Global Error Measure Research Articles

Ensemble of metamodels-assisted probability density evolution method for structural reliability analysis

An active-learning reliability method called the AEM-PDEM is proposed that combines adaptive ensemble of metamodels (EM) and the probability density evolution method (PDEM). Three critical aspects are addressed in this method. First, the ensemble of three diverse metamodels, i.e., the polynomial chaos Kriging (PCK), the low-rank approximation (LRA) and the support vector regression (SVR), is built by weighted combination according to their global error measures, which enables to provide both predicted value and variance. Second, the EM predictions at the training samples are replaced by the true computational model responses, so as to secure the accuracy of failure probability estimate. Third, according to the PDEM-oriented expected improvement function (PEIF), a multi-point enrichment process is developed based on the EM and the three component metamodels. Then, three numerical examples are investigated and comparisons are made between the AEM-PDEM and other existing reliability methods. Results demonstrate that, in comparison with the existing APCK-PDEM, the AEM-PDEM needs roughly 85-95% of the number of computational model evaluations. More importantly, it only requires approximately 30-45% of the number of iterations during the active-learning process. As a result, it just consumes nearly 35-50% of computational time of the APCK-PDEM, especially in high-dimensional dynamic problems and practical complex engineering problems.

Single-Stage Refinement CNN for Depth Estimation in Monocular Images

Depth reconstruction from single monocular images has been a challenging task due to the complexity and the quantity of depth cues that images have. Convolutional Neural Networks (CNN) have been successfully used to reconstruct depth of general object scenes; however, proposed works use several stages of training which make this process more complex and time consuming. As we aim to build a computational efficient model, we focus on single-stage training CNN. In this paper, we propose five different models for solving this task, ranging from a simple convolutional network, to one with residual, convolutional, refinement and upsampling layers. We compare our models with the current state of the art in depth reconstruction and measure depth reconstruction error for different datasets (KITTI, NYU), obtaining improvements in both global and local error measures.

Lattice Boltzmann Simulation of the Dynamic Behavior of Solids

AbstractThe Lattice Boltzmann Method (LBM) is a numerical method that is mainly used to simulate fluid flows but it can be applied to structural problems as well. In this work, different LBMs for solids subject to antiplane shear deformation are investigated with regard to their convergence and energy conservation behavior. In particular, the two‐dimensional models of Guangwu [1] and Chopard et al. [2] are analyzed. To compare the two models, the evolution of the total energy and the L2 norm of a global error measure are analyzed.

Application of the extended quadrature method of moments as a multi-moment parameterization scheme for raindrops sedimentation

In numerical weather prediction models, previous approaches have employed bulk parameterization schemes based on presumed-number-density-functions or quadrature methods of moments (QMOM). In the present work, a new parameterization based on the extended quadrature method of moments (EQMOM) introduced in Yuan et al. (2012) is applied to the case of pure sedimentation of rain drops (one-dimensional “rain-shaft” test case). In EQMOM, the drop size distribution is represented by a weighted sum of kernel density functions, combining elements of quadrature and presumed functional form methods. In cloud microphysics, moment parameterization is frequently based on Gamma distributions, which guided the choice of the kernel shape employed here. EQMOM allows inclusion of a number of prognostic moments in the method (e.g. M(0)-M(6)), which improves flexibility in the representation of a continuous size distribution. QMOM and EQMOM up to order 3 were applied in two drop sedimentation test cases previously presented in the literature, in which initial states consist of different cloud heights and drop size distribution shapes. Results were compared to a spectral reference model using a number of transported bin sizes showing good agreement. The analysis was focused in the sedimentation induced errors obtained by the different approaches. In QMOM, size sorting due to different fall velocities generates step patterns in the moment profiles. With EQMOM, on the other hand, these artifacts are significantly suppressed. Furthermore, predictions of the number concentration, total liquid content, radar reflectivity, mass mean diameter and rain rates are shown to be greatly improved when EQMOM is employed. Quantitatively, EQMOM is capable of reducing global error measures by nearly one order of magnitude, when compared to results obtained by previous methods in a common benchmark, showing the great potential of the method in the field of meteorology.

Evaluation of Modified Fish-Bone Model for Estimating Seismic Demands of Irregular MRF Structures

This paper evaluates the accuracy of the Modified Fish-Bone (MFB) model for estimating the maximum inter-story drift ratio of irregular moment resisting frame (MRF) structures. To make this model applicable to irregular MRF structures, some modifications are made to the MFB formula. In order to evaluate the accuracy of the MFB model, several irregular frames with different types of irregularities are considered when subjected to different ground motions with different intensities. A local and a global error measure are defined and they are calculated for different frame models subjected to different earthquake records. The effects of different irregularities, ductility demand and frame height on the accuracy of the MFB model are investigated. Based on the results obtained from this evaluation, two simple and effective approaches are suggested to improve the MFB models.

Many Phenotypes Without Many False Discoveries: Error Controlling Strategies for Multitrait Association Studies.

ABSTRACTThe genetic basis of multiple phenotypes such as gene expression, metabolite levels, or imaging features is often investigated by testing a large collection of hypotheses, probing the existence of association between each of the traits and hundreds of thousands of genotyped variants. Appropriate multiplicity adjustment is crucial to guarantee replicability of findings, and the false discovery rate (FDR) is frequently adopted as a measure of global error. In the interest of interpretability, results are often summarized so that reporting focuses on variants discovered to be associated to some phenotypes. We show that applying FDR‐controlling procedures on the entire collection of hypotheses fails to control the rate of false discovery of associated variants as well as the expected value of the average proportion of false discovery of phenotypes influenced by such variants. We propose a simple hierarchical testing procedure that allows control of both these error rates and provides a more reliable basis for the identification of variants with functional effects. We demonstrate the utility of this approach through simulation studies comparing various error rates and measures of power for genetic association studies of multiple traits. Finally, we apply the proposed method to identify genetic variants that impact flowering phenotypes in Arabidopsis thaliana, expanding the set of discoveries.

Uncertainty quantification in LES of a turbulent bluff-body stabilized flame

We address the forward uncertainty quantification problem in large eddy simulation (LES) of a turbulent non-premixed hydrocarbon flame, focusing on parametric uncertainty. More specifically, we examine the effect of uncertainty in the Smagorinsky coefficient and turbulent Prandtl and Schmidt numbers on specific quantities of interest. To conduct this analysis 25 LES simulations are performed, from which a surrogate model is built, based on polynomial chaos expansion, for the quantities of interest. This enables global sensitivity analysis and forward propagation of uncertainty, providing marginal and joint distributions on the quantities of interest. A non-intrusive method is used to construct the surrogate models, avoiding the need to modify the deterministic LES forward solver. The accuracy of the surrogates is examined using global error measures. The results provide insights into the underlying structure of the LES simulation, the impact of varying parameters on specific observables, and correlations among different quantities of interest.

A mixed isostatic 24 dof element for static and buckling analysis of laminated folded plates

A mixed, quadrilateral, 3D plate element is proposed for static linear and buckling analysis of folded laminated composite structures. Numerical results show accuracy, comparing to analytical and numerical references, and convergence rate h2 measured using an s-norm. These characteristics are due to the self-equilibrated, isostatic state of stress in the element, and to the element kinematics leading to element compliance and compatibility matrix calculations based solely on the interpolation along the element edges. For folded plates, the drilling rotations do not require penalty functions or non-symmetric formulations, thus avoiding spurious energy modes. Buckling analysis is achieved by a corotational formulation, which is possible thanks to the accuracy of rotation approximations. Benchmarking for laminated composite plates includes convergence of displacements and stress-resultants, global error measures, and comparison with literature results.

Intelligent noise detection and filtering using neuro-fuzzy system

In this paper, we propose a neuro-fuzzy based blind image restoration to remove impulse noise from low as well as highly corrupted images. Main components of the proposed technique include noise detection, histogram estimation and noise filtering process. Proposed technique constructs the fuzzy sets using fuzzy number construction algorithm. These fuzzy sets are used in noise filtering process to remove impulse noise from the noisy pixels using neuro-fuzzy inference system and fuzzy decider. Experimental results are based on global and local error measures, which prove that the proposed technique gives superior results than the present well known impulse noise filtering methods.

Various approaches for constructing an ensemble of metamodels using local measures

Metamodels are approximate mathematical models used as surrogates for computationally expensive simulations. Since metamodels are widely used in design space exploration and optimization, there is growing interest in developing techniques to enhance their accuracy. It has been shown that the accuracy of metamodel predictions can be increased by combining individual metamodels in the form of an ensemble. Several efforts were focused on determining the contribution (or weight factor) of a metamodel in the ensemble using global error measures. In addition, prediction variance is also used as a local error measure to determine the weight factors. This paper investigates the efficiency of using local error measures, and also presents the use of the pointwise cross validation error as a local error measure as an alternative to using prediction variance. The effectiveness of ensemble models are tested on several problems with varying dimensionality: five mathematical benchmark problems, two structural mechanics problems and an automobile crash problem. It is found that the spatial ensemble models show better performances than the global ensemble for the low-dimensional problems, while the global ensemble is a more accurate model than the spatial ensembles for the high-dimensional problems. Ensembles based on pointwise cross validation error and prediction variance provide similar accuracy. The ensemble models based on local measures reduce cross validation errors drastically, but their performances are not that impressive in reducing the error evaluated at random test points, because the pointwise cross validation error is not a good surrogate for the error at a point.

Semi-blind image restoration using a local neural approach

This work aims to define and experimentally evaluate an iterative strategy based on neural learning for semi-blind image restoration in the presence of blur and noise. Salient aspects of the proposed strategy are the use of a local error function derived from the conventional global constrained error measure and the assignment of a separate regularization parameter to each image pixel based on local gray level variance. This method can be viewed as a neural strategy where the pixels of the restored image are the synapse's weights the neural network tries to modify during learning to minimize the output error measurement. The method was experimentally evaluated in terms of restoration quality and speed using test images synthetically degraded and increasingly corrupted. To investigate whether the strategy can be considered an alternative to neural restoration procedures, the results were compared with those obtained by well known Hopfield-based restoration approaches. Results obtained show that our method performs significantly better and faster than other models considered.

Ab Initio Wavenumber Accurate Spectroscopy: 1CH2 and HCN Vibrational Levels on Automatically Generated IMLS Potential Energy Surfaces

We report here calculated J = 0 vibrational frequencies for (1)CH(2) and HCN with root-mean-square error relative to available measurements of 2.0 cm(-1) and 3.2 cm(-1), respectively. These results are obtained with DVR calculations with a dense grid on ab initio potential energy surfaces (PESs). The ab initio electronic structure calculations employed are Davidson-corrected MRCI calculations with double-, triple-, and quadruple-zeta basis sets extrapolated to the complete basis set (CBS) limit. In the (1)CH(2) case, Full CI tests of the Davidson correction at small basis set levels lead to a scaling of the correction with the bend angle that can be profitably applied at the CBS limit. Core-valence corrections are added derived from CCSD(T) calculations with and without frozen cores. Relativistic and non-Born-Oppenheimer corrections are available for HCN and were applied. CBS limit CCSD(T) and CASPT2 calculations with the same basis sets were also tried for HCN. The CCSD(T) results are noticeably less accurate than the MRCI results while the CASPT2 results are much poorer. The PESs were generated automatically using the local interpolative moving least-squares method (L-IMLS). A general triatomic code is described where the L-IMLS method is interfaced with several common electronic structure packages. All PESs were computed with this code running in parallel on eight processors. The L-IMLS method provides global and local fitting error measures important in automatically growing the PES from initial ab initio seed points. The reliability of this approach was tested for (1)CH(2) by comparing DVR-calculated vibrational levels on an L-IMLS ab initio surface with levels generated by an explicit ab initio calculation at each DVR grid point. For all levels ( approximately 200) below 20 000 cm(-1), the mean unsigned difference between the levels of these two calculations was 0.1 cm(-1), consistent with the L-IMLS estimated mean unsigned fitting error of 0.3 cm(-1). All L-IMLS PESs used in this work have comparable mean unsigned fitting errors, implying that fitting errors have a negligible role in the final errors of the computed vibrational levels with experiment. Less than 500 ab initio calculations of the energy and gradients are required to achieve this level of accuracy.

Multiple Surrogate Modeling for Axial Compressor Blade Shape Optimization

A major issue in surrogate model-based design optimization is the modeling fidelity. An effective approach is to employ multiple surrogates based on the same training data to offer approximations from alternative modeling viewpoints. This approach is employed in a compressor blade shape optimization using the NASA rotor 37 as the case study. The surrogate models considered include polynomial response surface approximation, Kriging, and radial basis neural network. In addition, a weighted average model based on global error measures is constructed. Sequential quadratic programming is used to search the optimal point based on these alternative surrogates. Three design variables characterizing the blade regarding sweep, lean, and skew are selected along with the three-level full factorial approach for design of experiment. The optimization is guided by three objectives aimed at maximizing the adiabatic efficiency, as well as the total pressure and total temperature ratios. The optimized compressor blades yield lower losses by moving the separation line toward the downstream direction. The optima for total pressure and total temperature ratios are similar, but the optimum for adiabatic efficiency is located far from them. It is found that the most accurate surrogate did not always lead to the best design. This demonstrated that using multiple surrogates can improve the robustness of the optimization at a minimal computational cost.

Evaluation of surrogate models for optimization of herringbone groove micromixer

Surrogate models have been applied to shape optimizations of a micromixer with the aim of assessing the performance of the models. The surrogate models considered include polynomial response surface approximation, Kriging, and radial basis neural network. In addition, a weighted average model based on global error measures is constructed. A mixing index at the exit of the micromixer is used as the objective function. The mixing index is calculated based on Navier-Stokes equations. Two cases of optimization, one with two design variables and the other with three design variables, have been tested. The design variables are selected among the ratio of the groove depth to channel height, the angle of groove, and the ratio of groove width to groove pitch. D-Optimal design generated sampling points are used for sampling. It is found that although the weighted average model does not predict the best optimal point, it does show consistent and reliable performance.

Transducer shape optimization for instability control of smart piezolaminated columns

In this article, we present an evolutionary technique to optimize the shape of piezoelectric transducers in order to extend the instability limits of laminated composite columns. A Co-continuous eight-node plate finite element with five degrees of freedom is employed. An evolutionary shape design procedure based on the residual voltages is developed. It aims at minimizing the quadratic measure of global displacement residual error between the desired and the current structural configuration. The use of evolutionary technique makes the present procedure computationally efficient. It also alleviates the possibility of checkerboard solutions that are difficult to interpret and manufacture. The performance of the design is demonstrated in modal control of a cantilever beam and control of a tip loaded cantilever column.

Cyclostationary error analysis and filter properties in a 3D wavelet coding framework

The reconstruction error due to quantization of wavelet subbands can be modeled as a cyclostationary process because of the linear periodically shift variant property of the inverse wavelet transform. For N-dimensional data, N-dimensional reconstruction error power cyclostationary patterns replicate on the data sample lattice. For audio and image coding applications this fact is of little practical interest since the decoded data is perceived in its wholeness, the error power oscillations on single data elements cannot be seen or heard and a global PSNR error measure is often used to represent the reconstruction quality. A different situation is the one of 3D data (static volumes or video sequences) coding, where decoded data are usually visualized by plane sections and the reconstruction error power is commonly measured by a P SNR [ n ] sequence, with n representing either a spatial slicing plane (for volumetric data) or the temporal reference frame (for video). In this case, the cyclostationary oscillations on single data elements lead to a global P SNR [ n ] oscillation and this effect may become a relevant concern. In this paper we study and describe the above phenomena and evaluate their relevance in concrete coding applications. Our analysis is entirely carried out in the original signal domain and can easily be extended to more than three dimensions. We associate the oscillation pattern with the wavelet filter properties in a polyphase framework and we show that a substantial reduction of the oscillation amplitudes can be achieved under a proper selection of the basis functions. Our quantitative model is initially made under high-resolution conditions and then qualitatively extended to all coding rates for the wide family of bit-plane quantization-based coding techniques. Finally, we experimentally validate the proposed models and we perform a subjective evaluation of the visual relevance of the P SNR [ n ] fluctuations in the cases of medical volumes and video coding.

Piezoelectric Sensor and Actuator Spatial Design for Shape Control of Piezolaminated Plates

Controlled actuation and sensing of structures by spatially distributing the piezoelectric material has been a topic of interest in recent years. We present an iterative technique to design the shape of piezoelectric actuators in order to achieve the desired shape of the structure. A gradientless shape design procedure based on the residual voltages is developed. It aims at minimizing the quadratic measure of global displacement residual error between the desired and the current structural configuration. The actuators gradually adapt to a shape that is most efficient in resisting the external excitation. The present technique can be well suited for any static and time-varying excitation. In vibration control it is often necessary to create modal sensors and actuators in order to observe or excite some specific modes. Such modal sensors and actuators alleviate spillover problems, and thus they avoid exhaustive signal processing. Several numerical examples for static as well as dynamic cases are presented to demonstrate the efficacy of the present technique.

An empirical measure of the performance of a document image segmentation algorithm

Document image segmentation is the first step in document image analysis and understanding. One major problem centres on the performance analysis of the evolving segmentation algorithms. The use of a standard document database maintained at the Universities/Research Laboratories helps to solve the problem of getting authentic data sources and other information, but some methodologies have to be used for performance analysis of the segmentation. We describe a new document model in terms of a bounding box representation of its constituent parts and suggest an empirical measure of performance of a segmentation algorithm based on this new graph-like model of the document. Besides the global error measures, the proposed method also produces segment-wise details of common segmentation problems such as horizontal and vertical split and merge as well as invalid and mismatched regions.

A 3-D HIERARCHICAL FE FORMULATION OF BIOT'S EQUATIONS FOR ELASTO-ACOUSTIC MODELLING OF POROUS MEDIA

A three-dimensional hierarchical finite element formulation of Biot's equation for low frequency elasto-acoustic wave propagation in fluid saturated porous media based on a weak formulation with fluid displacement and solid displacement as dependent variables is presented. A global error measure for evaluation of the convergence is proposed. Numerical simulations of an air saturated polyurethane foam material show faster convergence for the hierarchical extensions than for linear and quadratic serendipity finite element mesh refinement extensions.

Modelling the dynamics of visual classification learning

Classification learning of grey-level images is severely degraded in extrafoveal relative to foveal vision. Using a probabilistic virtual prototype (PVP) model we have recently demonstrated that this deficit is related to a reduced perceptual dimensionality of extrafoveally acquired class concepts relative to that of foveally developed representations [Jüttner, M., Rentschler, I., 1996. Reduced perceptual dimensionality in extrafoveal vision. Vision Research 36, 1007–1021]. Here we show how the PVP technique can be extended to capture the dynamics of classification learning. Unlike former attempts at such a description our approach does not primarily aim at modelling a learning curve, i.e., the gradual change of a global error measure. Rather it provides a means to trace the learning status of the observer by visualizing the changing pattern of classification errors. This allows one to assess the cognitive strategies observers employ during concept learning.