Presence Of Random Errors Research Articles

Robust finite element model updating using Taguchi method

A novel model updating technique is presented such that the parameters in an analytical finite element (FE) model can be updated in a robust way in presence of random errors in measured data and systematic errors in the analytical model. For efficient and robust updating, Taguchi method is applied to the optimization of the objective function, which is defined by the difference between measured and analytical vibration data. As reference data for updating, both cases of using frequency as well as modal data are discussed. To demonstrate the effectiveness of the proposed methods, FE models of truss structure and cantilever beam are used for numerical simulations of model updating in presence of random and systematic errors.

Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups

Given a quantum dynamical semigroup expressed as an exponential superoperator acting on a space of N-dimensional density operators, eigenvalue methods are presented by which canonical Kraus and Lindblad operator sum representations can be computed. These methods provide a mathematical basis on which to develop novel algorithms for quantum process tomography—the statistical estimation of superoperators and their generators—from a wide variety of experimental data. Theoretical arguments and numerical simulations are presented which imply that these algorithms will be quite robust in the presence of random errors in the data.

Statistical tolerancing using designed experiments in a noisy environment

We consider the method of designed experiments for statistical tolerance analysis, and study the impact of experimental error on its results. It is observed that presence of random error in the experiment environment (e.g. laboratory) could introduce bias in the moment estimators and increases their respective variances. We propose adjustments to the method that would reduce the bias as well as the variance of these estimators. A numerical example is presented.

Smoothing forecast ensembles with fitted probability distributions

AbstractForecast ensembles from the European Centre for Medium‐Range Weather Forecasts Ensemble Prediction System for surface‐weather variables are smoothed by fitting Gaussian distributions. The possibility of bifurcation or other non‐Gaussian behaviours in an ensemble is allowed for by including probability mixtures of two Gaussian distributions when justified by the data. Variables that are clearly non‐Gaussian (wind speed and cloud cover) are transformed before fitting, and multivariate data with dimensions as high as four are considered. The smoothed ensembles provide more‐accurate quantile and probability estimates in a perfect‐model setting, particularly for small ensemble sizes and more‐extreme events. This advantage increases in the presence of random errors in the ensemble means, but diminishes for underdispersed ensembles. Allowing representation of ensembles as Gaussian mixtures also leads to a sharper ‘spread–skill’ relationship in the data considered. Copyright © 2002 Royal Meteorological Society.

Modeling Subsystem Interactions: A Game Theoretic Approach

It is well documented in complex systems design that changing the design of one subsystem will affect the design of other subsystems. Many times capturing any relationship beyond experience-based heuristic rules is difficult because of the complexity of the disciplinary codes and the associated nonlinearities. In this paper, a probabilistic approach to modeling the effects any subsystem design change has on other subsystems is described. Computer-based simulation is used to build approximations of the interfaces and demonstrate how the necessary assumption of the presence of random error in probabilistic statistics is satisfied. A passenger aircraft example is used to verify and validate the approach.

Determination of densities and heat capacities from speed of sound measurements for 1,1,1,2-tetrafluoroethane

The speed of sound u is both formally independent of the amount of substance and can be measured easily with high precision (typically Δu/u< 1 · 10−5). Measurement of this quantity offers a favorable route for obtaining densityρ , molar isochoric heat capacity CV , m, and molar isobaric heat capacityCp , m values. This transformation from u to other thermodynamic properties, involves the solution of a second-order differential equation on either isobars, or isochores. In this paper, we compare both equation sets for 1,1,1,2-tetrafluoroethane (HFC-134a) which is a slightly polar fluid. In the absence of reliable experimental speed of sound data over the whole fluid surface, an accurate Helmholtz function equation of state for HFC-134a was used to simulate property data for this study. These data were generated at reduced temperaturesTr=T/TcbetweenTr= 0.75 and Tr= 1.25 and at reduced pressurespr=p/pcup topr= 6. The isochoric equation set was found to be more stable. For data and initial conditions without errors, the fractional uncertainties in ρ and CV ,mwere 0.002 and 0.02, respectively. Sensitivity studies were conducted on the isochoric equation set to document effects of interpolation step size, accuracy of initial conditions, and presence of random errors in the data. When all sources of error are included, the uncertainties in density and isochoric heat capacity were no worse than any of the individual sensitivity studies.

Estimating and Testing a Model of Welfare Participation: the Case of Supplementary Benefits in Britain

Evidence of incomplete participation in welfare programmes is often displayed. This paper analyses how such apparent failures to participate can be explained by the presence of random errors in assessing benefit eligibility, by income underreporting, by benefit misreporting, and by participation costs. We apply the model to the receipts of supplementary benefits in Britain. A bivariate extension of the use of generalized residuals in testing the robustness of limited‐dependent‐variable models is provided and fails to reject a number of our stochastic assumptions.

Optimizing Power Transmission by a Microwave Beam in the Presence of Random Errors of the Transmit Antenna Excitation

Optimizing Power Transmission by a Microwave Beam in the Presence of Random Errors of the Transmit Antenna Excitation

HDTV picture quality performance in the presence of random errors, analysis and measures for improvement

We study the performance of the picture quality of HDTV in the presence of random errors and find the different kinds of picture impairments that may arise. The problems associated with picture coding, including variable length and Huffman coding, are investigated in great detail. The use of DC differential coding and the loss of block synchronization cause errors to perpetuate to other regions of the picture, and hence are identified as the major causes of poor performance. Motivated by these observations, two novel techniques which significantly improve the picture quality are proposed, analyzed and evaluated. The first technique is based upon encoding the actual values of the DC coefficients instead of the commonly used differential DC coding. This is done by means of a new set of Huffman codewords. It is shown that, contrary to present belief, by coding the actual DC values it is possible to maintain the high compression obtained by the commonly employed differential DC coding and at the same time significantly improve the noise resistance of the coding scheme. The second proposed technique introduces a simple but effective synchronization scheme which restricts the effects of residual errors to within 32 × 16 pixel superblocks thus improving the quality of the received picture. This synchronization area is much smaller than the 5632, 4024 and 3072 pixel areas proposed by the four HDTV proposals. Incorporation of the two techniques yields a scheme which has excellent noise performance characteristics and increases the overall noise resistance of the HDTV system. This scheme is applied to both reference frames and inter-frames and improves the SNR at which the HDTV picture suddenly deteriorates by 2.5–3 dB. After that the deterioration is more graceful, as the error propagation is limited to the superblock boundaries.

Expectation Minimum (EM): A New Principle for the Solution of Ill-Posed Problems in Photothermal Science

The expectation-minimum (EM) principle is a new strategy for recovering robust solutions to the ill-posed inverse problems of photothermal science. The expectation-minimum principle uses the addition of well-characterized random noise to a model basis to be fitted to the experimental response by linear minimization or projection techniques. The addition of noise to the model basis improves the conditioning of the basis by many orders of magnitude. Multiple projections of the data onto the basis in the presence of noise are averaged, to give the solution vector as an expectation value which reliably estimates the global minimum solution for general cases, while the conventional approaches fail. This solution is very stable in the presence of random error on the data. The expectation-minimum principle has been demonstrated in conjunction with several projection algorithms. The nature of the solutions recovered by the expectation minimum principle is nearly independent of the minimization algorithms used and depends principally on the noise level set in the model basis.

Convergence conditions of the least squares method

Least squares estimation of parameters is considered. Sufficient conditions of strong consistency are obtained for a regression model in the presence of random errors.

Allowing for Random Errors in Radiation Dose Estimates for the Atomic Bomb Survivor Data

The presence of random errors in the individual radiation dose estimates for the A-bomb survivors causes underestimation of radiation effects in dose-response analyses, and also distorts the shape of dose-response curves. Statistical methods are presented which will adjust for these biases, provided that a valid statistical model for the dose estimation errors is used. Emphasis is on clarifying some rather subtle statistical issues. For most of this development the distinction between radiation dose and exposure is not critical. The proposed methods involve downward adjustment of dose estimates, but this does not imply that the dosimetry system is faulty. Rather, this is a part of the dose-response analysis required to remove biases in the risk estimates. The primary focus of this report is on linear dose-response models, but methods for linear-quadratic models are also considered briefly. Some plausible models for the dose estimation errors are considered, which have typical errors in a range of 30-40% of the true values, and sensitivity analysis of the resulting bias corrections is provided. It is found that for these error models the resulting estimates of excess cancer risk based on linear models are about 6-17% greater than estimates that make no allowance for dose estimation errors. This increase in risk estimates is reduced to about 4-11% if, as has often been done recently, survivors with dose estimates above 4 Gy are eliminated from the analysis.

Calibration enhancement and on line accuracy assessment for single six-port reflectometers employing a nonlinear Kalman filter

The calibration and measurement performance of a single six-port reflectometer is directly affected by the presence of random errors. A technique using a nonlinear Kalman filter that enhances calibration by a factor of two to ten is presented. The technique also provides statistical information, allowing simple online accuracy assessment. The technique is readily extended for use within dual six-port reflectometer systems. >

Design and Implementation of FEC Codecs using Reed-Solomon Codes

Along with a brief review, the generalised design philosophy of forward error correcting codecs using systematic primitive Reed-Solomon (R-S) codes over GF(2m) has been discussed. For decoding die R-S codes, the Berlekamp-Massey algorithm, the Chien search procedure and Forney's method of finding error magnitudes have been adopted. Software implementation of several Reed-Solomon codecs over GF(25), GF(26) and GF(27) and their performances in presence of random errors have been reported in this paper. The purpose of this paper is to help the designer to gain an insight into the complexities involved in the design and implementation of the R-S codes and to explore their features for required applications.

The mean-square convergence of stochastic iterative procedures in ill-posed problems

The regularization properties of iterative procedures in the norm of L 2 for ill-posed problems with deviation stopping rules in the presence of random errors is established.

On-line accuracy assessment for the dual six-port ANA: Statistical methods for random errors

A basic property of a measurement process is that repeated observations of the same quantity will not give identical results due to the presence of random errors. In order to assess the effects of random errors in our measurement process, we need to build in redundancy. This paper presents a brief summary of the statistical methods used to evaluate the random errors in dual six-port measurements of reflection coefficient and scattering parameters.

Robust Data Communication System Using Microprocessor-Based Sequential Decoder

A microprocessor-based sequential docoder employing Fano's algorithm for rate-half non-systematic convolutional code of constraint length three is discussed. The decoder is implemented on the VMC-85 microprocessor kit, which employs the Intel 8085A as its CPU. The encoder is realized through a hardware external to the microprocessor. Fixed and random errors are added to test the performance of the sequential decoder. Tests with fixed errors show that the decoder can correct any two errors in sixcode bits. Experimental performance of the decoder for data transmission in the presence of random errors has been evaluated and it is found that BER is improved from 10−3 at the input to better than 10−6 at the output. A coding gain of 0.8 dB at BER of 10−5 has been achieved.With the limited speed and limited memory of the microprocessor kit, it has been possible to achieve a data throughput rate of 600 bps. The microprocessor-based decoder would be useful in robust real-time data communication links up to a speed...

Influence of random errors in clustering on beamforming of a linear array

Random errors which include amplitude, phase errors, and element failures cause a beam response degradation such as an increase in side‐lobe level, beam‐pointing errors, and loss in directivity. In this paper we present results of systematic investigation of the effects of random errors on the beamforming performance of a linear array that includes different shading coefficients, clustering, and directional elements. Analysis and simulation results show that using a directional element, clustering, and various weights reduce the degradation of side‐lobe level due to random errors. Also discussed are the different tradeoffs necessary to achieve the desired beam response with different weighting, clustering, and directional elements in the presence of random errors. [This work sponsored by Naval Sea Systems Command.]

Effect of element failure and random errors in amplitude and phase on the sidelobe level attainable with a linear array

In experiments with linear arrays at sea, one frequently operates with an array which has not only errors in amplitude and phase between channels but also inoperative elements. Previous calculations have shown that in the presence of random errors in amplitude and phase, the sidelobe level of the mean beam pattern is the sum of that of the error-free pattern plus an angle-independent background level due to the random errors. If the time constant of the random process is much larger than the integration time of the beamformer (as is most often the case), then a more relevant statistic is the mean value of the peak sidelobe due to a single realization of the random process. Our numerical calculations show that this value can be substantially larger (approximately 6 dB) than the peak sidelobe of the mean beam pattern. When the error-related sidelobes are predominant, appreciably greater sidelobe suppression cannot be achieved by using a set of amplitude weights which yield an error-free sidelobe level less than that of the error-related level. Element failure also produces an elevated sidelobe level whose peak value can be estimated and in many cases bounded above by the ratio of the sum of the amplitude weights of the faulty elements to the sum of the amplitude weights of the functioning elements. This ratio is nearly linearly related to the rms amplitude and phase errors in the way in which each affects the peak sidelobe level. This allows one to construct a characteristic curve for the peak sidelobe level in the presence of all these degrading factors, given an array of N elements and a set of amplitude weights. Processing techniques are available which may allow one to regain the sidelobe suppression lost due to inoperative elements. Among such techniques are algorithms for adjusting the amplitude weights, cross-sensor beamforming, subaperture processing and a procedure for estimating the signal at inoperative elements by using those from neighboring elements.

Hydrogen-deuterium exchange in transition metal hydridocarbonyl cluster complexes. Standardization of a mass spectroscopic analytical technique

The facil exchange of H/sub 2/Re/sub 2/(CO)/sub 8/ and H/sub 2/Os/sub 3/(CO)/sub 10/ with D/sub 2/O in the presence of Florisil chromatographic adsorbent was monitored by mass spectrometry. Owing to the possibility of an isotope effect in the ionization process and the presence of random errors in the recording system, a determination of the accuracy and precision of this analytical method was undertaken. As an extension of thermal hydrogenation synthesis, several of the compounds used in these studies were prepared by photolytic hydrogenation of Re/sub 2/(CO)/sub 10/.