Stability Error Research Articles

Regression with Stable Errors Based on Order Statistics

Classical regression approaches are not robust when errors are heavy-tailed or asymmetric. That may be due to the non-existence of the mean or variance of the error distribution. Estimation based on trimmed data, which ignored outlier or leverage points, has an old history and frequently used. This procedure chooses fixed cut-off points. In this work, we use this idea recently applied for initial estimates of regression coefficients with heavy-tailed stable errors. We propose an effective procedure to calculate the cut-off points based on the tail index and skewness parameters of errors. We use the property of the existence of some moments of stable distribution order statistics. Data are trimmed based on ordered residuals of a least square regression. However, the trimmed data’s optimal number is determined based on the number of error order statistics whose variance exists. Then, we use the rest of the ordered data to estimate the regression coefficients. Based on these order statistics’ joint distribution, we analytically compute the bias and variance of the introduced estimator of regression parameters that was impossible for regression with stable errors.

Custom-Q versus Wavefront Optimized Photorefractive Keratectomy for Myopia with or without Astigmatism correction

Purpose:To compare the results between photorefractive keratectomy (PRK) with Custom-Q or with Wavefront-optimized (WFO) profiles in terms of asphericity and spherical aberrations, 6 months post-operative. Setting:Tertiary referral center (Centro Hospitalar e Universitario da Universidade de Coimbra, Coimbra, Portugal). Patients and Methods: Fifty-nine eyes (43 patients) were enrolled on this retrospective case series, including patients with myopia and/or astigmatism, submitted to refractive surgery with PRK (Allegretto WAVE Eye-Q Excimer Laser System, Alcon), in a Custom-Q ablation (38 eyes) or Wavefront-optimized procedure (21 eyes). We included patients with a minimum follow-up of 6 months; age over 21 years; stable refractive error for 2 years; spherical equivalent (SE) inferior to 5.50 diopters (D); percentage of altered tissue under 40% and expected final corneal curvature above 35 D. Eyes with other ophthalmological pathologies were excluded. Baseline and post-operative asphericity and optical aberrations were evaluated with Pentacam (Oculus Optikgerate, Wetzlar, Germany). Results: The demographic and preoperative refractive data was similar between groups (all p≥0.05). Post-operative spherical equivalent in the Custom-Q and Wavefront-optimized groups was within 0.50D in 100% and 78.90% of eyes, respectively and within 0.25D in 97.06% and 73.70% of eyes, respectively. Variation of Q-value was 0.62±0.34. (range -0.07-1.24) for Custom Q group, and 0.65±0.39 (range -0.05-1.40) in the Wavefront-optimized group (p=0.82). In a multivariate linear regression model, variation of Q-value was not influenced by the ablation profile (B=0.04, p=0.49, 95%CI [-0.08,0.17]). SE was a strong predictor (B=-0.30, p<0.01, 95%CI[-0.39,-0.21]). There was a significant increase in RMS higher-order aberrations (p<0.01for both groups) and no difference between groups (p=0.53). Discussion and Conclusion: In our sample,Custom-Q ablation was not significantly different from Wavefront optimized ablation regarding post-operative asphericity. Although the increase in higher-order aberrations, both techniques were effective and safe for myopic and/or astigmatic correction up to -5.50D SE.

Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole

In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving around the Kerr black hole embedded in an external magnetic field. Its successful construction is due to the contribution of a time transformation. The algorithm exhibits a good long-term numerical performance in stable Hamiltonian errors and computational efficiency. As its application, the dynamics of order and chaos of charged particles is surveyed. In some circumstances, an increase of the dragging effects of the spacetime seems to weaken the extent of chaos from the global phase-space structure on Poincaré sections. However, an increase of the magnetic parameter strengthens the chaotic properties. On the other hand, fast Lyapunov indicators show that there is no universal rule for the dependence of the transition between different dynamical regimes on the black hole spin. The dragging effects of the spacetime do not always weaken the extent of chaos from a local point of view.

Decentralised navigation systems for bearing-based position and velocity estimation in tiered formations

This paper presents a novel decentralised navigation system based on bearing measurements for tiered vehicle formations. In the proposed framework, some vehicles have access to measurements of their own position, whereas others have access to bearing measurements to one or more neighbouring vehicles. Depth measurement may also be available. Local observers for the position and fluid velocity are designed based on the derivation of an equivalent observable linear time-varying system, thus yielding globally exponentially stable error dynamics. The local observers rely on local measurements, as well as limited communications between the vehicles. The stability of the system as a whole is analysed by studying the robustness of the local observers to exponentially decaying perturbations. Thorough Monte Carlo simulations are presented and discussed to compare the performance of the proposed solution with the extended Kalman filter, the unscented Kalman filter, and the Bayesian Cramér-Rao bound.

Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of positions and momenta in the coherent equations, we establish extended phase-space symplectic-like integrators with the midpoint permutations. The velocities should be solved iteratively from the algebraic equations of the momenta defined by the Lagrangian during the course of numerical integrations. It is shown numerically that a fourth-order extended phase-space symplectic-like method exhibits good long-term stable error behavior in energy {and} angular momentum, as a fourth-order implicit symplectic method with a symmetric composition of three second-order implicit midpoint rules or a fourth-order Gauss-Runge-Kutta implicit symplectic scheme does. For given time step and integration time, the former method is superior to the latter integrators in computational efficiency. {The extended phase-space method is used to study the effects of the parameters and initial conditions on the orbital dynamics of the coherent Euler-Lagrange equations for a post-Newtonian circular restricted three-body problem. It is also applied to trace the effects of the initial spin angles, initial separation and initial orbital eccentricity on the dynamics of the coherent post-Newtonian Euler-Lagrange equations of spinning compact binaries.

Optimal Dataset Sizes for Constant Optimization in Published Theoretical Optical Formulae

ABSTRACT Purpose: To determine the optimal number of data points required for optimization of formulae for classical lens power calculation. Methods: A large dataset of preoperative biometric values was used to assess the convergence of formula constants in a number of established intraocular lens power calculation formulae. Results: In formulae with a single constant, 80–100 clinical data points are sufficient to obtain convergence. The Haigis formula (three constants) requires 200–300 data points although refractive error converges more rapidly. Conclusions: In all formulae, 80–100 clinical data points are sufficient to achieve a stable mean refractive error.

At the Traffic Intersection, Stopping, or Walking? Pedestrian Path Prediction Based on KPOF-GPDM for Driving Assistance

Pedestrian detection has always been a research hotspot in the Advanced Driving Assistance System (ADAS) with great progress in recent years. However, for the ADAS, we not only need to detect the behavior of pedestrians in front of the vehicle but also predict future action and the motion trajectory. Therefore, in this paper, we propose a human key point combined optical flow network (KPOF-Net) in the vehicle ADAS for the occlusion situation in the actual scene. When the vehicle encounters a blocked pedestrian at a traffic intersection, we used self-flow to estimate the global optical flow in the image sequence and then proposed a White Edge Cutting (WEC) algorithm to remove obstructions and simply modified the generative adversarial network to initialize pedestrians behind the obstructions. Next, we extracted pedestrian optical flow information and human joint point information in parallel, among which we trained four human key point models suitable for traffic intersections. At last, KPOF-GPDM fusion was proposed to predict the future status and walking trajectories of pedestrians, which combined optical flow information with human key point information. In the experiment, we did not merely compare our method with other four representative approaches in the same scene sequences. We also verified the accuracy of the pedestrian motion state and motion trajectory prediction of the system after fusion of human joint points and optical flow information. Taking into account the real-time performance of the system, in the low-speed and barrier-free environment, the comparative analysis only uses optical flow information, human joint point information, and KPOF-Net three prediction models. The results show that (1) in the same traffic environment, our proposed KPOF-Net can predict the change of pedestrian motion state about 5 frames (about 0.26 s) ahead of other excellent systems; (2) at the same time, our system predicts the trajectory of the pedestrian more accurately than the other four systems, which can achieve more stable minimum error ±0.04 m; (3) in a low-speed, barrier-free experimental environment, our proposed trajectory prediction model that integrates human joint points and optical flow information has higher prediction accuracy and smaller fluctuations than a single-information prediction model, and it can be well applied to automobiles’ ADAS.

In-sample tests of predictability are superior to pseudo-out-of-sample tests, even when data mining

This paper analyses straightforward Bonferroni adjustments to critical values of in-sample tests of predictability, when data mining is used to search across models. Unlike conventional pseudo-out-of-sample tests, these in-sample tests have stable family-wise error rates (FWERs) when searching for models that predict well. Furthermore, when data mining, these in-sample tests have more power than pseudo-out-of-sample tests for identifying true predictability.

Constructive observer design for Visual Simultaneous Localisation and Mapping

Visual Simultaneous Localisation and Mapping (VSLAM) is a well-known problem in robotics with a large range of applications. This paper presents a novel approach to VSLAM by lifting the observer design to a novel Lie group V SLAMn(3) on which the system output is equivariant. The perspective gained from this analysis facilitates the design of a non-linear observer with almost semi-globally asymptotically stable error dynamics. Simulations are provided to illustrate the behaviour of the proposed observer and experiments on data gathered using a fixed-wing UAV flying outdoors demonstrate its performance.

An Adaptive Sliding Mode Control for Single Machine Infinite Bus System under Unknown Uncertainties

The inherent uncertainties in a Single Machine Infinite Bus System (SMIBS) are governed by unmodeled dynamics or large disturbances such as the system's faults. The existence of these uncertainties demands robust controllers to guarantee the system's asymptotic stability under such exacting conditions. In this work, we propose an Adaptive Sliding Mode Control (ASMC) design implemented on a fifth-order nonlinear SMIBS to handle those uncertainties without prior knowledge about its upper bounds. We develop the ASMC with gains of two nested adaptive layers to asymptotically stabilize the system's internal states, the machine's terminal voltage, and power angle within a region of unknown bounded uncertainties while mitigating the chattering phenomena associated with conventional Sliding Mode Control (SMC). To verify the design's effectiveness and prove the conducted Lyapunov theoretical stability analysis, we simulate the occurrence of a large disturbance represented by a 3-phase fault at the system's universal bus. The results show that the ASMC can successfully achieve asymptotic stable output errors and stabilizing the SMIBS internal states after the clearance of the fault. Moreover, the ASMC noticeably outperforms the SMC in chattering mitigation, where the ASMC's signal is significantly smoother than that of the SMC.

Evaluation of ECMWF Precipitation Predictions in China during 2015–18

AbstractPrecipitation forecasts from the ECMWF model from March to September during 2015–18 were evaluated using observed precipitation at 2411 stations from the China Meteorological Administration. To eliminate the influence of varying climatology in different regions in China, the stable equitable error in probability space method was used to obtain criteria for 3- and 6-h accumulated precipitation at each station and classified precipitation into light, medium, and heavy precipitation. The model was evaluated for these categories using categorical and continuous methods. The threat score and the equitable threat score showed that the model’s forecasts of rainfall were generally more accurate at shorter lead times, and the best performance occurred in the middle and lower reaches of the Yangtze River basin. The miss ratio for heavy precipitation was higher in the northern region than in the southern region, while heavy precipitation false alarms were more frequent in southwestern China. Overall, the miss ratio and false alarm ratio for heavy precipitation were highest in northern China and western China, respectively. For light and medium precipitation, the model performed best in the middle and lower reaches of the Yangtze River basin. The model predicted too much light and medium precipitation, but too little heavy precipitation. Heavy precipitation was generally underestimated over all of China, especially in the western region of China, South China, and the Yungui Plateau. Heavy precipitation was systematically underestimated because of the resolution and the related parameterization of convection.

Decoupling motion tracking control for 4WD autonomous vehicles based on the path correction

Since one control loop input disturbs the control of another loop, the dynamic coupling of the longitudinal and lateral directions adversely affects the motion tracking accuracy of autonomous vehicles. With the ability to minimize the interactions between the longitudinal and lateral dynamics, the inverse system learned by the neural network is an effective way to decouple vehicle dynamics. After tracking the vehicle states projected from the desire motion, the dynamic decoupling and the motion tracking are both realized. However, the accumulation of vehicle state tracking errors causes the stable yaw tracking error and the lateral tracking divergence. To solve the accompanying problem, a path correction model is designed to periodically update the desired vehicle states. Moreover, the applicability of the inverse system decoupling method is improved in this paper, because the method usually adopted in distributed drive electric vehicles is applied to four-wheel driving vehicles representing the traditional driving form. Simulation results indicate that the decoupling motion tracking method with the path correction model is suitable for long-distance and complex conditions and has the highest comprehensive tracking accuracy compared with the integrated MPC (model predictive control) and the pure pursuit in the dynamic coupling conditions.

Hybrid Neural Adaptive Control for Practical Tracking of Markovian Switching Networks.

While neural adaptive control is widely used for dealing with continuous- or discrete-time dynamical systems, less is known about its mechanism and performance in hybrid dynamical systems. This article develops analytical tools to investigate the neural adaptive tracking control of the hybrid Markovian switching networks with heterogeneous nonlinear dynamics and randomly switched topologies. A gradient-descent adaptation law built on neural networks (NNs) is presented for efficient distributed adaptive control. It is shown that the proposed control scheme can guarantee a stable closed-loop error system for any positive control gain and tuning gain. The tracking error is demonstrated to be practically uniformly exponentially stable with a threshold in the mean-square sense. This study further reveals how the topological structure affects the NN function, by measuring the influence of the switched topologies on the learning performance.

Real-time clock recovery algorithm with high clock frequency offset tolerance

We propose a full real-time clock recovery algorithm based on the Gardner algorithm with extended first-in-first-out (FIFO), data buffer, and add/delete state machine parts. The proposed algorithm has long-term stable bit error rate (BER) performance as well as tolerates a maximum clock frequency offset up to 330 ppm when we conducted a real-time experiment with high clock frequency errors on the Altera Stratix-V 5SGXMA7K2F40C3 FPGA platform with a symbol rate of 2.5 GBaud.

Disturbance rejection control for PMSM using integral sliding mode based composite nonlinear feedback control with load observer

The low-speed high-torque permanent magnet synchronous motor (PMSM) drive system is a kind of typical nonlinear, strong-coupling and easy-parameter perturbation electromechanical coupling system. The control system is uncertainties and subject to unknown external interferences as well. In this paper, a disturbance rejection control method combining robust speed controller and load observer is proposed for low-speed high-torque PMSM. The robust speed controller combines the composite nonlinear feedback (CNF) which has advantage in improving the transient responsive performance and the integral sliding mode (ISM) advancing in improving system robustness. Subsequently, the effects of unknown external interferences are avoided by using a sliding mode observer (SMO), in which the chattering is reduced by introducing fuzzy control, and the observation is used for feed-forward compensation. The proposed robust speed controller solves the contradiction between the rapidity and overshoot of the traditional control method, and combines the load observer to compensate the influence of the load mutations and wide range of the load changes on the control system. Finally, the numerical simulation and experiments demonstrate that the proposed speed control method is able to achieve good transient performance in inhibiting system overshoot and reducing stable state error. Additionally, it successfully suppresses the influence of load disturbances and mutations, and shows the proposed method has better robustness.

Comprehensive study on complex-valued ZNN models activated by novel nonlinear functions for dynamic complex linear equations

This paper proposes two complex-valued zeroing neural network (Cv-ZNN) models for solving dynamic complex time-variant linear equations. The models involve two complex-valued nonlinear processing methods and adapt two real-valued activation functions. The convergence and robustness of the two Cv-ZNN models are analyzed comprehensively. Firstly, the convergence discussion shows that the corresponding stable error can rapidly converge to zero in finite time, with the upper limit of constriction time calculated. The upper limit of stable error is successfully obtained when the model implementation error is injected into the Cv-ZNN models, which displays their superior robustness. Besides, the results of numerical simulations reveal that the Cv-ZNN models effectively address the time-variant linear system of equations over complex field, even in noisy environments. The simulation results also demonstrate that two novel nonlinear activation functions perform much better than the Linear, Power, Bipolar Sigmoid Power-Sigmoid and Sign-bi-power activation functions.

Day-Ahead Electric Load Forecast for a Ghanaian Health Facility Using Different Algorithms

Ghana suffers from frequent power outages, which can be compensated by off-grid energy solutions. Photovoltaic-hybrid systems become more and more important for rural electrification due to their potential to offer a clean and cost-effective energy supply. However, uncertainties related to the prediction of electrical loads and solar irradiance result in inefficient system control and can lead to an unstable electricity supply, which is vital for the high reliability required for applications within the health sector. Model predictive control (MPC) algorithms present a viable option to tackle those uncertainties compared to rule-based methods, but strongly rely on the quality of the forecasts. This study tests and evaluates (a) a seasonal autoregressive integrated moving average (SARIMA) algorithm, (b) an incremental linear regression (ILR) algorithm, (c) a long short-term memory (LSTM) model, and (d) a customized statistical approach for electrical load forecasting on real load data of a Ghanaian health facility, considering initially limited knowledge of load and pattern changes through the implementation of incremental learning. The correlation of the electrical load with exogenous variables was determined to map out possible enhancements within the algorithms. Results show that all algorithms show high accuracies with a median normalized root mean square error (nRMSE) &lt;0.1 and differing robustness towards load-shifting events, gradients, and noise. While the SARIMA algorithm and the linear regression model show extreme error outliers of nRMSE &gt;1, methods via the LSTM model and the customized statistical approaches perform better with a median nRMSE of 0.061 and stable error distribution with a maximum nRMSE of &lt;0.255. The conclusion of this study is a favoring towards the LSTM model and the statistical approach, with regard to MPC applications within photovoltaic-hybrid system solutions in the Ghanaian health sector.

A Secure Visual Secret Sharing Scheme with Authentication Based on QR Code

With the rise of the Internet of Things (IoT), various devices in life and industry are closely linked. Because of its high payload, stable error correction capability, and convenience in reading and writing, Quick Response (QR) code has been widely researched in IoT. However, the security of privacy data in IoT is also a very important issue. At the same time, because IoT is developing towards low-power devices in order to be applied to more fields, the technology protecting the security of private needs to have the characteristics of low computational complexity. Visual Secret Sharing (VSS), with its features of safety and low computational cost, can fully meet the requirements of communication security in IoT. Therefore, a VSS scheme with QR code (VSS-QR) was proposed and has been applied to some extent. In VSS-QR, the secret is shared into a series of shares. These shares are usually common QR codes, which cannot cause the attention of the attacker. However, if there is dishonesty among participants, the secret cannot be recovered, which will lead to VSS-QR cannot be widely used due to its inadequate security. In this paper, we propose a visual secret sharing scheme with authentication based on QR code (VSSA-QR). Both the reconstructed secret QR code and shares can be verified whether they are forged by attackers. The abovementioned operations conveniently are performed on low-power QR scanning devices. Not only does the proposed scheme prevent some dishonest participants or attackers from cheating, but also prevent all participants from conspiring. In addition, the payload is the QR code itself, which is higher than other schemes. Theoretical analysis and experiments prove that the proposed scheme is effective.

An homogeneous space geometry for simultaneous localisation and mapping

Simultaneous Localisation and Mapping (SLAM) is the archetypal chicken and egg problem: Localisation of a robot with respect to a map requires an estimate of the map, while mapping an environment from data acquired by a robot requires an estimate of the robot localisation. The nonlinearity and co-dependence of the SLAM problem has made it an ongoing research problem for more than thirty years. The present paper details recent advances in understanding the SLAM problem, specifically the existence of an underlying geometry and symmetry structure that provides significant insight into the difficulties that have plagued many SLAM algorithms. To demonstrate the power of the geometric insight we derive a constant gain observer for the SLAM problem that; that does not depend on linearisation, has globally asymptotically stable error dynamics, is very robust, and operates in dynamic environments (estimating the landmark velocities as states in the observer).

Finite-time convergence disturbance rejection control for a flexible Timoshenko manipulator

This paper focuses on a new finite-time convergence disturbance rejection control scheme design for a flexible Timoshenko manipulator subject to extraneous disturbances. To suppress the shear deformation and elastic oscillation, position the manipulator in a desired angle, and ensure the finitetime convergence of disturbances, we develop three disturbance observers (DOs) and boundary controllers. Under the derived DOs-based control schemes, the controlled system is guaranteed to be uniformly bounded stable and disturbance estimation errors converge to zero in a finite time. In the end, numerical simulations are established by finite difference methods to demonstrate the effectiveness of the devised scheme by selecting appropriate parameters.