Proposed Error Model Research Articles

A measure of average error variance of line features

ABSTRACTThis article presents a new development in measuring the positional error of line features in Geographic Information Systems (GIS), in the form of a new measure for estimating the average error variance of line features, including line segment, polyline, polygon, and curved lines. This average error measure is represented in the form of a covariance matrix derived by an analytical approach. Corresponding error indicators are derived from this matrix. The error of line features mainly results from two factors: (1) an error propagated from the original component points of line features and (2) a model error of interpolation between these points. In this study, a method of average error estimation has been derived regarding the first type error of line features that are interpolated by either linear or cubic interpolation methods. The main contribution of the research is the provision of an error measure to assess the quality of spatial data in application settings. The proposed error models for estimating average error variance of line features in a GIS are illustrated by both simulated and practical experiments. The results show that the line accuracy from a linear interpolation is better than a line interpolated using a cubic model.

Performance of Multi-Hop Cooperative Networks Subject to Timing Synchronization Errors

In this paper, we propose a mathematical model for timing synchronization errors in a cascaded virtual multi-hop multiple-input multiple-output (MIMO) system that incorporates cooperation at each hop using decode-and-forward (DF) algorithm. Specifically, the DF relays are grouped to form clusters and one cluster transmits the same data to the next cluster over orthogonal fading channels. The proposed error model is used to study the statistics of the timing error from one cluster to the next and it has been shown that the variance of the timing errors gradually increases as the data traverse the multi-hop network. The effects of the timing errors on the bit error probability (BEP) performance of the system have been quantified. For that purpose, the closed-form expressions of the BEP for the network are derived for every hop with a particular number of nodes per hop. The results indicate that the BEP performance of the system degrades as the data propagates from hop to hop. We quantify the minimum required SNR and the optimal number of relays per cluster that guarantee successful traversal of data to a specified number of hop while keeping overall BEP below a defined threshold.

On the model order reduction of a direct current motor

Neglecting the armature inductance, La, is a common approach for model order reduction for a class of brush DC motors. Some authors, however, make a partial or incomplete interpretation for neglecting La, leading students to wrong results and misunderstandings. The existing conditions in the literature and in introductory control systems textbooks are either based on the time constant of the mechanical system being greatly larger than that of the electrical system, or La ≈ 0. These conditions are not supported analytically and no corresponding error analysis of any kind is provided. This paper analyzes and criticizes the eligibility of these conditions and provides an error model that corresponds to the model order reduction associated with neglecting La, and another that corresponds to neglecting the non-dominant pole. Experimental results are included to illustrate the suitability of the proposed error models and the suitability of employing such models in basic control designs.

Multivariate distributed ensemble generator: A new scheme for ensemble radar precipitation estimation over temperate maritime climate

Summary It is broadly recognized that large uncertainties are associated with radar rainfall (RR) estimates, which could propagate in the hydrologic forecast system and contaminate its final outcomes. Ensemble generation of probable true rainfall is an elegant and practical solution to characterize the uncertainty of RR estimates and behavior in the hydrologic forecast system. In this study, we have proposed a fully formulated uncertainty model that can statistically quantify the characteristics of the RR errors and their spatial and temporal structure, which is a novel method of its kind in the radar data uncertainty field. The error model is established based on the distribution of gauge rainfall conditioned on radar rainfall (GR|RR). It’s spatial and temporal dependencies are simulated based on the t-copula function. With this proposed error model, a Multivariate Distributed Ensemble Generator (MDEG) driven by the copula and autoregressive filter is designed and applied in the Brue catchment (135 km 2 ), an extensively gauged site in the United Kingdom. The products from MDEG include a time series of ensemble rainfall fields with each of them representing a probable true rainfall. A series of tests show that the ensemble fields generated by MDEG have realistically maintained the spatial and temporal structure of the random error in RR as they have relatively low mean absolute errors (MAEs) of spatio-temporal correlation towards the observed ones. In addition, the results show that the simulated uncertainty bands derived by the 500 realizations of ensemble rainfall encompass most of the reference rain gauge measurements, indicating that the proposed scheme is statistically reliable.

Recursive least square perceptron model for non-stationary and imbalanced data stream classification

Classifying non-stationary and imbalanced data streams encompasses two important challenges, namely concept drift and class imbalance. “Concept drift” (or non-stationarity) is changes in the underlying function being learnt, and class imbalance is vast difference between the numbers of instances in different classes of data. Class imbalance is an obstacle for the efficiency of most classifiers and is usually observed in two-class datasets. Previous methods for classifying non-stationary and imbalanced data streams mainly focus on batch solutions, in which the classification model is trained using a chunk of data. Here, we propose an online perceptron model. The main contribution is a new error model inspired from the error model of recursive least square (RLS) filter. In the proposed error model, non-stationarity is handled with the forgetting factor of RLS error model and for handling class imbalance two different errors weighting strategies are proposed. These strategies are verified with convergence and tracking theories from adaptive filters theory. The proposed methods is evaluated on two synthetic and six real-world two-class datasets and compared with seven previous online perceptron models. The results show statistically significant improvement to previous methods.

Investigation on IEEE 802. 16m Networks under Developed Error Model

based bandwidth request mechanism is suggested for best effort services in WiMAX networks. The design of contention mechanism depends on the error model that reflects the transmission failure. In this paper, we have developed an error model by integrating the collisions due to contention, unavailability of bandwidth and channel error. The conventional exponential increase and exponential decrease (EIED) backoff witnessed low contention efficiency and high access delay with the proposed error model. Hence, we modify the EIED scheme by computing the backoff factors with average contention window and estimating the response time to reduce the waiting time of stations. The performance of WiMAX network is studied with varying number of stations, error rates and the number of slots allocated for bandwidth request. The effectiveness of the developed model is validated by means of simulation results. Keywordsresolution, medium access control, WiMAX, EIED backoff, bandwidth request.

A statistical simulation model for positional error of line features in Geographic Information Systems (GIS)

This paper presents a new error band model, the statistical simulation error model, for describing the positional error of line features by incorporating both analytical and simulation methods. In this study, line features include line segments, polylines, and polygons. In existing error models, an infinite number of points on the line segment are considered as the stochastic variables and the error band of a line segment is obtained from the union of all intermediate points on the line segment, while that of a polyline/polygon is obtained from the union of all error bands of the composite line segments. Our proposed error band model, however, regards the entire line feature (line segment/polyline/polygon) as the stochastic variable, instead of the infinite number of points on the line segment. Based solely on the statistical characteristics of the endpoints of the line feature and the predefined confidence level, our proposed error model is created by a simulation method that integrates a population of line segments/polylines/polygons computed from the entire solution set of the error model's defining equation.A comprehensive comparison of the proposed and existing error band models is carried out through both simulated and practical experiments. The experimental results show the following: (1) For line segments, the proposed standard statistically simulated error band matches that of existing error models (for example, the G-band). Further, it is found that a scaled G-band with a specific scale factor (e.g.,χ42(α)) matches the proposed statistically simulated error band with probability (1−α)×100%. (2) For polylines and polygons, if we correlate the errors of all the endpoints of the polyline/polygon, there is a marked difference between the proposed statistically simulated error band and existing error bands. The reason for the difference is explained as follows. The existing error model defines the error band of a polyline/polygon as the union of all error bands of the composite line segments, thereby only accounting for the correlation between the two endpoints of each composite line segment. However, our proposed error band model considers the entire polyline/polygon as a whole by accounting for the variance–covariance matrix of all vertices of the polyline/polygon when constructing the statistically simulated error band.

Data error quantification in spectral induced polarization imaging

Induced polarization (IP) imaging is being increasingly used in near-surface geophysical studies, particularly for hydrogeologic and environmental applications. However, the analysis of IP data error has received little attention, even though the importance of an adequate error parameterization has been demonstrated for electrical resistivity imaging. Based on the analysis of data sets measured in the frequency range from 1 Hz to 1 kHz, we proposed a model for the quantification of phase data errors in IP measurements. The analyzed data sets were collected on an experimental tank containing targets of different polarizability. Our study is based on the common practice that the discrepancy of measurements taken in normal and reciprocal configuration can be considered as a measure of data error. Statistical analysis of the discrepancies between normal and reciprocal measurements revealed that the phase error decreases with increasing resistance (i.e., signal strength). We proposed an inverse power-law model to quantify the phase error as a function of the measured resistances. We found that the adequate implementation of the proposed error model in an inversion scheme leads to improved IP imaging results in laboratory experiments. Application to a data set collected at the field-scale also demonstrated the superiority of the new model over previous assumptions.

Discretization Error Estimation in Multidisciplinary Simulations

This paper proposesmethods to estimate the discretization error in the system output of coupledmultidisciplinary simulations. In such systems, the governing equations for each discipline are numerically solved by a different computational code, and each discipline has different mesh size parameters. A classic example of multidisciplinary analysis involves fluid–structure interaction, where the element sizes in fluid and structure meshes are typically different. The general case of three-dimensional steady-state problems is considered in the current paper, where mesh refinement is possible in all three spatial directions for each discipline. Two aspects of discretization error, which are of interest in multidisciplinary analysis, are considered: disciplinary mesh sizes and the mismatch of disciplinary meshes at the interface at which boundary conditions are exchanged. Two alternate representations for the discretization error for the previously specified generic case are presented: 1) ignoring mesh mismatch at the interface and 2) considering mesh mismatch at the interface. Polynomial, rational function, and Gaussian process error models are used to represent the discretization error. The proposed error models are illustrated using a threedimensional fluid–structure interaction problem of an aircraft wing.

Importance of replication in analyzing time-series gene expression data: Corticosteroid dynamics and circadian patterns in rat liver

BackgroundMicroarray technology is a powerful and widely accepted experimental technique in molecular biology that allows studying genome wide transcriptional responses. However, experimental data usually contain potential sources of uncertainty and thus many experiments are now designed with repeated measurements to better assess such inherent variability. Many computational methods have been proposed to account for the variability in replicates. As yet, there is no model to output expression profiles accounting for replicate information so that a variety of computational models that take the expression profiles as the input data can explore this information without any modification.ResultsWe propose a methodology which integrates replicate variability into expression profiles, to generate so-called 'true' expression profiles. The study addresses two issues: (i) develop a statistical model that can estimate 'true' expression profiles which are more robust than the average profile, and (ii) extend our previous micro-clustering which was designed specifically for clustering time-series expression data. The model utilizes a previously proposed error model and the concept of 'relative difference'. The clustering effectiveness is demonstrated through synthetic data where several methods are compared. We subsequently analyze in vivo rat data to elucidate circadian transcriptional dynamics as well as liver-specific corticosteroid induced changes in gene expression.ConclusionsWe have proposed a model which integrates the error information from repeated measurements into the expression profiles. Through numerous synthetic and real time-series data, we demonstrated the ability of the approach to improve the clustering performance and assist in the identification and selection of informative expression motifs.

An integrated bundle adjustment approach to range camera geometric self-calibration

This paper describes a new method for integrated range camera system self-calibration in which both traditional camera calibration parameters and rangefinder systematic error parameters are estimated simultaneously in a free-network bundle adjustment of observations to signalised targets. Its mathematical basis is collinearity and range observation equations augmented with correction models for systematic error sources identified in the data. The self-calibration results from datasets captured with two different range cameras, a SwissRanger SR3000 and a SwissRanger SR4000, are presented and analysed in detail. The method’s effectiveness is demonstrated in terms of systematic error removal and independent accuracy assessment. Up to a 54% reduction in the residual RMS was achieved by inclusion of the proposed error models in the self-calibration adjustment. An improvement of at least 74% in the RMS of object point co-ordinate differences, over that achieved without calibration or provided by the manufacturer’s software (in the case of the SR3000), was realised in an independent accuracy assessment. In addition, the effects of several influencing variables, including the range stochastic error model, the network geometry and the range measurements themselves, on key correlation mechanisms are analysed in detail.

Thermal Error Modeling of a Machine Tool Using Data Mining Scheme

In this paper the knowledge discovery technique is used to build an effective and transparent mathematic thermal error model for machine tools. Our proposed thermal error modeling methodology (called KRL) integrates the schemes of K-means theory (KM), rough-set theory (RS), and linear regression model (LR). First, to explore the machine tool's thermal behavior, an integrated system is designed to simultaneously measure the temperature ascents at selected characteristic points and the thermal deformations at spindle nose under suitable real machining conditions. Second, the obtained data are classified by the KM method, further reduced by the RS scheme, and a linear thermal error model is established by the LR technique. To evaluate the performance of our proposed model, an adaptive neural fuzzy inference system (ANFIS) thermal error model is introduced for comparison. Finally, a verification experiment is carried out and results reveal that the proposed KRL model is effective in predicting thermal behavior in machine tools. Our proposed KRL model is transparent, easily understood by users, and can be easily programmed or modified for different machining conditions.

Error modeling for an untethered ultra-wideband system for construction indoor asset tracking

This paper analyzes the performance of an ultra-wideband (UWB) wireless network system for mobile asset tracking at a dynamic construction site. Static and dynamic error tests were performed on a commercial UWB system in different building spaces including open/closed spaces, steel/wood framed construction sites, and a closed office area. All tests were carried out with an untethered UWB configuration for more flexible deployment of the UWB system at construction sites. Statistical approaches including regression analysis, outlier detection, and Kalman filtering were used to build an error model. The research found that each site has a unique pattern of producing errors caused by various types of interference, e.g., electromagnetic interference, multi-path propagation, fading and scattering of signals. Approximately 25% of the errors were reduced by using the proposed error modeling process. The paper concludes that a statistically developed error model process can significantly reduce random errors and improve position accuracy for indoor mobile asset tracking applications in construction.

Vision-Based Roadway Geometry Computation

Geometric data in transportation, such as roadway geometry, are important for asset management and for safety analysis. Traditional roadway geometric data are measured in the field, which is time consuming, costly, and dangerous. This paper proposes an algorithm to compute roadway geometric data, including roadway length, lane width, line width, and pavement marking size, from images. This paper makes two major contributions. First, the paper proposes a generalized roadway geometry computation algorithm using emerging vision technology based on two-dimensional (2D)/three-dimensional (3D) image reconstruction. The proposed algorithm consists of four steps, which are camera calibration from vanishing points, roadway vanishing line computation, homography computation and 2D/3D reconstruction, and, finally, roadway geometry computation. Second, the paper develops an error model, called roadway geometry error model (RGEM), to spatially quantify and visualize computation errors so that decision makers can choose measurement locations with an acceptable error. The geometric interpretation to RGEM is also presented in terms of roadway vanishing line. The proposed algorithm has been tested using two sets of images that were collected from the Georgia Tech campus and from actual video log images provided by the Georgia Department of Transportation. The roadway geometry was computed and the computation errors were analyzed. The test results show that the computation errors increase when the computation locations approach the roadway vanishing line. For the computation location with a distance of 190 pixels to the roadway vanishing line, the pavement lane width computation error is less than 3 cm. The experimental results also demonstrate that the proposed error model, RGEM, is able to reliably evaluate the roadway geometry computation errors. Applications of the proposed algorithm for modern and intelligent transportation system are also discussed.

Uncertainties on mean areal precipitation: assessment and impact on streamflow simulations

Abstract. This paper investigates the influence of mean areal rainfall estimation errors on a specific case study: the use of lumped conceptual rainfall-runoff models to simulate the flood hydrographs of three small to medium-sized catchments of the upper Loire river. This area (3200 km2) is densely covered by an operational network of stream and rain gauges. It is frequently exposed to flash floods and the improvement of flood forecasting models is then a crucial concern. Particular attention has been drawn to the development of an error model for rainfall estimation consistent with data in order to produce realistic streamflow simulation uncertainty ranges. The proposed error model combines geostatistical tools based on kriging and an autoregressive model to account for temporal dependence of errors. It has been calibrated and partly validated for hourly mean areal precipitation rates. Simulated error scenarios were propagated into two calibrated rainfall-runoff models using Monte Carlo simulations. Three catchments with areas ranging from 60 to 3200 km2 were tested to reveal any possible links between the sensitivity of the model outputs to rainfall estimation errors and the size of the catchment. The results show that a large part of the rainfall-runoff (RR) modelling errors can be explained by the uncertainties on rainfall estimates, especially in the case of smaller catchments. These errors are a major factor limiting accuracy and sharpness of rainfall-runoff simulations, and thus their operational use for flood forecasting.

THE LOCALIZED GENERALIZATION ERROR MODEL FOR SINGLE LAYER PERCEPTRON NEURAL NETWORK AND SIGMOID SUPPORT VECTOR MACHINE

We had developed the localized generalization error model for supervised learning with minimization of Mean Square Error. In this work, we extend the error model to Single Layer Perceptron Neural Network (SLPNN) and Support Vector Machine (SVM) with sigmoid kernel function. For a trained SLPNN or SVM and a given training dataset, the proposed error model bounds above the error for unseen samples which are similar to the training samples. As the major component of the localized generalization error model, the stochastic sensitivity measure formula for perceptron neural network derived in this work has relaxed the assumptions of same distribution for all inputs and each sample perturbed only once in previous works. These make the sensitivity measure applicable to pattern classification problems. The stochastic sensitivity measure of SVM with Sigmoid kernel is also derived in this work as a component of the localized generalization error model. At the end of this paper, we discuss the advantages of the proposed error bound over existing error bound.

An error model for protein quantification

Quantitative experimental data is the critical bottleneck in the modeling of dynamic cellular processes in systems biology. Here, we present statistical approaches improving reproducibility of protein quantification by immunoprecipitation and immunoblotting. Based on a large data set with more than 3600 data points, we unravel that the main sources of biological variability and experimental noise are multiplicative and log-normally distributed. Therefore, we suggest a log-transformation of the data to obtain additive normally distributed noise. After this transformation, common statistical procedures can be applied to analyze the data. An error model is introduced to account for technical as well as biological variability. Elimination of these systematic errors decrease variability of measurements and allow for a more precise estimation of underlying dynamics of protein concentrations in cellular signaling. The proposed error model is relevant for simulation studies, parameter estimation and model selection, basic tools of systems biology. Matlab and R code is available from the authors on request. The data can be downloaded from our website www.fdm.uni-freiburg.de/~ckreutz/data.

A statistical error model for image sensors and its testing

AbstractSince images obtained from image sensor devices are commonly tested by performing a manual inspection or by means of procedures that involve large amounts of image processing, the growth in testing costs as the size of such devices increases poses a significant problem. Several approaches to automating the testing process have been proposed with a view to reducing testing costs but trial and error is needed to set the parameters required by such test procedures. In this paper we propose an error model for images taken by image sensor devices that can perform a quantitative evaluation with a small number of free parameters. Image quality testing can be performed relatively easily using this model since it replaces a previously ambiguous error model by one that can be determined uniquely. In addition, since the proposed error model is defined statistically in terms of the brightness levels of pixels in each of the individual images, even if there are individual differences between the image sensor devices, these have no influence on the testing procedure. Experimental results demonstrate that an image quality testing based on the proposed error model has the same level of accuracy as manual inspections performed by an experienced technician. © 2007 Wiley Periodicals, Inc. Syst Comp Jpn, 38(11): 1– 11, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20804

Using a multi‐dimensional satellite rainfall error model to characterize uncertainty in soil moisture fields simulated by an offline land surface model

In this study, we investigate the significance of using an improved error modeling strategy to characterize the spatio‐temporal characteristics of uncertainty in simulation of soil moisture fields from an off‐line land surface model forced with satellite rainfall data. We coupled a Two‐Dimensional Satellite Rainfall Error Model (SREM2D) with the Common Land Model to propagate ensembles of simulated satellite rain fields for the prediction of soil moisture at depths of 5 cm (near surface) and 50 cm (root zone). Our investigations revealed that multi‐dimensional error modeling captures the spatio‐temporal characteristics of soil moisture uncertainty with higher consistency than simpler bi‐dimensional error modeling strategies. The proposed error modeling strategy appears to have the potential for delineating a more robust framework for the optimal integration of satellite rainfall data into models towards the study of global water and energy cycle.

Using Bayesian Statistics to Capture the Effects of Modelling Errors in Inverse Problems

When the parameters of a numerical model are adjusted, so that the predictions of the model match measurements from the real system, we need to take account of two sources of errors. These being measurement errors and modelling errors. Measurement errors are commonly considered, and a number of different approaches are in general usage, the most common being the weighted sum of squares method. In this paper the standard Bayesian equation, used for inverse problems, is reformulated so as to make it more intuitive to use. This allows the inclusion of both a modelling error and correlations between measurements to be carried out easily. The results are tested on a simple one-parameter numerical model and a cross-sectional model of a petroleum reservoir. In the first case the proposed error model appears to work well. In the second case it appears that the objective function is multimodal, leading to multiple acceptable solutions. The results of this paper are important to those whose numerical models are thought to contain significant modelling error. This encompasses many areas of modelling related to earth science and engineering.