceThis work presents radical enhancements in the stability of nonlinear methods for biomedical EIT applications.

Attitude control design for reusable launch vehicles using adaptive fuzzy control with compensation controller

This paper describes the design of attitude control for reusable launch vehicles during reentry phase using adaptive fuzzy control strategy with compensation controller that assures a stable and accurate attitude tracking despite having parameter uncertainties and external disturbances in the plant model. Firstly, the six-degrees-of-freedom dynamic model of the reusable launch vehicles is established, followed by a model transformation of rotational and kinematic dynamic equations, which results in a strict-feedback form attitude control system. Secondly, a fuzzy logic system combined with the adaptive technique is employed to model the system uncertainty term online. Then an attitude tracking controller based on adaptive fuzzy control approach is designed to assure tracking of guidance commands. Furthermore, to attenuate the adverse effects of fuzzy modeling errors on the control performance and system stability, a compensation controller is introduced to the control strategy. In addition, the stability of the closed-loop system is proved by using the Lyapunov theory, and the attitude tracking error converges to a small neighborhood of the origin. Finally, the simulation results and discussions are provided to verify the effectiveness of the proposed control strategy in tracking the guidance commands.

Characterizing the impact of model error in hydrologic time series recovery inverse problems

Hydrogeologic models are commonly over-smoothed relative to reality, owing to the difficulty of obtaining accurate high-resolution information about the subsurface. When used in an inversion context, such models may introduce systematic biases which cannot be encapsulated by an unbiased "observation noise" term of the type assumed by standard regularization theory and typical Bayesian formulations. Despite its importance, model error is difficult to encapsulate systematically and is often neglected. Here, model error is considered for a hydrogeologically important class of inverse problems that includes interpretation of hydraulic transients and contaminant source history inference: reconstruction of a time series that has been convolved against a transfer function (i.e., impulse response) that is only approximately known. Using established harmonic theory along with two results established here regarding triangular Toeplitz matrices, upper and lower error bounds are derived for the effect of systematic model error on time series recovery for both well-determined and over-determined inverse problems. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. A possible diagnostic criterion for blind transfer function characterization is also uncovered.

Evaluating the effects of modeling errors for isolated finite three-dimensional targets

Optical three-dimensional (3-D) nanostructure metrology utilizes a model-based metrology approach to determine critical dimensions (CDs) that are well below the inspection wavelength. Our project at the National Institute of Standards and Technology is evaluating how to attain key CD and shape parameters from engineered in-die capable metrology targets. More specifically, the quantities of interest are determined by varying the input parameters for a physical model until the simulations agree with the actual measurements within acceptable error bounds. As in most applications, establishing a reasonable balance between model accuracy and time efficiency is a complicated task. A well-established simplification is to model the intrinsically finite 3-D nanostructures as either periodic or infinite in one direction, reducing the computationally expensive 3-D simulations to usually less complex two-dimensional (2-D) problems. Systematic errors caused by this simplified model can directly influence the fitting of the model to the measurement data and are expected to become more apparent with decreasing lengths of the structures. We identify these effects using selected simulation results and present experimental setups, e.g., illumination numerical apertures and focal ranges, that can increase the validity of the 2-D approach.

Effect of unrepresented model errors on estimated soil hydraulic material properties

Abstract. Unrepresented model errors influence the estimation of effective soil hydraulic material properties. As the required model complexity for a consistent description of the measurement data is application dependent and unknown a priori, we implemented a structural error analysis based on the inversion of increasingly complex models. We show that the method can indicate unrepresented model errors and quantify their effects on the resulting material properties. To this end, a complicated 2-D subsurface architecture (ASSESS) was forced with a fluctuating groundwater table while time domain reflectometry (TDR) and hydraulic potential measurement devices monitored the hydraulic state. In this work, we analyze the quantitative effect of unrepresented (i) sensor position uncertainty, (ii) small scale-heterogeneity, and (iii) 2-D flow phenomena on estimated soil hydraulic material properties with a 1-D and a 2-D study. The results of these studies demonstrate three main points: (i) the fewer sensors are available per material, the larger is the effect of unrepresented model errors on the resulting material properties. (ii) The 1-D study yields biased parameters due to unrepresented lateral flow. (iii) Representing and estimating sensor positions as well as small-scale heterogeneity decreased the mean absolute error of the volumetric water content data by more than a factor of 2 to 0. 004.

Robust Computerized Ionospheric Tomography Based on Spaceborne Polarimetric SAR Data

Due to the dispersion nature of the ionosphere, the spaceborne polarimetric synthetic aperture radar (PolSAR) systems at L or lower frequencies will generally experience more severe effects in comparison to frequencies above L-band. Correspondingly, according to the mechanism of how ionosphere destroys the scattering matrix of PolSAR data, the total electron content (TEC), an important input in computerized ionospheric tomography (CIT), can be retrieved by model inversion. Thus, this paper presents a technique of CIT based on the spaceborne PolSAR data. The CIT technique is a means to obtain the spatial distribution of ionospheric electron density from the TEC values. Because of the high spatial resolution of spaceborne SAR, the kilometer-scale TEC information can be obtained by the PolSAR data where such resolution was previously inaccessible. The spatial distribution of ionospheric electron density with high resolution can therefore be obtained. In addition, the potential limitation of previous CIT based on SAR imaging information is the difficulty in requiring strong point targets with high signal-to-clutter (SCR) ratio in scenes. In contrast, the CIT reconstruction based on scattering matrix information can be easily realized without aforementioned special requirements. In this paper, by using the simulated data of the Advanced Land Observing Satellite (ALOS) Phased-Array L-band Synthetic Aperture Radar (PALSAR) full-pol data, the International Reference Ionosphere (IRI) 2007, and the International Geomagnetic Reference Field (IGRF) models, the reconstruction of ionospheric electron density distribution is first simulated to validate the feasibility of the proposed technique. Then, possible effects of SAR system and model errors on the reconstruction results are also simulated and analyzed to show the applicability.

Effects of model error on cardiac electrical wave state reconstruction using data assimilation.

Reentrant electrical scroll waves have been shown to underlie many cardiac arrhythmias, but the inability to observe locations away from the heart surfaces and the restriction of observations to only one or two state variables have made understanding arrhythmia mechanisms challenging. Recently, we showed that data assimilation from spatiotemporally sparse surrogate observations could be used to reconstruct a reliable time series of state estimates of reentrant cardiac electrical waves including unobserved variables in one and three spatial dimensions. However, real cardiac tissue is unlikely to be described accurately by mathematical models because of errors in model formulation and parameterization as well as intrinsic but poorly described spatial heterogeneity of electrophysiological properties in the heart. Here, we extend our previous work to assess how model error affects the accuracy of cardiac state estimates achieved using data assimilation with the Local Ensemble Transform Kalman Filter. We focus on one-dimensional states of discordant alternans characterized by significant wavelength oscillations. We demonstrate that data assimilation can provide high-quality estimates under a wide range of model error conditions, ranging from varying one or more parameter values to using an entirely different model to generate the truth state. We illustrate how multiplicative and additive inflation can be used to reduce error in the state estimates. Even when the truth state contains underlying spatial heterogeneity, we show that using a homogeneous model in the data assimilation algorithm can achieve good results. Overall, we find data assimilation to be a robust approach for reconstructing complex cardiac electrical states corresponding to arrhythmias even in the presence of model error.

On the “spring predictability barrier” for strong El Niño events as derived from an intermediate coupled model ensemble prediction system

Using predictions for the sea surface temperature anomaly (SSTA) generated by an intermediate coupled model (ICM) ensemble prediction system (EPS), we first explore the “spring predictability barrier” (SPB) problem for the 2015/16 strong El Nino event from the perspective of error growth. By analyzing the growth tendency of the prediction errors for ensemble forecast members, we conclude that the prediction errors for the 2015/16 El Nino event tended to show a distinct season-dependent evolution, with prominent growth in spring and/or the beginning of the summer. This finding indicates that the predictions for the 2015/16 El Nino occurred a significant SPB phenomenon. We show that the SPB occurred in the 2015/16 El Nino predictions did not arise because of the uncertainties in the initial conditions but because of model errors. As such, the mean of ensemble forecast members filtered the effect of model errors and weakened the effect of the SPB, ultimately reducing the prediction errors for the 2015/16 El Nino event. By investigating the model errors represented by the tendency errors for the SSTA component, we demonstrate the prominent features of the tendency errors that often cause an SPB for the 2015/16 El Nino event and explain why the 2015/16 El Nino was under-predicted by the ICM EPS. Moreover, we reveal the typical feature of the tendency errors that cause not only a significant SPB but also an aggressively large prediction error. The feature is that the tendency errors present a zonal dipolar pattern with the west poles of positive anomalies in the equatorial western Pacific and the east poles of negative anomalies in the equatorial eastern Pacific. This tendency error bears great similarities with that of the most sensitive nonlinear forcing singular vector (NFSV)-tendency errors reported by Duan et al. and demonstrates the existence of an NFSV tendency error in realistic predictions. For other strong El Nino events, such as those that occurred in 1982/83 and 1997/98, we obtain the tendency errors of the NFSV structure, which cause a significant SPB and yield a much larger prediction error. These results suggest that the forecast skill of the ICM EPS for strong El Nino events could be greatly enhanced by using the NFSV-like tendency error to correct the model.

Research on Adaptive H Control of Tank Gun Control System Based on Wavelet Neural Network Identification

Focusing on the unknown plant model, an adaptive wavelet neural network (WNN) identification robust control scheme of tank gun control system was proposed. According to input and output data, the unknown tank gun control system model parts were reconstructed using wavelet neural network (WNN). The parameters of online adaptive regulating law and output control laws were designed in the sense of Lyapunov, so the tank gun control system achieves dynamic decoupling. In order to reduce the effect of modeling errors and external disturbance, sliding mode variable structure control (SMVSC) was integrated into the adaptive control algorithm, and the robust compensator was added in order to achieve a robust tracking performance. Further the robust and steady performance of gun control system was analyzed. The results showed that wavelet neural network can be a good approximation nonlinear function, the system was insensitive to the parameters uncertainties and load disturbance and had shown a good track performance.

Assessing the value of information in residential building simulation: Comparing simulated and actual building loads at the circuit level

Building energy simulation tools are now being used in a number of new roles such as building operation optimization, performance verification for efficiency programs, and – recently – building energy code analysis, design, and compliance verification in the residential sector. But increasing numbers of studies show major differences between the results of these simulations and the actual measured performance of the buildings they are intended to model. The accuracy and calibration of building simulations have been studied extensively in the commercial sector, but these new applications have created a need to better understand the performance of home energy simulations.In this paper, we assess the ability of the DOE’s EnergyPlus software to simulate the energy consumption of 106 homes using audit records, homeowner survey records, and occupancy estimates taken from monitored data. We compare the results of these simulations to device-level monitored data from the actual homes to provide a first measure of the accuracy of the EnergyPlus condensing unit, central air supply fan, and other energy consumption model estimates in a large number of homes. We then conduct sensitivity analysis to observe which physical and behavioral characteristics of the homes and homeowners most influence the accuracy of the modeling.Results show that EnergyPlus models do not accurately or consistently estimate occupied whole-home energy consumption. While some models accurately predict annual energy consumption to within 1% of measured data, none of the modeled homes meet ASHRAE criteria for a calibrated model when looking at hourly interval data. The majority of this error is due to appliance and lighting energy overestimates, followed by AC condensing unit use. These inaccuracies are due to factors such as occupant behaviors and differences in appliance and lighting stocks which are not well-captured in traditional energy audit reports. We identify a number of factors which must be specified for an accurate model, and others where using a default value will produce a similar result.The use of building simulation tools reflects a shift from a component-focused approach to a systems approach to residential code analysis and compliance verification that will serve to better identify and deploy efficiency measures in homes. By better understanding the limitations of home energy simulations and adopting strategies to mitigate the effects of model errors, simulation models can serve as valuable decision making tools in the residential sector.

Estimation of ballistic coefficients of space debris using the ratios between different objects

This paper proposes a new method to estimate the ballistic coefficient (BC) of low earth orbit space debris. The data sources are the historical two-line elements (TLEs). Since the secular variation of semi-major axes is mainly caused by the drag perturbation for space objects with perigee altitude below 600km, the ballistic coefficients are estimated based on variation of the mean semi-major axes derived from the TLEs. However, the approximate parameters used in the calculation have error, especially when the upper atmosphere densities are difficult to obtain and always estimated by empirical model. The proportional errors of the approximate parameters are cancelled out in the form of ratios, greatly mitigating the effects of model error. This method has been also been validated for space objects with perigee altitude higher than 600km. The relative errors of estimated BC values from the new method are significantly smaller than those from the direct estimation methods used in numerical experiments. The estimated BC values are used for the prediction of the semi-major axes, and good performance is obtained. This process is also a feasible method for prediction over a long period of time without an orbital propagator model.

An Empirical Cumulative Density Function Approach to Defining Summary NWP Forecast Assessment Metrics

Abstract The empirical cumulative density function (ECDF) approach can be used to combine multiple, diverse assessment metrics into summary assessment metrics (SAMs) to analyze the results of impact experiments and preoperational implementation testing with numerical weather prediction (NWP) models. The main advantages of the ECDF approach are that it is amenable to statistical significance testing and produces results that are easy to interpret because the SAMs for various subsets tend to vary smoothly and in a consistent manner. In addition, the ECDF approach can be applied in various contexts thanks to the flexibility allowed in the definition of the reference sample. The interpretations of the examples presented here of the impact of potential future data gaps are consistent with previously reported conclusions. An interesting finding is that the impact of observations decreases with increasing forecast time. This is interpreted as being caused by the masking effect of NWP model errors increasing to become the dominant source of forecast error.

Optimal fuzzy control of exponential synchronisation via genetic algorithm

ABSTRACTIn this study, a novel approach via GA-based fuzzy control is proposed to realize the exponential optimal H∞ synchronisation of MTDC systems. A robustness design of model-based fuzzy control is first presented to overcome the effect of modelling errors between the MTDC systems and T-S fuzzy models. Next, a delay-dependent exponential stability criterion is derived in terms of Lyapunov's direct method to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are reformulated into LMIs. According to the LMIs, a fuzzy controller is then synthesised to exponentially stabilise the error systems. Moreover, the capability of GA in random search for near-optimal solutions, the lower and upper bounds of the search space based on the feedback gains via LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers to speed up the synchronisation. Additionally, an IGA was proposed to overcome both the shortcomings of premature convergence of GA and local search. According to the IGA, a fuzzy controller is synthesised not only to realise the exponential synchronisation but also to achieve the optimal H∞ performance by minimising the disturbance attenuation level.

Measurement system design for civil infrastructure using expected utility

For system identification, most sensor-placement strategies are based on the minimization of the model-parameter uncertainty. However, reducing the uncertainty in remaining-life prognosis of structures is often more relevant. This paper proposes an optimization strategy using utility theory and probabilistic behavior prognoses based on model falsification to support decisions related to monitoring interventions. This approach, illustrated by the full-scale case study of a bridge, allows quantification of the expected utility of measurement systems while also indicating the profitability of monitoring actions. In addition, this approach is able to determine when the expected performance of monitoring configurations is reduced due to over-instrumentation. The use of model falsification for system identification allows for explicit inclusion of engineering heuristics in this knowledge intensive task while also offering robustness to effects of systematic modeling errors that are associated with idealization of complex civil structures.

IOD-related optimal initial errors and optimal precursors for IOD predictions from reanalysis data

This study explored the spatial patterns of winter predictability barrier (WPB)-related optimal initial errors and optimal precursors for positive Indian Ocean dipole (IOD) events, and the associated physical mechanisms for their developments were analyzed using the Simple Ocean Data Assimilation dataset. Without consideration of the effects of model errors on “predictions,” it was assumed that different “predictions” are caused by different initial conditions. The two types of WPB-related optimal initial errors are almost opposite for the start months of July (–1) and July (0), although they both present a west-east dipole pattern in the tropical Indian Ocean, with the maximum errors located at the thermocline depth. Bjerknes feedback and ocean waves play important roles in the growth of prediction errors. These two physical mechanisms compete during July–December and ocean waves dominate during January–June. The spatial patterns of optimal precursors and the physical mechanisms for their developments are similar to those of WPB-related optimal initial errors. It is worth noting that large values of WPB-related optimal initial errors and optimal precursors are concentrated within a few locations, which probably represent the sensitive areas of targeted observations for positive IOD events. The great similarities between WPB-related optimal initial errors and optimal precursors suggest that were intensive observations performed over these areas, this would not only reduce initial errors and thus, prediction errors, but it would also permit the detection of the signal of IOD events in advance, greatly improving the forecast skill of positive IOD events.

Probabilistic damage identification of a designed 9-story building using modal data in the presence of modeling errors

Validity and accuracy of model based identification techniques such as linear finite element (FE) model updating are sensitive to modeling errors. Models used for the design and performance assessment of civil structures often contain large modeling errors for certain frequency ranges of response. In other words, modeling errors have unequal effects on different vibration modes of structures. Therefore, the performance of FE model updating for damage identification is sensitive to the type and the subset of data used and to the residual weight factors. This study proposes a process to mitigate the effects of modeling errors by selecting the optimal subset of modes and the optimal modal residual weights. Multiple model updating classes are defined based on different subsets of modes and different weight factors. Structural damage is then identified using Bayesian model class selection and model averaging techniques over the results of all the considered model updating classes. In addition, a new likelihood function is defined to allow damage identification without the need for calibrating a reference FE model. Performance of the proposed damage identification process and the new likelihood function is evaluated numerically at multiple levels of modeling errors and structural damage on the SAC 9-story steel moment frame. It is shown that the structural damages can be identified with negligible bias when the proposed likelihood and updating process is implemented.

An Idealized Study of Coupled Atmosphere–Ocean 4D-Var in the Presence of Model Error

AbstractAtmosphere-only and ocean-only variational data assimilation (DA) schemes are able to use window lengths that are optimal for the error growth rate, nonlinearity, and observation density of the respective systems. Typical window lengths are 6–12 h for the atmosphere and 2–10 days for the ocean. However, in the implementation of coupled DA schemes it has been necessary to match the window length of the ocean to that of the atmosphere, which may potentially sacrifice the accuracy of the ocean analysis in order to provide a more balanced coupled state. This paper investigates how extending the window length in the presence of model error affects both the analysis of the coupled state and the initialized forecast when using coupled DA with differing degrees of coupling.Results are illustrated using an idealized single-column model of the coupled atmosphere–ocean system. It is found that the analysis error from an uncoupled DA scheme can be smaller than that from a coupled analysis at the initial time, due to faster error growth in the coupled system. However, this does not necessarily lead to a more accurate forecast due to imbalances in the coupled state. Instead coupled DA is more able to update the initial state to reduce the impact of the model error on the accuracy of the forecast. The effect of model error is potentially most detrimental in the weakly coupled formulation due to the inconsistency between the coupled model used in the outer loop and uncoupled models used in the inner loop.

Discrete-Time Circular Walking Pattern for Biped Robots

When biped robots make turns fast, they may fall due to the action of centrifugal force. This is why one needs to consider the Zero Moment Point (ZMP) equations with respect to cylindrical coordinate system. Those ZMP equations are, however, so coupled and highly nonlinear even for the simple inverted pendulum model that it is hard to find a closed-form solution. Therefore, in this paper, they have been converted through temporal discretization to difference equations that admit numerical solution by most on-board computers. Thus-obtained walking patterns have been characterized and applied to several cases of different speed for comparison purposes. In so doing, the steady patterns have been blended with a type of transitional patterns to change the walking speed in the beginning and/or mid course of walking. Finally, those combined patterns have been put to test on a multi-body robot model by ADAMS®. Test results show that the robot could walk along a sample circular path as predicted at rapid speeds despite some modeling error, distributed mass and ground contact effects, validating efficacy of the suggested approach.