Stability Error Research Articles

Investigation of Position and Velocity Stability of the Nanometer Resolution Linear Motor Stage with Air Bearings by Shaping of Controller Transfer Function

Modern industrial enterprises require high accuracy and precision feedback systems to fulfil cutting edge requirements of technological processes. As demand for a highly accurate system grows, a thin gap between throughput and quality exists. The conjunction of ultrafast lasers and modern control strategies of mechatronic systems can be taken into account as an effective solution to reach both throughput and tolerances. In the present paper, the dynamic errors of the moving platform of the one degree of freedom stage, based on linear motor and air bearings, have been analyzed. A precision positioning system is investigated as a symmetric system which is based on symmetric linear motor. The goal of the present article is to investigate the controllers of the different architecture and to find the best controller that can ensure a stable and small dynamic error of the displacement of the stage platform at four different constant velocities of the moving platform. The relations between the controller order, velocity and the displacement dynamic error have been investigated. It is determined that higher-order controllers can reduce the dynamic error significantly at low velocities of the moving platforms: 1 and 5 mm/s. On the contrary, the low order controllers of 4th-degree polynomials of the transfer function can also provide small dynamic errors of the displacement of the platform.

Sales Forecasting of Perishable Foods With Multiple Stores and Communities-An Empirical Study of Convenience Stores in Taiwan

Purpose: In recent years, smart retailing has been gradually acknowledged and has slowly impacted countless industries. This study takes smart retailing as the starting point and explores the increased attention on the perishable food (fresh food) market in convenience stores. Remarkable improvements in the general food consumer population in Taiwan and the advent of an aging society with changes in social structure and consumer style are also taken into consideration. As perishable goods (fresh food products) easily spoil, the scrap rate of fresh food in convenience stores has always been a topic of great importance. Design/methodology/approach: Perishable food from well-known convenience store chains in Taiwan is taken as the subject of this study, and sales data of stores in different regions are used to establish sales forecast models for the convenience store chains. The optimal sales forecast model for each store's products was established through a data analysis, and the characteristics and differences of all products are explored to establish decision-making advices for enterprises in ordering perishable food. Multiple stores and perishable foods with two-year sales data of 11 perishable foods in every six stores in different county are adopted to establish the predictive models in this study, including time series, support vector machine (SVM), Lagrangian support vector machine (LSVM), random forest, neural network, generalized linear, and generalized linear mixed models. Findings: Results show that the time series model and SVM have lower prediction error values and better prediction results among all the established sales forecast models. Given the influence of region and population characteristics, varying models are applicable to stores in different regions. Thus, the difficulty of prediction will also vary. Practical implications: Different commodities will have varying levels of prediction difficulty due to dissimilarities in commodity attributes. Convenience stores are generally willing to predict the sales of fresh food through an artificial intelligence model. Different forecasting models should be selected by stores. If one or more forecasting models are used for prediction, the model with a stable forecasting error should be selected for implementation. Originality/value: This research analyzes the products sold in multiple stores and applies different time series and machine learning algorithms to build predictive models. The results show that the most suitable algorithms for stores of products are different. If a convenience store wants to build a predictive model, differentiated models must be established for different stores and commodities.

ℓ2–ℓ∞ proportional–integral observer design for systems with mixed time‐delays under round–robin protocol

AbstractIn this article, the design problem of ℓ2–ℓ∞ proportional–integral observer (PIO) is investigated for a class of discrete‐time systems with mixed time‐delays. The mixed time‐delays comprise both the discrete time‐varying delays and infinitely distributed delays. The round–robin protocol (RRP) is employed to schedule the data transmissions from the sensors to the observer so as to mitigate the communication burden and prevent the data collisions. A novel PIO is developed whose observer gain is dependent on the data transmission order as a reflection of the effects induced by the RRP scheduling. By resorting to the token‐dependent Lyapunov functional and the matrix inequality technique, the desired PIO is designed with exponentially stable error dynamics of the state estimation and guaranteed ℓ2–ℓ∞ disturbance attenuation/resistance capacity. Finally, a simulation example is exploited to verify the validity of the proposed observer design method.

Fractal Pattern for Multiscale Digital Image Correlation

Digital Image Correlation (DIC) is based on the matching, between reference and deformed state images, of features contained in patterns that are deposited on test sample surfaces. These features are often suitable for a single scale, and there is a current lack of multiscale patterns capable of providing reliable displacement measurements over a wide range of scales. Here, we aim to demonstrate that a pattern based on a fractal (self-affine) surface would make a suitable pattern for multiscale DIC. A method to numerically generate patterns directly from a desired auto-correlation function is introduced. It is then enhanced by a Mean Intensity Gradient (MIG) improvement process based on grey level redistribution. Numerical experiments at multiple scales are performed for two different imposed displacement fields and results for one of the patterns generated are compared with those obtained for a random pattern and a Perlin noise one. The proposed pattern is shown to lead to DIC errors comparable to those found with the two others for the first scales, but has much greater robustness. More importantly, the pattern generated here exhibits stable errors and robustness with respect to the scale whereas these two outputs become significantly degraded for the other two patterns as the scale increases. As a result, scale invariance properties of the pattern based on fractal surfaces correspond to scale invariance in DIC errors as well. This is of great interest regarding the use of such patterns in multiscale DIC.

The mollification method based on a modified operator to the ill-posed problem for 3D Helmholtz equation with mixed boundary

The paper is considered a Cauchy problem for Helmholtz equation with mixed boundary in three-dimensional case. The problem is severely ill-posed (small deviation in the data may produce large errors in the computed solution), to solve this problem, a mollification method based on modified bivariate de la Vallée Poussin operator is proposed. The stable error estimates are obtained in Sobolev space under the suitable choice of mollification parameters and the a priori bounds assumption, the major approach to obtain the convergence estimates is to divide the real plane R2 into 25 regions. The numerical experiments support the feasible, stable and convergent of our algorithm.

A kind of operator regularization method for Cauchy problem of the Helmholtz equation in a multi-dimensional case

In this paper, a Cauchy problem of Helmholtz equation in a multi-dimensional case is investigated. This problem is severely ill-posed and small perturbations to measurement data can result in large changes in the solution. A kind of operator regularization method is proposed. The stable error estimates are obtained in the norm and norm under the conditions that m is even, md>x, mk>1, and suitable choice of regular parameters. Error estimates show that the regularized solution depends continuously on the perturbation noisy data and wave number. Our method makes up the limitation of small waves. Three numerical experiments show that our proposed method is effective and stable, especially in the case of a large wave number.

Verification of Solid Precipitation Forecasts from Numerical Weather Prediction Models in Norway

AbstractAssessing the quality of precipitation forecasts requires observations, but all precipitation observations have associated uncertainties making it difficult to quantify the true forecast quality. One of the largest uncertainties is due to the wind-induced undercatch of solid precipitation gauge measurements. This study discusses how this impacts the verification of precipitation forecasts for Norway for one global model [the high-resolution version of the ECMWF Integrated Forecasting System (IFS-HRES)], and one high-resolution, limited-area model [Applications of Research to Operations at Mesoscale (MEPS)]. First, the forecasts are compared with high-quality reference measurements (less undercatch) and with more simple measurement equipment commonly available (substantial undercatch) at the Haukeliseter observation site. Then the verification is extended to include all Norwegian observation sites: 1) stratified by wind speed, since calm (windy) conditions experience less (more) undercatch; and 2) by applying transfer functions, which convert measured precipitation to what would have been measured with high-quality equipment with less undercatch, before the forecast–observation comparison is performed. Results show that the wind-induced undercatch of solid precipitation has a substantial impact on verification results. Furthermore, applying transfer functions to adjust for wind-induced undercatch of solid precipitation gives a more realistic picture of true forecast capabilities. In particular, estimates of systematic forecast biases are improved, and to a lesser degree, verification scores like correlation, RMSE, ETS, and stable equitable error in probability space (SEEPS). However, uncertainties associated with applying transfer functions are substantial and need to be taken into account in the verification process. Precipitation forecast verification for liquid and solid precipitation should be done separately whenever possible.

Global economic activity, crude oil price and production, stock market behaviour and the Nigeria-US exchange rate

This paper investigates the dynamic relationship among oil price, Nigeria-US exchange rate, stock market activity, Kilian's global economic activity index, and global oil production. We develop a robust, stable single-equation error correction model where the exchange rate solely bears the burden of short-run adjustments with causal influences from the rest of the variables included in the model. We find a role for asymmetry in the long run, confirming the presence of equilibrium-path adjustment asymmetry and suggesting that the positive and negative variations must be accounted for in designing the policymaking process to enforce stable exchange rate movement. By comparing the linear and nonlinear models, we find that the two models are complementary and that each is horizon-bound in its forecasting ability. • Link between oil price, Nigeria exchange rate, equity, global activity index and oil production. • A robust, stable single-equation error correction model is developed. • We find a role for asymmetry in the long-run, confirming the presence of equilibrium-path. • Find that the positive and negative variations must be adopted in model building. • We find linear and nonlinear models as complementary.

Zeroing neural network with comprehensive performance and its applications to time-varying Lyapunov equation and perturbed robotic tracking

The time-varying Lyapunov equation is an important problem that has been extensively employed in the engineering field and the Zeroing Neural Network (ZNN) is a powerful tool for solving such problem. However, unpredictable noises can potentially harm ZNN’s accuracy in practical situations. Thus, the comprehensive performance of the ZNN model requires both fast convergence rate and strong robustness, which are not easy to accomplish. In this paper, based on a new neural dynamic, a novel Noise-Tolerance Finite-time convergent ZNN (NTFZNN) model for solving the time-varying Lyapunov equations has been proposed. The NTFZNN model simultaneously converges in finite time and have stable residual error even under unbounded time-varying noises. Furthermore, the Simplified Finite-te convergent Activation Function (SFAF) with simpler structure is used in the NTFZNN model to reduce model complexity while retaining finite convergence time. Theoretical proofs and numerical simulations are provided in this paper to substantiate the NTFZNN model’s convergence and robustness performances, which are better than performances of the ordinary ZNN model and the Noise-Tolerance ZNN (NTZNN) model. Finally, simulation experiment of using the NTFZNN model to control a wheeled robot manipulator under perturbation validates the superior applicability of the NTFZNN model.

RESISTANCE OF A RED LATOSOL TO PENETRATION: COMPARISON OF PENETROMETERS, MODEL ADJUSTMENT, AND SOIL WATER CONTENT CORRECTION

ABSTRACT Penetration resistance can be determined directly in the field or in the laboratory. However, data obtained using the two methods are not directly comparable. Considering soil moisture influences penetration resistance, penetration resistance data obtained using the two methods can be corrected based on common moisture values. To enable comparison of the data, the measured data should be adjusted using mathematical models. Consequently, the objective of the present study was to compare soil penetration resistance values measured in a Red Latosol using a static penetrometer and a bench-top electronic penetrometer. The comparison was carried out using samples collected from different soil layers, based on moisture levels ranging from 0.15 to 0.28 kg kg-1. In addition, the reliability of some mathematical models was compared using bench-penetrometer data. Finally, the Busscher method and a new proposed method for moisture correction were tested. According to the comparison of results between the equipment, it is necessary to correct data using a linear type equation. The Jakobsen & Dexter (1987) model had the optimal performance (R2: 0.89; RMSD: 0.70). The new proposed corrected method was tested using several reference moisture values and it presented minor (< 0.30 RMSD) and stable errors.

Design and implementation of real‐time monitoring system for atmospheric particles based on a cloud platform

In order to reduce the cost of data acquisition and arrange the data acquisition nodes flexibly to meet the requirements of mobile pollution sources and unfixed data collection points, a real-time monitoring system for atmospheric particles based on a cloud platform is proposed here. The movable data acquisition nodes for atmospheric particles are designed to collect the particle concentration data, which are uploaded to the cloud platform through the general packet radio service (GPRS) network. The android application gets the atmospheric particle concentration data from the cloud platform in real time. Data acquisition nodes can be flexibly added to the system. It greatly improves the sharing of atmospheric particle concentration data. The test results show that the system has stable performance and low error rate.

Evaluation of acoustic emission source localization accuracy in concrete structures

Acoustic emission source localization is a promising monitoring technique for concrete structures. However, the accuracy of acoustic emission source localization is influenced by many factors, such as the presence of cracks, which are commonly observed in existing reinforced concrete structures. In this article, the acoustic emission source localization is evaluated using a numerical model with a total number of 11,827,200 independent simulated tests. In this work, the investigated influential factors include the presence of cracks, arrival time picking error, and senor layout. The accuracy of source localization is quantified by the characteristic error defined in this article. Using the proposed wave propagation properties, a relatively stable characteristic error of 150 mm is estimated in the detection zone with the maximum sensor spacing less than 1 m. The evaluation approach and simulated characteristic error are validated experimentally by comparing the 200 manually generated signals using hammer hits on a cracked concrete beam.

Long baseline navigation filter with clock offset estimation

In underwater navigation, the global positioning system is unavailable; hence, other solutions must be pursued in the development of navigation systems. In this paper, filters for the position, linear velocity, and acceleration of underwater vehicles are derived by combining a long baseline acoustic positioning system with an inertial navigation system. A dynamic model is devised via state augmentation, including the bias of the pseudo-ranges, which accounts for the effect of the unknown offset between the emitters’ and receivers’ clocks. With this technique, the resulting dynamics are linear, in spite of the original nonlinear nature of the problem. The proposed solution, which includes the explicit dynamic estimation of the bias of the pseudo-ranges, is a linear Kalman filter. The observability of the system is assessed, which allows to establish globally exponentially stable error dynamics. The performance of the solution is evaluated with realistic simulation results, considering sensor noise and discrete-time measurements. Finally, the comparison with the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the Bayesian Cramer–Rao bound is presented, including Monte Carlo simulations. This comparison shows the goodness of the proposed solution, which converges for all initial conditions and exhibits performance comparable to the EKF and the UKF, whereas the EKF and UKF are shown to lack global convergence.

Bias correction of ensemble precipitation forecasts in the improvement of summer streamflow prediction skill

In recent years, ensemble precipitation forecasting has been able to provide more uncertainty information and plays an increasingly important role in basin-scale hydrologic predictions. The Global Ensemble Forecast System (GEFS) reforecast data released by the National Centers for Environmental Prediction (NCEP) has a long-term data archive and relatively stable systematic error, which shows great potential in hydrologic applications. This paper aims to bias correct the GEFS reforecast precipitation forecasts and analyze the impact of bias-corrected ensemble precipitation forecasts on the improvement of summer streamflow prediction skill. Driven by the GEFS reforecast ensemble precipitation forecasts, the Variable Infiltration Capacity (VIC) distributed hydrological model is applied to simulate the 2000–2010 summer streamflow over the Huaihe River basin.The results show that the GEFS reforecast data generally underestimates the precipitation amount with the increasing leadtime and the streamflow simulation tends to underestimate the peak due to the spatial precipitation error. In this study, both the frequency matching method (FMM) and the analog method are applied to calibrate the GEFS reforecast ensemble precipitation forecasts. The searching criteria of the analog method has been improved based on the basin-scale areal precipitation.After bias correction, the FMM method mainly improves the forecast skill of light rain and moderate rain for the 1–8 d leadtime. By contrast, the analog method improves probabilistic precipitation forecasts and increases ensemble spread to alleviate the underdispersion of raw ensemble forecasts for the 1–8 d leadtime. The analog method can also improve spatial distributions with the downscaling information from the observed precipitation, producing better probabilistic precipitation forecasts. The streamflow prediction using bias-corrected precipitation forecasts better resembles the observed streamflow. The analog-corrected precipitation forecasts can effectively improve the streamflow simulations for the 1–5 d leadtime, with the maximum improvements at the 2–3 d leadtime. The FMM method only improves the streamflow predictions for the 2 d leadtime.For the heavy flood events caused by extreme rainstorms in the summer of 2003, the ensemble mean forecasts have limited forecast skill, but probabilistic precipitation forecasts show great potential in predicting the magnitude of extreme rainfall events. Meanwhile, the ensemble streamflow predictions using the analog-corrected precipitation forecasts have larger ensemble spread and a higher Nash coefficient of extreme streamflow.The encouraging results suggest that the reforecast ensemble dataset exhibits a great value to improve hydrometeorological predictions for operational applications.

Verification of accuracy of warfarin stable dose prediction models in Shandong population

To compare the accuracy of five warfarin-dosing algorithms and warfarin stable dose model (2.5 mg/day) for Shandong population. One hundred and twenty five patients who achieved stable warfarin dose were enrolled. Clinical and genetic data were used to evaluate the value of each algorithm by calculating the percentage of patients whose predicted warfarin dose was within 20% of the actual stable therapeutic dose and mean absolute error (MAE). The frequency of patients with CYP2C9*1/*1, CYP2C9*1/*3 and CYP2C9*1/*2 genotype was 92.00%, 7.20%, 0.80%, respectively. That of VKORC1-1639 AA, AG and GG genotype was 82.40%, 15.20%, 2.40%, respectively. CYP4F2*1/*1, *1/*3, *3/*3 genotype was 50.40%, 39.20%, 10.40%, respectively. With the same genotypes for other loci, patients who carried at least one VKORC1-16398G mutant allele had increased warfarin stable daily dose compared with VKORC1-1639AA. Compared with CYP4F2*1/*1, those carrying at least one CYP4F2*3 mutant allele had warfarin stable daily dose increased by 5.9%-13.00%. The percentage of ideal prediction calculated from IWPC model (59.20%), Huang model (57.60%) and Ohno model (52.80%) were higher than others. The MAE were 0.35 (95%CI: 0.11-0.49), 0.15 (95%CI: 0.10-0.32), 0.39 (95%CI: 0.12-0.51), respectively. The polymorphisms of CYP2C9, VKORC1 and CYP4F2 genes can influence the stable dose of warfarin in Shandong population. IWPC algorithm is suitable for guiding the use of warfarin in this population.

MPPT control of PV array based on PSO and adaptive controller

In general, photovoltaic (PV) array is not able to generate maximum power automatically, because some partial shading caused by trees, clouds, or buildings. Irradiation imperfections received by the PV array are overcome by applying maximum power point tracking (MPPT) to the output of the PV array. In order to overcome these partial shading problems, this system is employing particle swarm optimization (PSO) as MPPT method. It optimizes the output power of the solar PV array by Zeta converter. Output voltage of MPPT has high rate such that it needs stepdown device to regulate certain voltage. Constant voltage will be the input voltage of buck converter and controlled using adaptive PID. Adaptive control based on model reference adaptive control (MRAC) has design that almost same as the conventional PID structure and it has better performance in several conditions. The proposed system is expected to have stable output and able to perfectly emulate the response of the reference model. From the simulation results, it appears that PSO have high tracking accuracy and high tracking speed to reach maximum power of PV array. In the output voltage regulation, adaptive control does not have a stable error status and consistently follows the set point value.

Safety‐constrained robust adaptive control for a class of MIMO non‐linear systems

This study proposes two new safety-constrained robust indirect adaptive control schemes for a class of multi-input multi-output non-linear systems subject to unstructured additive model uncertainties and external disturbances. The controllers are designed using a novel error transformation and a new asymptotically stable closed-loop non-linear error dynamics. The model uncertainties of the actual system are approximated by constructing a neural network-based auxiliary observer dynamics. The weights of the neural network are updated using a robust Lyapunov stable weight update rule. Using the estimation information of model uncertainties, two different asymptotically and finite-time exponentially stable tracking controllers are designed to minimise the error between auxiliary observer states and reference signals. It is proven that the closed-loop states of the actual system will remain bounded by the imposed state constraints and the steady-state tracking error of the system will converge asymptotically (or exponentially in finite time) to a user-defined domain. The beauty of the proposed control designs lies in the fact that they are easy to design and implement, and provide design freedom to impose constraints on an individual component of the system states. The effectiveness of the proposed techniques is shown by controlling a two-link robot manipulator in a constrained environment.

An Unknown Input Multiobserver Approach for Estimation and Control Under Adversarial Attacks

We address the problem of state estimation, attack isolation, and control of discrete-time linear time-invariant systems under (potentially unbounded) actuator and sensor false data injection attacks. Using a bank of unknown input observers, each observer leading to an exponentially stable estimation error (in the attack-free case), we propose an observer-based estimator that provides exponential estimates of the system state despite actuator and sensor attacks. Exploiting sensor and actuator redundancy, the estimation scheme is guaranteed to work if a sufficiently small subset of sensors and actuators is under attack. Using the proposed estimator, we provide tools for reconstructing and isolating actuator and sensor attacks, and a control scheme capable of stabilizing the closed-loop dynamics by switching off isolated actuators. Simulation results are presented to illustrate the performance of our tools.

Вплив числа електродних пар на похибку електрохімічного давача поляризаційного опору для вимірювання шидкості атмосферної корозії

Investigate the influence of the number of electrode pairs of multi-electrode co-surface electrochemical polarization resistance sensors on the error of measurement of polarization resistance, and, accordingly, on the corrosion rate under atmospheric conditions. Method of polarization resistance. Determination of the contact area of electrodes with the aluminum substrate by the method of obtaining a print on a flat surface. Graphical modeling of the contact surface of the sensing element from the steel electrodes to the anodized aluminum substrate. Investigation results of the influence of the electrode pairs number of multielectrode cosurface electrochemical polarization resistance sensor, sensing element of which is steel-made and is located on the thermoconductive anodized aluminum substrate, on the measurement error of corrosion rate in atmospheric conditions are presented. It was shown that in determining of the corrosion rate by polarization resistance method the increasing of the electrode pairs number of sensor from one to four increases the reproducibility of measurement results and their convergence with the gravimetric data. Taking into account the form of prints of four-pair sensitive element, the area of surface contact of sensitive element of eight-pair sensor with aluminum substrate was graphically simulated. It was taken into account during modeling, that the design feature of the sensor is a possibility of full contact of one pair of the electrodes with the substrate, which explains the reason of measurement error increasing with increasing the number of electrodes’ pairs. Increasing the pairs number from one to four and then to eight decreases the part of surface of sufficiently tight contact of sensitive element with aluminum substrate from 100% to 50% and further up to 30 %. The extreme dependence of the measurement error on the number of electrodes pairs due to the increasing area of the working surface of the electrodes and reducing the area of tight contact with the aluminum heat-conducting base was revealed. It was found that four electrodes pairs for the presented sensor design is optimal. It was established that the reason of increasing of the error of polarization resistance measurement under atmospheric conditions and, accordingly, the corrosion rate, by using the electrochemical multi-electrode co-surface sensors of polarization resistance under increasing the electrode pairs number (from one to eight) is the decreasing in the surface part of a sufficiently dense contact of the sensitive element (about two or three times). Another tendency that leads to decreasing in error is decreasing in the error of setting the corresponding polarization while increasing the total area of the electrodes. The extreme dependence of this error on the number of electrode pairs with a minimum for a four-pair sensor is shown. The problem of uncontrolled variation of the measurement error by using the polarization resistance sensor of the considered construction was solved and the optimal number of electrode pairs (four) was determined. Using such of a sensor will allow to evaluate the corrosivity of the atmospheric air environment with respect to the responsible metal structures and their corrosion state in local corrosion-dangerous places with stable and minimal error.

Cloud connection oriented real‐time monitoring system for atmospheric particles

To meet the requirements of data acquisition from mobile pollution sources and unfixed data acquisition points in atmospheric particle monitoring system, this study designs a real-time monitoring system for atmospheric particles such as PM2.5 based on a single-chip microcomputer, an ET-iLink open cloud platform and an Android operating system. The movable data acquisition nodes for atmospheric particles are designed. The laser scattering method is used to obtain the data of atmospheric particle concentration, which are uploaded to the cloud platform through the GPRS network. The Android application obtains the real time data of atmospheric particle concentration from the cloud platform. Thus the real-time remote monitoring for atmospheric particles is realised. The test results show that the system has the following advantages: stable performance, high scalability and low error rate.