Error Propagation Model Research Articles

A model of error propagation in the presence of an error-enhancing drug

A mathematical model is considered that describes error propagation in protein synthesis, with emphasis on the role of an error-enhancing drug such as streptomycin. The subject of error propagation has been investigated in a number of works since an original proposal by Orgel in 1963. From experiments, it is known that streptomycin given to a bacterium culture in small concentration increases the error level, but at a certain concentration threshold the bacteria die. This two-fold behavior has, in some papers, lead to the proposal that another effect of the drugs besides that of error propagation leads to the death of the bacteria. In the present work, we use a model related to kinetic models of selection in protein synthesis which include the combined effect of ribosome and synthetase action. The model shows very clear threshold effects: for small values of the parameter that represents the drug action, a stable situation is found that has an increased error level but still attains a rather high accuracy. At a certain threshold, this is no longer maintained. The main emphasis here is on the time evolution of relevant parameters, and it is also shown how this can be quite drastic: the accuracy may decrease rather smoothly to a critical point, where it is drastically lost and where the bacteria may die out very suddenly.

A methodology for machine tools error correction using reference parts

Abstract In this paper, a methodology is presented for machine tool error correction which uses reference parts as metiological standards. These reference parts have the same geometric shape and weight as real workpieces. Consequently, the proposed methodology minimizes the uncertainty which arises from geometric interpolation, but still yields satisfactory results for multi-axis machine error characterization. A generalized error model is derived lo describe the relative error motion between the tool and the workpiccc. Iterative search algorithms are presented which increase the effectiveness of the error characterization process. Three case studies arc described which demonstrate the application of the methodology for four sample reference parts on three different machines. The results from these studies show that the error correction method can be used to characterize the positioning errors with estimation accuracy approaching the resolution of the machines.

Propagation of particles due to an explosion in elliptic orbit

Introduction I recent years, the short-term propagation of orbital debris has been modeled' mainly by applying the relative motion along a circular orbit. Although some methods consider eccentric orbits by using series expansions, these lack the compactness of a closed-form analytical solution. This Note is motivated by the leading publications on the elliptic relative motion: Brumberg, Danby, and Broucke. Because of the uncertainty in the initial conditions, a model for error propagation is essential. Brumberg presented the general idea but did not give an explicit solution. A recent paper suggested a solution to the propagation of the covariance along circular orbits. In the present Note, the simple form of the isotropic initial velocities distribution is used to form a closedform solution for the volume as well as the covariance propagation along a general elliptic orbit.

Stochastic error propagation in robot arms

Static error propagation in positioning robot arms has been extensively analyzed based on linearized error propagation models. These models are used for robot design and calibration. Most results were calculated using normally distributed errors in the different robot joints and links. In reality not all joints and links errors are normally distributed, and a mix of suitable symmetric and nonsymmetric probability distributions should be used in the error propagation model. The paper presents the general model for propagating errors with different distributions applicable to any system whose model can be linearized. Numerical examples are given for a general beta distribution of errors, and for a mix of symmetric and nonsymmetric distributions. Within the work-volume, the different configurations that a robot arm may attain during its life span can be expressed by a probability distribution. The paper includes the analysis of the effect of this distribution on the position error of the end-effector.

Development of intelligent geographical information systems

Abstract The analysis of geographical information is compared with other production processes in which a user can only accept an end-product if it meets certain quality requirements. Whereas users are responsible for defining the levels of quality they need to use the results of the analyses of geographical information systems in their work, database managers, experts and modellers could greatly assist users to achieve the quality of results they seek by formalizing information on: (1) data collection, level of resolution and quality; (2) the use of the basic analytical functions of the geographical information system; and (3) the data requirements, sensitivity and error propagation in models. These meta-data could be incorporated in a knowledge base alongside the geographical information system where, together with procedures for on-line error propagation, a user could be advised on the best way to achieve a desired aim. If the analysis showed that the original constellation of data, methods and models could not achieve the aim with the desired quality, the intelligent geographical information system would present a range of alternative strategies—better methods, more data, different data, better models, better model calibration, or better spatial resolution—and their costs by which the user's aims could reasonably be achieved.

Modeling the errors of multi-axis machines: a general methodology

A methodology is presented to obtain a generalized error model for multi-axis machines of arbitrary configuration. The model accounts for errors due to inaccuracies in the geometry, finite stiffness, and thermal deformation of the machine's components. Special statistical techniques are applied to the calibration data to obtain an empirical model for each of the errors. In a feedback loop, the identified significant parameters in these models are used for the computer-aided optimization of artefact-based test procedures. Results are shown for a five-axis milling machine and a three-axis coordinate measuring machine.

FOCUS: an experimental environment for fault sensitivity analysis

FOCUS, a simulation environment for conducting fault-sensitivity analysis of chip-level designs, is described. The environment can be used to evaluate alternative design tactics at an early design stage. A range of user specified faults is automatically injected at runtime, and their propagation to the chip I/O pins is measured through the gate and higher levels. A number of techniques for fault-sensitivity analysis are proposed and implemented in the FOCUS environment. These include transient impact assessment on latch, pin and functional errors, external pin error distribution due to in-chip transients, charge-level sensitivity analysis, and error propagation models to depict the dynamic behavior of latch errors. A case study of the impact of transient faults on microprocessor-based jet-engine controller is used to identify the critical fault propagation paths, the module most sensitive to fault propagation, and the module with the highest potential for causing external errors. >

Expert systems for guiding backpropagation training of layered perceptrons

Abstract The backward error propagation (or backpropagation) model for training neural networks is time consuming. Some theorems and “rules of thumb” are available to guide the process, but the former tend to be nonconstructive and the latter are not universally applicable. Neural networks are appealing for representing nonlinear, stochastic, or ill-conditioned transformations by searching “transformation space” for a good approximation. However, very little is known about navigating through transformation space. In this study, we describe the use of expert systems to learn about and supervise that navigation process.

Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination

Current models of spatial frequency (SF) and orientation discrimination are based on contrast discrimination data. In these “error propagation” models, the precision of all discrimination tasks is limited by “peripheral” noise in contrast-sensitive channels. Therefore, all discrimination thresholds should be proportional to the contrast Weber fraction Δc/c. To test this prediction, increment thresholds were measured for contrast, SF, orientation and temporal frequency (TF) for contrasts ranging from 2 to 50%. All measurements used the same stimuli, procedures and observers. For contrasts of 2% and higher, the contrast discrimination threshold Δc rises with approximately the 0.6 power of contrast, while SF and TF discrimination are independent of contrast. Furthermore, orientation discrimination is nearly independent of contrast at a SF of 4 cpd. No error-propagation model can explain these results. Therefore, SF and TF discrimination, and orientation discrimination at 4 cpd are limited by contrast-independent central noise.

Modeling and measurement of error propagation in a multimodule computing system

An error propagation model has been developed for multimodule computing systems in which the main parameters are the distribution functions of error propagation times. A digraph model is used to represent a multimodule computing system, and error propagation in the system is modeled by general distributions of error propagation times between all pairs of modules. Two algorithms are developed to compute systematically and efficiently the distributions of error propagation times. Experiments are also conducted to measure the distributions of error propagation times with the fault-tolerant microprocessor (FTMP). Statistical analysis of experimental data shows that the error propagation times in FTMP do not follow a well-known distribution, thus justifying the use of general distributions in the present model. >

A Generalized Geometric Error Model for Multi-Axis Machines

A methodology has been presented to build a generalized error model of a multi-axis machine of arbitrary configuration. It is based on the assumption of rigid body motions and utilizes homogeneous transform matrices. The developed error model accounts for errors due to inaccuracies in the geometry and mutual relationships of the machine's structural elements as well as for errors resulting from the relative motion between these elements. The model is particularly useful for identifying the dominant contributors to the overall error within the machine's working volume.

Model of error propagation in systems of communicating processes

The subject of the present paper is the error propagation model for systems of communicating processes in distributed computer systems. This has been used to express a new idea about an error recovery method in a system of processes which does not need any limitation on communication. It has been assumed that the technique of error recovery is based on state restoration, and that the recovery function is implemented in a distributed way. The notion of recovery line and a method for its construction have been discussed. Next it has been argued that the recovery function should be implemented as a protocol.

Metabolism of ingested U and Ra.

The literature on metabolism of U and Ra for man relevant to deriving drinking water standards has been reviewed and summarized. Radium is well understood, but significant gaps remain in our knowledge about U metabolism. Limits should be based on an equilibrium model where a constant relationship between intake and organ burden is established, using the best and most likely metabolic parameters. For the skeleton we conclude that the best estimate of skeletal burden expressed in days equivalent intake are 25 days for 226Ra, 10 days for 228Ra, and 0.3 days for 224Ra. For long-lived isotopes of U, we chose 11 days, with a range between 1 and 35 days. The committee believes that intake of natural U in water should be limited by considerations of toxicity to the kidney, and we believe that the metabolic model of Spoor and Hursh with a modified gastrointestinal (GI) absorption (1.4%) should be used to infer kidney content. Our review and analysis of the world literature leads us to believe the average human GI absorption of U is most likely 1-2% and is probably reasonably independent of age or the mass of U ingested. Using a safety factor of 50-150, the committee recommends a limit of U in water of 100 micrograms/l in order to limit toxic effects in the kidney. One hundred micrograms/liter is equivalent to 67 pCi/l of long-lived alpha-emitting natural U isotopes. Further research into the distribution of U in the human body is desirable, especially at natural levels in kidney and skeleton, the time-dependent pharmacokinetics of U in animals, the GI absorption of U in man from water and food, toxicological and U distribution studies in animals under conditions of chronic oral U intake, and metabolic model error propagation.

Bias and Error Propagation in Logistic Production Models

Maximum sustainable yield (MSY) and the effort at MSY (EMSY) are estimated from simulated catch and effort data to determine the biasing and susceptibility to error propagation of three commonly used techniques. The effects of smoothing, distribution of error between catch and effort, and delays in the density-dependent growth are investigated with respect to forming such estimates. It is found that MSY and EMSY levels derived from these methods suffer in varying degrees to bias (sometimes greater than a factor of 2) and variability (sometimes a coefficient of variation greater than 1). These results are dependent upon the method used and the parameters used to produce the data, especially how dynamic the modeled stock is. Therefore, information about the biological nature of the stock, especially the intrinsic growth rate, is important to correct the biasing of an estimation method. It is concluded that Gulland's and Schnute's methods should both be used keeping in mind the expected biases from this study.Key words: production model, management, maximum sustainable yield, error propagation

Energy related mathematical models: Annotated bibliography

The evaluation of various options for energy sources, energy conversion, and efficient use of energy has led to the use of computer-based mathematical models. To insure that these models are reasonably accurate representations of the situation being studied, it is desirable to have available information concerning the analysis of error propagation in mathematical models when implemented on computers. As an aid to energy model builders who seek methods of analysis for their own work, as well as to provide a helpful guide for the research computer scientists working on the development of new methods for analysis of propagation of error, a classification scheme of error propagation methods is presented and an annotated bibliography of energy-related mathematical models classified by validation and error analysis methods is provided.

Roundoff analyses and sparse data

Techniques are emerging which automatically determine the effects of rounding error upon numerical methods of a certain type. Meaningful testing presupposes a reasonable basis for comparison. Typically, the error's effects upon a given method are compared either (i) with the effects of perturbing the computational problem or (ii) with the effects of rounding error upon a competing method. We show that the result of a type (ii) comparison often remains valid when the two methods are adapted for "sparse" data, though the comparison might be based upon a model of error propagation which requires that special care be taken. This observation sometimes provides a rationale for preferring comparisons (ii), since the results of type (i) comparisons may well not carry over to sparse data.

Lunar Surface Navigation

The adverse environment of the lunar surface requires the implementation of unique land vehicle navigation techniques, concepts, and components to perform postulated future lunar surface navigation functions. Subject to the lunar environmental constraints, three generalized lunar surface navigation concepts are modeled and analyzed. The generalized hybrid concepts, consisting of both position fix and dead reckoning subconcepts, are a passive non-gyro, and inertial, and rf system. A generalized error model of the lunar surface navigation function, is applied to assess navigation system accuracy for each of the three systems. The analytical approach to model derivation is basically the covariance technique where 3 sigma error parameters of equipment errors and 3 sigma error measures of lunar physical uncertainties are related to a 3 sigma vehicle position error ellipsoid about a true point on the lunar surface. The error model digital computer program is applied to the navigation concepts and results are shown which indicate representative component and total concept accuracy requirements for lunar surface navigation in the 1972 to 1985 era.

Unnormalized Floating Point Arithmetic

Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of one-stage error propagation is developed for each operation; a suggested statistical model for long-run error propagation is also set forth.