Initial Condition Errors Research Articles

A Hybrid Model Algorithm for Hypersonic Glide Vehicle Maneuver Tracking Based on the Aerodynamic Model

In order to solve the problem of an uncertain initial state and big errors for hypersonic glide vehicle (HGV) tracking, a hybrid model algorithm is proposed by combining a single model algorithm with a multiple model algorithm. To develop the tracking algorithm with the Cubature Kalman filter, in every model filter the process equation is established based on the HGV aerodynamic model and the measurement equation is established based on the radar measurement principle. The proposed hybrid model algorithm is developed by using the multiple model algorithm in the initial tracking stage and using the single model algorithm in the stable tracking stage, and they are divided by a proposed parameter. The former can avoid divergence and reduce the errors caused by the uncertain initial state. The latter can track the HGV at higher accuracy. The simulation indicates that the proposed hybrid model has high speed accuracy in the whole tracking stage and high position accuracy in the stable tracking stage. The average position root mean square error (RMSE) using the hybrid model algorithm is almost the same as that using the single model algorithm but the average speed RMSE using the single model algorithm is about 30% greater than that using the hybrid model algorithm. In a system for defending the HGV, the speed accuracy has more effect on the trajectory prediction as time goes on. Thus, the hybrid model algorithm is an engineering algorithm for HGVs with high accuracy. In future research, the hybrid model algorithm will be studied for general maneuvering target tracking.

Improved forecasts of winter weather extremes over midlatitudes with extra Arctic observations

Recent cold winter extremes over Eurasia and North America have been considered to be a consequence of a warming Arctic. More accurate weather forecasts are required to reduce human and socioeconomic damages associated with severe winters. However, the sparse observing network over the Arctic brings errors in initializing a weather prediction model, which might impact accuracy of prediction results at midlatitudes. Here we show that additional Arctic radiosonde observations from the Norwegian young sea ICE cruise project 2015 drifting ice camps and existing land stations during winter improved forecast skill and reduced uncertainties of weather extremes at midlatitudes of the Northern Hemisphere. For two winter storms over East Asia and North America in February 2015, ensemble forecast experiments were performed with initial conditions taken from an ensemble atmospheric reanalysis in which the observation data were assimilated. The observations reduced errors in initial conditions in the upper troposphere over the Arctic region, yielding more precise prediction of the locations and strengths of upper troughs and surface synoptic disturbances. Errors and uncertainties of predicted upper troughs at midlatitudes would be brought with upper level high potential vorticity (PV) intruding southward from the observed Arctic region. This is because the PV contained a ‘‘signal’’ of the additional Arctic observations as it moved along an isentropic surface. This suggests that a coordinated sustainable Arctic observing network would be effective not only for regional weather services but also for reducing weather risks in locations distant from the Arctic.

The convergence analysis of P-type iterative learning control with initial state error for some fractional system

In this paper, the convergence of iterative learning control with initial state error for some fractional equation is studied. According to the Laplace transform and the M-L function, the concept of mild solutions is showed. The sufficient conditions of convergence for the open and closed P-type iterative learning control are obtained. Some examples are given to illustrate our main results.

Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity

We introduce a method for quantifying the predictability of the event that the evolution of a deterministic dynamical system enters a specific subset of state space at a given lead time. The main idea is to study the distribution of finite-time growth rates of errors in initial conditions along the attractor of the system. The predictability of an event is measured by comparing error growth rates for initial conditions leading to that event with all possible growth rates. We illustrate the method by studying the predictability of extreme amplitudes of traveling waves in the Lorenz-96 model. Our numerical experiments show that the predictability of extremes is affected by several routes to chaos in a different way. In a scenario involving intermittency due to a periodic attractor disappearing through a saddle-node bifurcation we find that extremes become better predictable as the intensity of the event increases. However, in a similar intermittency scenario involving the disappearance of a 2-torus attractor we find that extremes are just as predictable as nonextremes. Finally, we study a scenario which involves a 3-torus attractor in which case the predictability of extremes depends nonmonotonically on the prediction lead time.

Dynamic Learning from Adaptive Neural Control of Uncertain Robots with Guaranteed Full-State Tracking Precision

A dynamic learning method is developed for an uncertain n-link robot with unknown system dynamics, achieving predefined performance attributes on the link angular position and velocity tracking errors. For a known nonsingular initial robotic condition, performance functions and unconstrained transformation errors are employed to prevent the violation of the full-state tracking error constraints. By combining two independent Lyapunov functions and radial basis function (RBF) neural network (NN) approximator, a novel and simple adaptive neural control scheme is proposed for the dynamics of the unconstrained transformation errors, which guarantees uniformly ultimate boundedness of all the signals in the closed-loop system. In the steady-state control process, RBF NNs are verified to satisfy the partial persistent excitation (PE) condition. Subsequently, an appropriate state transformation is adopted to achieve the accurate convergence of neural weight estimates. The corresponding experienced knowledge on unknown robotic dynamics is stored in NNs with constant neural weight values. Using the stored knowledge, a static neural learning controller is developed to improve the full-state tracking performance. A comparative simulation study on a 2-link robot illustrates the effectiveness of the proposed scheme.

Decentralized iterative learning control for large-scale linear discrete-time systems with fixed initial state errors

AbstractThis article addresses the problem of iterative learning control for large-scale linear discrete-time systems with fixed initial state errors. And two kinds of the system structures are considered in this article, one of them is the system whose input signal's dimension is less than or equal to the output dimension and the other one is the system whose output signal's dimension is less than or equal to the input dimension. According to the characteristics of the systems, decentralized learning schemes are proposed for such large-scale linear discrete-time systems, and the corresponding discrete-time output limiting trajectories under the action of the decentralized learning schemes are presented. The proposed controller of each subsystem only relies on local output variables without any information exchanging with other subsystems. Using the contraction mapping method, we show that the schemes can guarantee the output of each subsystem to converge uniformly to the corresponding discrete-time output limiting trajectory over all the given discrete-time points within a finite time interval. Furthermore, the decentralized initial rectifying strategies are applied to the large-scale linear discrete-time systems for eliminating the effect of the fixed initial state errors, and the corresponding decentralized learning schemes are established. When the learning schemes are applied to the large-scale linear discrete-time systems, the output of each subsystem can converge to the desired reference trajectory of each subsystem over all the given discrete-time points within a pre-specified interval no matter what value the fixed state error takes. Simulation examples illustrate the effectiveness of the proposed method.

Flyback CCM inverter for AC module applications: iterative learning control and convergence analysis

ABSTRACTThis paper presents an iterative learning controller (ILC) for an interleaved flyback inverter operating in continuous conduction mode (CCM). The flyback CCM inverter features small output ripple current, high efficiency, and low cost, and hence it is well suited for photovoltaic power applications. However, it exhibits the non-minimum phase behaviour, because its transfer function from control duty to output current has the right-half-plane (RHP) zero. Moreover, the flyback CCM inverter suffers from the time-varying grid voltage disturbance. Thus, conventional control scheme results in inaccurate output tracking. To overcome these problems, the ILC is first developed and applied to the flyback inverter operating in CCM. The ILC makes use of both predictive and current learning terms which help the system output to converge to the reference trajectory. We take into account the nonlinear averaged model and use it to construct the proposed controller. It is proven that the system output globally converges to the reference trajectory in the absence of state disturbances, output noises, or initial state errors. Numerical simulations are performed to validate the proposed control scheme, and experiments using 400-W AC module prototype are carried out to demonstrate its practical feasibility.

Improved Stator Flux Estimation for Direct Torque Control of Induction Motor Drives

<p>Stator flux estimation using voltage model is basically the integration of the induced stator back electromotive force (emf) signal. In practical implementation the pure integration is replaced by a low pass filter to avoid the DC drift and saturation problems at the integrator output because of the initial condition error and the inevitable DC components in the back emf signal. However, the low pass filter introduces errors in the estimated stator flux which are significant at frequencies near or lower than the cutoff frequency. Also the DC components in the back emf signal are amplified at the low pass filter output by a factor equals to . Therefore, different integration algorithms have been proposed to improve the stator flux estimation at steady state and transient conditions. In this paper a new algorithm for stator flux estimation is proposed for direct torque control (DTC) of induction motor drives. The proposed algorithm is composed of a second order high pass filter and an integrator which can effectively eliminates the effect of the error initial condition and the DC components. The amplitude and phase errors compensation algorithm is selected such that the steady state frequency response amplitude and phase angle are equivalent to that of the pure integrator and the multiplication and division by stator frequency are avoided. Also the cutoff frequency selection is improved; even small value can filter out the DC components in the back emf signal. The simulation results show the improved performance of the induction motor direct torque control drive with the proposed stator flux estimation algorithm. The simulation results are verified by the experimental results.</p>

Prediction and predictability of land and atmosphere initialized CCSM4 climate forecasts over North America

AbstractSubseasonal‐to‐seasonal prediction is influenced by slowly varying surface fields such as sea surface temperature (SST) and soil moisture. Fully coupled hindcasts were recently completed in the Community Climate System Model version 4.0 (CCSM4) as part of the North American Multi‐Model Ensemble project. Using similar land and atmosphere initialization strategies, but with prescribed climatological SSTs, we attempt to determine the isolated impact of combined observed atmosphere and land initialization and of observed atmosphere initialization on monthly precipitation and 2 m temperature prediction‐estimated skill (i.e., skill assessed without SST variability) and predictability on monthly time scales. CCSM4 has been cited as having low land‐atmosphere coupling, and while combined land and atmosphere initialization significantly increases the estimated skill of precipitation and temperature in the first month after initialization (lead 0), land initialization influence is weak, consistent with low land‐atmosphere coupling in CCSM4. In contrast, atmosphere initialization is a stronger contributor to prediction skill and predictability. We find stronger influence of land and atmosphere initialization on precipitation in CCSM4 versus results from CCSM3. Predictability results show that there is potential skill to be gained for both precipitation and temperature should model errors, atmosphere or land initial state errors, and/or land‐atmosphere coupling improve.

Noise covariance identification for time-varying and nonlinear systems

ABSTRACTKalman-based state estimators assume a priori knowledge of the covariance matrices of the process and observation noise. However, in most practical situations, noise statistics and initial conditions are often unknown and need to be estimated from measurement data. This paper presents an auto-covariance least-squares-based algorithm for noise and initial state error covariance estimation of large-scale linear time-varying (LTV) and nonlinear systems. Compared to existing auto-covariance least-squares based-algorithms, our method does not involve any approximations for LTV systems, has fewer parameters to determine and is more memory/computationally efficient for large-scale systems. For nonlinear systems, our algorithm uses full information estimation/moving horizon estimation instead of the extended Kalman filter, so that the stability and accuracy of noise covariance estimation for nonlinear systems can be guaranteed or improved, respectively.

Evaluation of Atmosphere and Ocean Initial Condition Uncertainty and Stochastic Exchange Coefficients on Ensemble Tropical Cyclone Intensity Forecasts

Tropical cyclone (TC) intensity forecasts are impacted by errors in atmosphere and ocean initial conditions and the model formulation, which motivates using an ensemble approach. This study evaluates the impact of uncertainty in atmospheric and oceanic initial conditions, as well as stochastic representations of the drag Cd and enthalphy Ck exchange coefficients on ensemble Advanced Hurricane WRF (AHW) TC intensity forecasts of multiple Atlantic TCs from 2008 to 2011. Each ensemble experiment is characterized by different combinations of either deterministic or ensemble atmospheric and/or oceanic initial conditions, as well as fixed or stochastic representations of Cd or Ck. Among those experiments with a single uncertainty source, atmospheric uncertainty produces the largest standard deviation in TC intensity. While ocean uncertainty leads to continuous growth in ensemble standard deviation, the ensemble standard deviation in the experiments with Cd and Ck uncertainty levels off by 48 h. Combining atmospheric and oceanic uncertainty leads to larger intensity standard deviation than atmosphere or ocean uncertainty alone and preferentially adds variability outside of the TC core. By contrast, combining Cd or Ck uncertainty with any other source leads to negligible increases in standard deviation, which is mainly due to the lack of spatial correlation in the exchange coefficient perturbations. All of the ensemble experiments are deficient in ensemble standard deviation; however, the experiments with combinations of uncertainty sources generally have an ensemble standard deviation closer to the ensemble-mean errors.

Error propagation characteristic analysis of halo orbit based on condition number of state transition matrix

The error propagation characteristics of different points of a halo orbit are studied in this paper. The condition number of state transition matrix after a period is used to estimate the sensitivity of different positions on a halo orbit to the state errors. Then the covariance propagation method is applied to compute the error covariance matrix under the initial state errors, and the results are validated by Monte Carlo simulation. The variations of the position error are compared with the variations of the condition number. The results show that the variation trend of the position error after a period of that halo orbit is the same as the variation trend of the condition number. Moreover, this identified property is verified by testing the halo orbits with different amplitudes and the halo orbits in systems with different mass ratios. Finally, the variation trends of the condition numbers against propagation time corresponding to different points on the halo orbit are analyzed. It is shown that the largest point in the negative \(z\) direction of the north halo orbit and its vicinity are more sensitive to state errors than other positions on the halo orbit, and they should not be selected as the injection point.

Iterative tuning strategy for setting phase splits with anticipation of traffic demand in urban traffic network

Facing large-scale urban traffic network, countless effort has been made toward intelligent and efficient urban traffic control system to better use existing traffic infrastructures. Recently, a novelty pre-timed traffic signal control strategy known as iterative tuning (IT) has been developed by exploiting repetitive characteristic of junction's vehicle throughput on working days, which is sufficiently efficient in under-saturated traffic conditions. This study further improves IT strategy in saturated traffic conditions with consideration of traffic demand including vehicle throughput and residual queued vehicles. Unlike conventional pre-timed strategies, preparation of signal schedules is not required in IT strategy and fine-tuning process executes iteratively and automatically. This study proposes a generalised traffic model to describe urban network dynamics and explicit split tuning algorithm. Without specific control trajectories, rigorous analysis generates sufficient condition for guaranteeing the convergence of IT strategy globally over repetitions. The robustness of IT controller to variations of traffic flow patterns and errors of initial conditions is also analysed in details. Commonwealth Avenue, an area with heavy traffic in Singapore, is demonstrated in simulations and simulation results indicate the effectiveness and robustness of IT strategy.

Iterative learning control for linear discrete‐time systems with high relative degree under initial state vibration

For linear discrete-time multiple-input–multiple-output (MIMO) systems with high relative degree, this study presents three average operator-based iterative learning control (ILC) algorithms to investigate the effect of initial state vibration on ILC tracking error. The proposed ILC laws include an initial rectifying action against initial state vibration at certain time points, and pursue the reference trajectory tracking beyond the initial time points. It is proved that, when the proposed ILC laws are applied to linear discrete-time MIMO systems with high relative degree, the effect of the initial state vibration on ILC tracking error beyond the initial time points can be exactly decided. Moreover, the ILC tracking error beyond the initial time points can be driven to zero against a progressive fixed initial state error. Numerical examples are used to illustrate the effectiveness of the proposed ILC laws.

Constraints on methane emissions in North America from future geostationary remote-sensing measurements

Abstract. The success of future geostationary (GEO) satellite observation missions depends on our ability to design instruments that address their key scientific objectives. In this study, an Observation System Simulation Experiment (OSSE) is performed to quantify the constraints on methane (CH4) emissions in North America obtained from shortwave infrared (SWIR), thermal infrared (TIR), and multi-spectral (SWIR+TIR) measurements in geostationary orbit and from future SWIR low-Earth orbit (LEO) measurements. An efficient stochastic algorithm is used to compute the information content of the inverted emissions at high spatial resolution (0.5° × 0.7°) in a variational framework using the GEOS-Chem chemistry-transport model and its adjoint. Our results show that at sub-weekly timescales, SWIR measurements in GEO orbit can constrain about twice as many independent flux patterns than in LEO orbit, with a degree of freedom for signal (DOF) for the inversion of 266 and 115, respectively. Comparisons between TIR GEO and SWIR LEO configurations reveal that poor boundary layer sensitivities for the TIR measurements cannot be compensated for by the high spatiotemporal sampling of a GEO orbit. The benefit of a multi-spectral instrument compared to current SWIR products in a GEO context is shown for sub-weekly timescale constraints, with an increase in the DOF of about 50 % for a 3-day inversion. Our results further suggest that both the SWIR and multi-spectral measurements on GEO orbits could almost fully resolve CH4 fluxes at a spatial resolution of at least 100 km × 100 km over source hotspots (emissions > 4 × 105 kg day−1). The sensitivity of the optimized emission scaling factors to typical errors in boundary and initial conditions can reach 30 and 50 % for the SWIR GEO or SWIR LEO configurations, respectively, while it is smaller than 5 % in the case of a multi-spectral GEO system. Overall, our results demonstrate that multi-spectral measurements from a geostationary satellite platform would address the need for higher spatiotemporal constraints on CH4 emissions while greatly mitigating the impact of inherent uncertainties in source inversion methods on the inferred fluxes.

Analysis of Missed Summer Severe Rainfall Forecasts

Abstract Despite considerable progress in mesoscale numerical weather prediction (NWP), the ability to predict summer severe rainfall (SSR) in terms of amount, location, and timing remains very limited because of its association with convective or mesoscale phenomena. In this study, two representative missed SSR events that occurred in the highly populated Great Lakes regions are analyzed within the context of moisture availability, convective instability, and lifting mechanism in order to help identify the possible causes of these events and improve SSR forecasts/nowcasts. Results reveal the following limitations of the Canadian regional NWP model in predicting SSR events: 1) the model-predicted rainfall is phase shifted to an undesired location that is likely caused by the model initial condition errors, and 2) the model is unable to resolve the echo-training process because of the weakness of the parameterized convection and/or coarse resolutions. These limitations are related to the ensuing model-predicted features: 1) vertical motion in the areas of SSR occurrence is unfavorable for triggering parameterized convection and grid-scale condensation; 2) convective available potential energy is lacking for initial model spinup and later for elevating latent heating to higher levels through parameterized convection, giving rise to less precipitation; and 3) the conversion of water vapor into cloud water at the upper and middle levels is underpredicted. Recommendations for future improvements are discussed.

Intrinsic versus Practical Limits of Atmospheric Predictability and the Significance of the Butterfly Effect

Abstract Limits of intrinsic versus practical predictability are studied through examining multiscale error growth dynamics in idealized baroclinic waves with varying degrees of convective instabilities. In the dry experiment free of moist convection, error growth is controlled primarily by baroclinic instability under which forecast accuracy is inversely proportional to the amplitude of the baroclinically unstable initial-condition error (thus the prediction can be continuously improved without limit through reducing the initial error). Under the moist environment with strong convective instability, rapid upscale growth from moist convection leads to the forecast error being increasingly less sensitive to the scale and amplitude of the initial perturbations when the initial-error amplitude is getting smaller; these diminishing returns may ultimately impose a finite-time barrier to the forecast accuracy (limit of intrinsic predictability and the so-called “butterfly effect”). However, if the initial perturbation is sufficiently large in scale and amplitude (as for most current-day operational models), the baroclinic growth of large-scale finite-amplitude initial error will control the forecast accuracy for both dry and moist baroclinic waves; forecast accuracy can be improved (thus the limit of practical predictability can be extended) through the reduction of initial-condition errors, especially those at larger scales. Regardless of the initial-perturbation scales and amplitude, the error spectrum will adjust toward the slope of the background flow. Inclusion of strong moist convection changes the mesoscale kinetic energy spectrum slope from −3 to ~−5/3. This change further highlights the importance of convection and the relevance of the butterfly effect to both the intrinsic and practical limits of atmospheric predictability, especially at meso- and convective scales.

Fundamental limitations to high-precision tests of the universality of free fall by dropping atoms

Tests of the universality of free fall and the weak equivalence principle probe the foundations of General Relativity. Evidence of a violation may lead to the discovery of a new force. The best torsion balance experiments have ruled it out to 10^-13. Cold-atom drop tests have reached 10^-7 and promise to do 7 to 10 orders of magnitude better, on the ground or in space. They are limited by the random shot noise, which depends on the number N of atoms in the clouds. As mass-dropping experiments in the non-uniform gravitational field of Earth, they are sensitive to the initial conditions. Random accelerations due to initial condition errors of the clouds are designed to be at the same level as shot noise, so that they can be reduced with the number of drops along with it. This sets the requirements for the initial position and velocity spreads of the clouds with given N. In the STE-QUEST space mission proposal aiming at 2x10^-15 they must be about a factor 8 above Heisenberg's principle limit, and the integration time required to reduce both errors is 3 years, with a mission duration of 5 years. Instead, offset errors at release between different atom clouds are systematic and give rise to a systematic effect which mimics a violation. Such offsets must be demonstrated to be as small as required in all drops, must be small by design and must be measured. For STE-QUEST to meet its goal they must be several orders of magnitude smaller than the size of each individual cloud, which in its turn must be at most 8 times larger than the uncertainty principle limit. Even if all technical problems are solved and the clouds are released with negligible systematic errors, still they must be measured. Then, Heisenberg's principle dictates that the measurement lasts as long as the experiment and the systematic nature of the effect requires many measurements for it to be ruled out as a source of violation.

Diagnosing Model Errors from Time-Averaged Tendencies in the Weather Research and Forecasting (WRF) Model

Abstract Accurate predictions in numerical weather models depend on the ability to accurately represent physical processes across a wide range of scales. This paper evaluates the utility of model time tendencies, averaged over many forecasts at a given lead time, to diagnose systematic forecast biases in the Advanced Research version of the Weather Research and Forecasting (WRF) Model during the 2010 North Atlantic hurricane season using continuously cycled ensemble data assimilation (DA). Erroneously strong low-level heating originates from the planetary boundary layer parameterization as a consequence of using fixed sea surface temperatures, impacting the upward surface sensible heat fluxes. Warm temperature bias is observed with a magnitude 0.5 K in a deep tropospheric layer centered 700 hPa, originating primarily from the Kain–Fritsch convective parameterization. This study is the first to diagnose systematic forecast bias in a limited-area mesoscale model using its forecast tendencies. Unlike global models where relatively fewer time steps typically encompass a DA cycling period, averaging all short-term forecast tendencies can require potentially large data. It is shown that 30-min averaging intervals can sufficiently represent the systematic model bias in this modeling configuration when initializing forecasts from an ensemble member that is generated using a DA system with an identical model configuration. However, the number of time steps before model error begins to dominate initial condition (IC) errors may vary between modeling configurations. Model and IC error are indistinguishable in short-term forecasts when initialized from the ensemble mean, a global analysis from a different model, and an ensemble member using a different parameterization.

The Effect of Initial State Error for Nonlinear Systems with Delay via Iterative Learning Control

An iterative learning control problem for nonlinear systems with delays is studied in detail in this paper. By introducing theλ-norm and being inspired by retarded Gronwall-like inequality, the novel sufficient conditions for robust convergence of the tracking error, whose initial states are not zero, with time delays are obtained. Finally, simulation example is given to illustrate the effectiveness of the proposed method.