Systematic Model Errors Research Articles

Effect of the Azimuth Axis Tilt Error on the Tracking Performance of a Solar Dish Concentrator System

A solar dish concentrator system has a large windward area and heavy structural mass, and under the action of wind loads and self-weight loads, foundation settlement can easily occur and cause the column (the azimuth axis) to tilt. Upon tilting, the azimuth axis is no longer perpendicular to the horizontal plane, causing a tracking error in the service of the solar dish concentrator system. In this paper, a tracking error model of a solar dish concentrator system is established based on the rigid body motion theory, which considers the azimuth axis tilt error. In this model, a radial angle and tangential angle parameters are used to describe the azimuth axis’s tilt angle and tilt direction. Under the tilt error of the azimuth axis, we analyze, in detail, the initial tracking position of a solar dish concentrator system, the system operation area, and the variation rule of tracking performance in long-term operation. The results show that under the azimuth axis tilt error of the solar dish concentrator system, the deviation of the initial tracking position of the solar dish concentrator system in the horizontal or vertical plane will reduce its tracking performance and the stability of tracking performance compared with the initial tracking position being due east. The tracking performance of a solar dish concentrator system and its stability are better in areas with a relatively low latitude. In different areas with close latitude, the tracking performance of the solar dish concentrator system and its stability are better, particularly with lower longitudes. During a whole year operation period, the tracking performance of an solar dish concentrator system in the first quarter and the fourth quarter is relatively better, and its stability in June and July is relatively better. This work can provide a theoretical basis for the installation, debugging, and error control of solar dish concentrator systems.

Using an Explainable Machine Learning Approach to Characterize Earth System Model Errors: Application of SHAP Analysis to Modeling Lightning Flash Occurrence

AbstractComputational models of the Earth System are critical tools for modern scientific inquiry. Efforts toward evaluating and improving errors in representations of physical and chemical processes in these large computational systems are commonly stymied by highly nonlinear and complex error behavior. Recent work has shown that these errors can be effectively predicted using modern Artificial Intelligence (A.I.) techniques. In this work, we go beyond these previous studies to apply an explainable A.I. technique to not only predict model errors but also move toward understanding the underlying reasons for successful error prediction. We use XGBoost classification trees and SHapley Additive exPlanations analysis to explore the errors in the prediction of lightning occurrence in the NASA Goddard Earth Observing System model, a widely used Earth System Model. This explainable error prediction system can effectively predict the model error and indicates that the errors are strongly related to convective processes and the characteristics of the land surface.

Anomaly Format of Atmospheric Governing Equations with Climate as a Reference Atmosphere

To reduce numerical instability and increase forecast accuracy of a numerical weather prediction (NWP) model, one approach is to subtract a reference atmosphere from atmospheric governing equations. In the past, scientists have proposed one-dimensional, two-dimensional, and three-dimensional static (in time) reference atmospheres with respect to temperature and pressure. These three reference atmospheres were first reviewed, and their corresponding perturbation equations were derived. Then, a new four-dimensional (space and time) all-variable (temperature, pressure, wind, moisture, etc.) reference atmosphere was defined using observed climatic states. Unlike the previous three approaches, the perturbations derived from this new method are actual anomalies relative to climate and directly a part of individual weather systems in both structure and strength. By subtracting climatic states, anomaly equations were derived and analyzed. Finally, the benefits and challenges of the anomaly-equation-based NWP model were discussed. Theoretically, an anomaly model should reduce model systematic errors (bias) and should avoid model climate drift to significantly enhance a model’s performance. An example of tropical cyclone track forecasts using the Beta advection model (vorticity) was demonstrated. The separation of model physics into climatic and anomalous physics is a significant challenge if a pure anomaly-equation-based NWP model is desired. Fortunately, a model including both anomaly and climatic equations should work with current full physics. In an anomaly climate mixed model, the anomaly part needs to be predicted and the climate parts are precalculated constants. It is hoped that this study will inspire model developers to explore the approach, which could be a possible new direction in developing next-generation NWP models. A high-resolution reanalysis is also key to the success of this new approach.

Event-triggered attitude maneuver control of spacecraft under angular velocity constraints

Considering the spacecraft attitude system subject to angular velocity constraints, limited communication resources, the inaccurate moment of inertia, and external interference, a neural network-based adaptive event-triggered attitude maneuver control scheme is proposed. Specifically, the angular velocity constraint is first transformed into the performance boundary constraint based on the prescribed performance method, and then the equivalent error model of the attitude system is established using error transformation, which tactfully transforms the attitude maneuver control problem with angular velocity constraints into the state-bounded stability control problem of the unconstrained error system. Subsequently, by applying the radial basis function neural network, an adaptive online updating law is designed to approximate the uncertainty term caused by the unknown moment of inertia online. Meanwhile, considering the limited communication resources, a unified time-varying event-triggered mechanism is developed by establishing the explicit relationship between the trigger control signal and the real-time control one. The control command and the adaptive law are synchronously updated once the trigger condition is satisfied. By doing so, the frequent network signal transmissions between the controller and the actuator are reduced significantly. In addition, the time-varying term in the event-triggered mechanism strictly guarantees that no Zeno phenomenon occurs. The simulation results show that the proposed attitude control algorithm can achieve the specified attitude maneuver task with higher accuracy, stability, and robustness and reduce frequent control signal updates by about 97.50%, significantly reducing the on-board communication burden.

Multi-Robot Leader Grouping Consistent Formation Control Method Research with Low Convergence Time Based on Nonholonomic Constraints

Aiming at the formation and maintenance of the multiple formations of nonholonomic constrained multi-robots, a leader-follower formation control method under the grouping consistency is proposed on the trajectory tracking of a nonholonomic constrained mobile robots with the low convergence time. The distributed control structure in the leader-follower formation is adopted. The multi-robot cooperative formation is realized by using the consistency algorithm of graph theory. According to the graph theory, the communication topology matrixes are designed by the consistency algorithm. The mathematical model of nonholonomic constrained robot is established with the wheeled structure as the mobile structure under the nonholonomic constraints. Then the navigation following model is transformed into the error model of a local coordinate system through the global coordinate transformation. The formation control law of multi-robot cooperative motion is put forward based on the leader-follower model. Its convergence is proved by the Lyapunov function. By setting the reasonable communication protocol parameters, the MATLAB software (Natick, MA, USA, R2016b) is employed on the simulation verification and result comparison. Through the comparison of the two leader formation control methods, the convergence time of the algorithm in this article can be 25% less than that of PFC. The effectiveness and feasibility of the formation control law are verified under the leader-follower method. The proposed control method lays a foundation for reducing the convergence time to improve the multi-robot cooperative motion under nonholonomic constraints.

Adaptive neural network control for image‐based visual servoing of robot manipulators

This paper presents a novel adaptive neural network control strategy for image-based visual servoing (IBVS) of robotic manipulators with both eye-in-hand and eye-to-hand camera configurations in the presence of unknown dynamics and external disturbances. The IBVS method is combined with the adaptive neural network to construct the proposed adaptive neural network controller to solve the visual servoing control problem of robots. The adaptive neural network based IBVS controller is designed based on the depth-independent interaction matrix, which can be trained on-line to identify the visual servoing robotic system modeling errors. Moreover, the proposed method can approach the unknown nonlinear dynamics for both eye-in-hand and eye-to-hand camera configurations without requiring the robot dynamics to be linearly parameterizable, and the exact knowledge of the robot structure is not needed. On the basis of the nonlinear robot dynamics, the Lyapunov stability analysis is given to prove the asymptotical convergence of the image position and velocity errors. Simulation results for both camera configurations are provided to demonstrate the performance of the proposed adaptive neural network based approach.

Analysis of thermal error model of ball screw feed system based on experimental data

In order to investigate the effect of thermal expansion on the ball screw feed system (BSFS) of a precision machine tool, theoretical modeling of and experimental study on thermally induced error are focused in this paper. A series of thermal experiments are conducted on the machine tool to measure the temperature of the main heat source and measuring points of BSFS. This study is to classify the main heat sources and discuss the impact on the ball screw feed system separately. By the experimental data of ball screw system, the thermal model of screw shaft in the axial direction is analyzed and verified. Based on the heat generation and transfer analysis of ball screw system, thermal expansion of screw shaft in the axial direction is modeled mathematically. In addition, by analyzing the effects of machining parameters such as rotational speed, preloads, and lead, we get the parameter influence of BSFS’s temperature rising and thermal deformation. This work can help us reduce thermal deformation effectively and improve the precision of CNC machining.

Bézier trajectory tracking control of The Omnidirectional Mobile Robot based on a linear time- varying state feedback controller

Introduction: The controller design method based on linear time varying state feedback controller is proposed to enforce an omnidirectional mobile robots (OMRs) to track a given Bézier trajectory. Methods: Initially, the linear error model of the robot system is obtained and used in the design of the linear time varying state feedback controller. Next, the controller gains are determined according to the linear and angular velocities for the desired trajectory to providing small errors. To verify the effectiveness of the proposed control strategy, simulation is carried out with desired Bézier trajectory for the OMR to reduce sudden speed changes. Results: The simulation results are presented, which have verified the good performance of the proposed controller for tracking the complex motion trajectories. Conclusion: Therefore, it is possible to apply this result to control the OMRS in logistics applications of the modern manufacturing systems.

Correction of the inertial navigation system using a genetic algorithm

The problem of compensating errors for an inertial navigation system with an unstable signal of a satellite navigation system is considered. The error model of the inertial navigation system, with the help of which its errors are predicted is built under the conditions of the signals disappearance from the satellite navigation system. The prediction of inertial navigation system errors are used for correction in the output signal. Predictive models are built using a genetic algorithm. Correction for small unmanned aerial vehicles, it is proposed to carry out using a scalar model of inertial navigation system errors and generated reduced measurements. Keywords aircraft, inertial navigation system, satellite navigation system, correction, genetic algorithm, reduced measurements

Probabilistic prediction and calibration for residual shear strength of corroded reinforced concrete columns

Degradation of shear strength for reinforced concrete (RC) columns caused by steel corrosion is one of the prominent factors for shortening the entire service life of RC structures. In this work, probabilistic prediction and calibration methods for residual shear strength of corroded RC columns were developed by combining theoretical analysis with available experimental data. Deterministic shear strength degradation model accounting for the cross-sectional area reduction and mechanical properties degradation of steel reinforcement and concrete was derived first based on the truss and arch mechanisms. Then probabilistic prediction model was proposed by introducing probabilistic model parameters and systematic error. Meanwhile, probabilistic model parameters regarding the influences of prior variation coefficients and update times were investigated using the Bayesian theory. Moreover, probabilistic method was implemented to calibrate seven available deterministic shear strength models based on probability density function and confidence interval. Results indict that the proposed model can not only quantify the probabilistic characteristics of shear strength and predict the residual shear strength for any given corrosion level and guarantee rate, but also provide a suitable approach for calibrating the applicability of conventional deterministic shear strength models.

A Two‐Stage Bayesian Data‐Driven Method to Improve Model Prediction

AbstractBecause of the earth system complexity, groundwater/hydrology models are always built with structural errors, which may lead to systematic errors in model predictions. Bayesian data‐driven methods (DDMs) provide a feasible way to correct systematic model errors statistically. Generally, the physical and statistical model parameters, namely physical parameters and hyperparameters, are assumed to be independent and jointly calibrated. However, this assumption may be unreasonable and lead to over‐adjusted parameter estimation and biased model prediction. This study proposes a two‐stage DDM to calibrate physical parameters and hyperparameters separately, which does not make the independence assumption. Three case studies, including a groundwater solute transport analytical model, a three‐dimensional groundwater flow model, and a real‐world snowmelt runoff model, were used to evaluate the predictive performance of this two‐stage DDM. Based on the three case studies, we found that the independence assumption of physical parameters and hyperparameters could lead to the over‐fitting of parameter estimation and deviations in model predictions. Two‐stage DDM can constrain the systematic error model calibration; that is, physical parameters are first calibrated in the entire hyperparameter prior probability space, and then hyperparameters are calibrated in the posterior probability space of physical parameters obtained previously. As a result, compared with traditional joint calibration‐based DDM, two‐stage DDM can alleviate parameter over‐fitting and improve model predictive performance.

Research on Thermal Characteristics of Ball Screw Feed System Considering Nut Movement

The heat generated by the ball screw feed system will produce thermal errors, which will cause the positioning accuracy to decrease. The thermal simulation modeling of the ball screw feed system is the basis for compensating thermal errors. The current thermal characteristic modeling method simplifies the reciprocating movement of the nut pair on the screw shaft to varying degrees, which leads to a decrease in simulation accuracy. In this paper, the nut is regarded as a moving heat source, and a novel method is adopted to make the moving process of the heat source closer to the actual nut movement process. The finite difference method is used to simulate the temperature field and thermal error of the ball screw feed system under different working conditions. Firstly, based on the heat transfer theory, the heat conduction differential equation of the feed system is established and discretized. The thermal error model of the ball screw feed system is established. Then, the relationship between nut heat source position and operating time is established to simulate nut reciprocating motion. Finally, the temperature and thermal error experiments of the ball screw feed system were carried out, and the temperature experiment results were compared with the simulation results of the finite difference method. The results show that the maximum simulation error of the average temperature in the operating interval is 11.4%, and the maximum simulation error of thermal error is 16.4%, which verifies the validity and correctness of the method. The thermal characteristic modeling method of the ball screw feed system proposed in this paper has a substantial application value for accurately obtaining the temperature field of the feed system.

Finite‐time adaptive event‐triggered asynchronous state estimation for Markov jump systems with cyber‐attacks

AbstractThis article considers the issue of finite‐time asynchronous state estimation for event‐triggered nonlinear Markovian jump systems subject to cyber‐attacks. An adaptive event‐triggered scheme is introduced to cope with the capacity constraint of the networked resources. It is assumed that the transmitted sensor measurements may experience randomly malicious cyber‐attacks. Considering the effect of the adaptive event‐triggered scheme and the occurrence of cyber‐attacks, we establish a new state estimation error system model. Sufficient conditions of the finite‐time boundedness and the finite‐time boundedness are developed for the augmented system. Then, the design methods of the asynchronous estimator gains are derived, which can ensure the finite‐time boundedness of the estimation error system. Finally, a numerical example is given to show the effectiveness of the theoretical results.

Online Dynamic Response Reconstruction in the Presence of Observation Outliers

Previous studies show that Kalman filter (KF)-based dynamic response reconstruction of a structure has distinct advantages in the aspects of combining the system model with limited measurement information and dealing with system model errors and measurement Gaussian noises. However, because the recursive KF aims to achieve a least-squares estimate of state vector by minimizing a quadratic criterion, observation outliers could dramatically deteriorate the estimator’s performance and considerably reduce the response reconstruction accuracy. This study addresses the KF-based online response reconstruction of a structure in the presence of observation outliers. The outlier-robust Kalman filter (OKF), in which the outlier is discerned and reweighted iteratively to achieve the generalized maximum likelihood (ML) estimate, is used instead of KF for online dynamic response reconstruction. The influences of process noise and outlier duration to response reconstruction are investigated in the numerical study of a simple 5-story frame structure. The experimental work on a simply-supported overhanging steel beam is conducted to testify the effectiveness of the proposed method. The results demonstrate that compared with the KF-based response reconstruction, the proposed OKF-based method is capable of dealing with the observation outliers and producing more accurate response construction in presence of observation outliers.

Evaluation of Gaussian process regression kernel functions for improving groundwater prediction

Systematic model error is caused by the unreasonable simplification of real groundwater system, which damages the reliability of groundwater model prediction. Gaussian process regression (GPR) is a popular data-driven method used to build a statistical complementary model to correct systematic prediction error and improve model prediction. Kernel function is a crucial component of GPR, it represents the assumptions on systematic prediction error that we want to learn. In order to evaluate the influence of GPR kernel on capturing systematic prediction error, we compared the performances of GPR with nine kernels in groundwater predictions. These kernels include three commonly used single kernels, i.e., squared exponential (SE), Matérn class (MT), and rational quadratic (RQ) kernels, and six new kernels formed by combining these single kernels as sum or product of pairs (SE_MT_s, SE_RQ_s, MT_RQ_s, SE_MT_p, SE_RQ_p, and MT_RQ_p). Moreover, three groundwater case studies, including two analytical cases and one real case, are used to test these kernels, and four metrics are applied to measure the performances of these kernels. The evaluation results show that kernel functions have apparent influence on the ability of the GPR-based complementary model to capture the systematic prediction error of groundwater model. The single kernel RQ-based GPR yields the best performance in improving groundwater predictions among the nine kernels for all case studies. The combined kernels MT_RQ_s, SE_RQ_s also perform well in groundwater predictions, and the commonly used SE kernel has mediocre performance in predicting groundwater observations.

Characterising extratropical near‐tropopause analysis humidity biases and their radiative effects on temperature forecasts

AbstractA cold bias in the extratropical lowermost stratosphere in forecasts is one of the most prominent systematic temperature errors in numerical weather prediction models. Hypothesized causes of this bias include radiative effects from a collocated moist bias in model analyses. Such biases would be expected to affect extratropical dynamics and result in the misrepresentation of wave propagation at tropopause level. Here the extent to which these humidity and temperature biases are connected is quantified. Observations from radiosondes are compared to operational analyses and forecasts from the European Centre for Medium‐Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) and Met Office Unified Model (MetUM) to determine the magnitude and vertical structure of these biases. Both operational models over‐estimate lowermost stratospheric specific humidity, with a maximum moist bias around 1 km above the tropopause where humidities are around of the observed values on average. This moist bias is already present in the initial conditions and changes little in forecasts over the first five days. Though temperatures are represented well in the analyses, the IFS forecasts anomalously cool in the lower stratosphere, relative to verifying radiosonde observations, by 0.2 K day. The IFS single column model is used to show this temperature change can be attributed to increased long‐wave radiative cooling due to the lowermost stratospheric moist bias in the initial conditions. However, the MetUM temperature biases cannot be entirely attributed to the moist bias, and another significant factor must be present. These results highlight the importance of improving the humidity analysis to reduce the extratropical lowermost stratospheric cold bias in forecast models and the need to understand and mitigate the causes of the moist bias in these models.

Formula omitted] filter design for discrete-time networked systems with adaptive event-triggered mechanism and hybrid cyber attacks

This paper focuses on the design of H∞ filter for a class of discrete-time networked systems. Given that the network communication resources are becoming limited with the ever-increasing network traffic, an adaptive event-triggered mechanism (AETM) is adopted for the systems to mitigate the pressure of network bandwidth. The considered discrete-time networked systems are envisioned to suffer from both Deception attacks and denial-of-service (DoS) attacks, thereby a novel hybrid cyber attacks model is firstly constructed to integrate the two kinds of attacks. Then, a filtering error system model is established for the discrete-time networked systems under AETM and hybrid cyber attacks. Based on the constructed model, the sufficient conditions that guaranteeing the asymptotic stability and H∞ performance of the concerned filtering error system are analyzed based on Lyapunov–Krasovskii stability theory. Furthermore, the corresponding parameters of the designed filter are derived by solving a set of linear matrix inequalities (LMIs). The effectiveness of the designed filter is finally demonstrated by conducting a numerical example.

Significant additional Antarctic warming in atmospheric bias-corrected ARPEGE projections with respect to control run

Abstract. In this study, we use run-time bias correction to correct for the Action de Recherche Petite Echelle Grande Echelle (ARPEGE) atmospheric model systematic errors on large-scale atmospheric circulation. The bias-correction terms are built using the climatological mean of the adjustment terms on tendency errors in an ARPEGE simulation relaxed towards ERA-Interim reanalyses. The bias reduction with respect to the Atmospheric Model Intercomparison Project (AMIP)-style uncorrected control run for the general atmospheric circulation in the Southern Hemisphere is significant for mean state and daily variability. Comparisons for the Antarctic Ice Sheet with the polar-oriented regional atmospheric models MAR and RACMO2 and in situ observations also suggest substantial bias reduction for near-surface temperature and precipitation in coastal areas. Applying the method to climate projections for the late 21st century (2071–2100) leads to large differences in the projected changes of the atmospheric circulation in the southern high latitudes and of the Antarctic surface climate. The projected poleward shift and strengthening of the southern westerly winds are greatly reduced. These changes result in a significant 0.7 to 0.9 K additional warming and a 6 % to 9 % additional increase in precipitation over the grounded ice sheet. The sensitivity of precipitation increase to temperature increase (+7.7 % K−1 and +9 % K−1) found is also higher than previous estimates. The highest additional warming rates are found over East Antarctica in summer. In winter, there is a dipole of weaker warming and weaker precipitation increase over West Antarctica, contrasted by a stronger warming and a concomitant stronger precipitation increase from Victoria to Adélie Land, associated with a weaker intensification of the Amundsen Sea Low.

Constrained visual predictive control of tendon-driven continuum robots

Due to their compliance, continuum robots (CRs) hold great potential for many applications. However, despite intensive recent research, their control poses significant challenges. The nonlinear kinematic behavior, limited actuation channels, and physical and environmental constraints typically associated with CRs hinder the development of effective control strategies. In this paper, a visual predictive position control method for tendon-driven continuum robots is proposed. The developed control approach integrates the advantages of image-based visual servoing and model predictive control techniques to enable direct end-point control in the presence of constraints and improve the control robustness to system uncertainties, sensing noise, and modeling errors. Both simulation and experimental results demonstrate the effectiveness of the method.

Sources of Uncertainty in Multimodel Large Ensemble Projections of the Winter North Atlantic Oscillation

AbstractProjections of the winter North Atlantic circulation exhibit large spread. Coupled Model Intercomparison Project archives typically provide only a few ensemble members per model, rendering it difficult to quantify reducible model structural uncertainty and irreducible internal variability (IV) in projections. We estimate using the Multimodel Large Ensemble Archive that model structural differences explain two‐thirds of the spread in late 21st century (2080–2099) projections of the winter North Atlantic Oscillation (NAO). This estimate is biased by systematic model errors in the forced NAO response and IV. Across the North Atlantic, the NAO explains a substantial fraction of the spread in mean sea level pressure (MSLP) projections due to IV, except in the central North Atlantic. Conversely, the spread in North Atlantic MSLP projections associated with model differences is largely unexplained by the NAO. Therefore, improving understanding of the NAO alone may not constrain the reducible uncertainty in North Atlantic MSLP projections.