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The updated statistical inversion technique to the evaluation of Umkehr observations

In the present study the standard retrieval Umkehr method to estimate the vertical distribution of ozone was updated using a statistical approach to the mathematical inversion scheme. The vertical ozone profile covariance matrix was used as a priori information for the inverse problem. A new method of the ozonesonde data organization according to air mass types helped to improve the covariance matrix quality. A retrieval method was developed using eigenvector technique. An optimal vertical ozone profile resolution was determined from the mathematical inversion scheme analysis based on the same technique. The sun radiation transfer was accounted for multiple scattering and atmospheric sphericity in this calculation. The retrievals using actual Umkehr Dobson spectrophotometer observations were also performed to provide the comparison of the standard and updated methods with concurrent ozone sound data at Boulder U.S. The comparison has revealed that the present method has some advantages in both resolution and accuracy, as compared to the standard one, especially for the atmospheric layers below ozone maximum.

Frolov, Alexander D.↗

Metrology Optical Power Budgeting in SIM Using Statistical Analysis Techniques

The Space Interferometry Mission (SIM) is a space-based stellar interferometry instrument, consisting of up to three interferometers, which will be capable of micro-arc second resolution. Alignment knowledge of the three interferometer baselines requires a three-dimensional, 14-leg truss with each leg being monitored by an external metrology gauge. In addition, each of the three interferometers requires an internal metrology gauge to monitor the optical path length differences between the two sides. Both external and internal metrology gauges are interferometry based, operating at a wavelength of 1319 nanometers. Each gauge has fiber inputs delivering measurement and local oscillator (LO) power, split into probe-LO and reference-LO beam pairs. These beams experience power loss due to a variety of mechanisms including, but not restricted to, design efficiency, material attenuation, element misalignment, diffraction, and coupling efficiency. Since the attenuation due to these sources may degrade over time, an accounting of the range of expected attenuation is needed so an optical power margin can be book kept. A method of statistical optical power analysis and budgeting, based on a technique developed for deep space RF telecommunications, is described in this paper and provides a numerical confidence level for having sufficient optical power relative to mission metrology performance requirements.

stellar interferometry↗

Statistical Analysis Techniques for Small Sample Sizes

The small sample sizes problem which is encountered when dealing with analysis of space-flight data is examined. Because of such a amount of data available, careful analyses are essential to extract the maximum amount of information with acceptable accuracy. Statistical analysis of small samples is described. The background material necessary for understanding statistical hypothesis testing is outlined and the various tests which can be done on small samples are explained. Emphasis is on the underlying assumptions of each test and on considerations needed to choose the most appropriate test for a given type of analysis.

Navard, S. E.↗

Some statistical analysis techniques for the effect of systematic instrument errors on the results of measurements in a space experiment

Mathematical models of certain systematic telemetry signal errors arising during the passage of the signal through the recording and transmitting blocks of the physical instruments aboard the spacecraft are classified and constructed. Statistical analysis methods are used to determine the background function and relative sensitivity coefficients of the channels of a charged particle detector. Results are presented. A block diagram for a method taking into account the effect of distortions is given.

Kondakov, S. P.↗

Effective techniques for the identification and accommodation of disturbances

The successful control of dynamic systems such as space stations, or launch vehicles, requires a controller design methodology that acknowledges and addresses the disruptive effects caused by external and internal disturbances that inevitably act on such systems. These disturbances, technically defined as uncontrollable inputs, typically vary with time in an uncertain manner and usually cannot be directly measured in real time. A relatively new non-statistical technique for modeling, and (on-line) identification, of those complex uncertain disturbances that are not as erratic and capricious as random noise is described. This technique applies to multi-input cases and to many of the practical disturbances associated with the control of space stations, or launch vehicles. Then, a collection of smart controller design techniques that allow controlled dynamic systems, with possible multi-input controls, to accommodate (cope with) such disturbances with extraordinary effectiveness are associated. These new smart controllers are designed by non-statistical techniques and typically turn out to be unconventional forms of dynamic linear controllers (compensators) with constant coefficients. The simplicity and reliability of linear, constant coefficient controllers is well-known in the aerospace field.

Johnson, C. D.↗

Comparison of Statistical Estimation Techniques for Mars Entry, Descent, and Landing Reconstruction from MEDLI-like Data Sources

Flight data from an entry, descent, and landing (EDL) sequence can be used to reconstruct the vehicle's trajectory, aerodynamic coefficients and the atmospheric profile experienced by the vehicle. Past Mars missions have contained instruments that do not provide direct measurement of the freestream atmospheric conditions. Thus, the uncertainties in the atmospheric reconstruction and the aerodynamic database knowledge could not be separated. The upcoming Mars Science Laboratory (MSL) will take measurements of the pressure distribution on the aeroshell forebody during entry and will allow freestream atmospheric conditions to be partially observable. This data provides a mean to separate atmospheric and aerodynamic uncertainties and is part of the MSL EDL Instrumentation (MEDLI) project. Methods to estimate the flight performance statistically using on-board measurements are demonstrated here through the use of simulated Mars data. Different statistical estimators are used to demonstrate which estimator best quantifies the uncertainties in the flight parameters. The techniques demonstrated herein are planned for application to the MSL flight dataset after the spacecraft lands on Mars in August 2012.

Dutta, Soumyo↗

Urban environmental health applications of remote sensing, summary report

Health and its association with the physical environment was studied based on the hypothesis that there is a relationship between the man-made physical environment and health status of a population. The statistical technique of regression analysis was employed to show the degree of association and aspects of physical environment which accounted for the greater variation in health status. Mortality, venereal disease, tuberculosis, hepatitis, meningitis, shigella/salmonella, hypertension and cardiac arrest/myocardial infarction were examined. The statistical techniques were used to measure association and variation, not necessarily cause and effect. Conclusions drawn show that the association still exists in the decade of the 1970's and that it can be successfully monitored with the methodology of remote sensing.

Rush, M.↗

Analysis of Piezoelectric Structural Sensors with Emergent Computing Techniques

The purpose of this project was to try to interpret the results of some tests that were performed earlier this year and to demonstrate a possible use of emergence in computing to solve IVHM problems. The test data used was collected with piezoelectric sensors to detect mechanical changes in structures. This project team was included of Dr. Doug Ramers and Dr. Abdul Jallob of the Summer Faculty Fellowship Program, Arnaldo Colon-Lopez - a student intern from the University of Puerto Rico of Turabo, and John Lassister and Bob Engberg of the Structural and Dynamics Test Group. The tests were performed by Bob Engberg to compare the performance two types of piezoelectric (piezo) sensors, Pb(Zr(sub 1-1)Ti(sub x))O3, which we will label PZT, and Pb(Zn(sub 1/3)Nb(sub 2/3))O3-PbTiO, which we will label SCP. The tests were conducted under varying temperature and pressure conditions. One set of tests was done by varying water pressure inside an aluminum liner covered with carbon-fiber composite layers (a cylindrical "bottle" with domed ends) and the other by varying temperatures down to cryogenic levels on some specially prepared composite panels. This report discusses the data from the pressure study. The study of the temperature results was not completed in time for this report. The particular sensing done with these piezo sensors is accomplished by the sensor generating an controlled vibration that is transmitted into the structure to which the sensor is attached, and the same sensor then responding to the induced vibration of the structure. There is a relationship between the mechanical impedance of the structure and the resulting electrical impedance produced in the in the piezo sensor. The impedance is also a function of the excitation frequency. Changes in the real part of impendance signature relative to an original reference signature indicate a change in the coupled structure that could be the results of damage or strain. The water pressure tests were conducted by pressurizing the bottle on a test stand, and running sweeps of excitations frequencies for each of the piezo sensors and recording the resulting impedance. The sweeps were limited to 401 points by the available analyzer, and it was decided to perform individual sweeps at five different excitation frequency ranges. The frequency ranges used for the PZTs were different in two of the five ranges from the ranges used for the SCP. The bottles were pressurized to empty (no water), 0psig, 77 psig, 155 psig, 227 psig in nearly uniform increments of about 77psi. One of each of the two types of piezo sensors was fastened on to the bottle surface at two locations: about midway between the ends on cylindrical portion of the bottle and at the very edge of one of the end domes. The data was collected in files by sensor type (2 cases), by location (2 cases), by frequency range (5 cases), and pressure (5cases) to produce 100 data sets of 401 impedances. After familiarization with the piezo sensing technology and obtaining the data, the team developed a set of questions to try to answer regarding the data and made assignments of responsibilities. The next section lists the questions, and the remainder of the report describes the data analysis work performed by Dr. Ramers. This includes a discussion of the data, the approach to answering the question using statistical techniques, the use of an emergent system to investigate the data where statistical techniques were not usable, conclusions regarding the data, and recommendations.

Ramers, Douglas L.↗

Scalability Testing Approach for Internet of Things for Manufacturing SQL and NoSQL Database Latency and Throughput

The proliferation of low-cost sensors and industrial data solutions has continued to push the frontier of manufacturing technology. Machine learning and other advanced statistical techniques stand to provide tremendous advantages in production capabilities, optimization, monitoring, and efficiency. The tremendous volume of data gathered continues to grow, and the methods for storing the data are critical underpinnings for advancing manufacturing technology. This work aims to investigate the ramifications and design tradeoffs within a decoupled architecture of two prominent database management systems (DBMS): sql and NoSQL. A representative comparison is carried out with Amazon Web Services (AWS) DynamoDB and AWS Aurora MySQL. The technologies and accompanying design constraints are investigated, and a side-by-side comparison is carried out through high-fidelity industrial data simulated load tests using metrics from a major US manufacturer. The results support the use of simulated client load testing for comparing the latency of database management systems as a system scales up from the prototype stage into production. As a result of complex query support, MySQL is favored for higher-order insights, while NoSQL can reduce system latency for known access patterns at the expense of integrated query flexibility. Here, by reviewing this work, a manufacturer can observe that the use of high-fidelity load testing can reveal tradeoffs in IoTfM write/ingestion performance in terms of latency that are not observable through prototype-scale testing of commercially available cloud DB solutions.

AWS↗

Statistical classification techniques for engineering and climatic data samples

Fisher's sample linear discriminant function is modified through an appropriate alteration of the common sample variance-covariance matrix. The alteration consists of adding nonnegative values to the eigenvalues of the sample variance covariance matrix. The desired results of this modification is to increase the number of correct classifications by the new linear discriminant function over Fisher's function. This study is limited to the two-group discriminant problem.

Temple, E. C.↗

An analytic technique for statistically modeling random atomic clock errors in estimation

Minimum variance estimation requires that the statistics of random observation errors be modeled properly. If measurements are derived through the use of atomic frequency standards, then one source of error affecting the observable is random fluctuation in frequency. This is the case, for example, with range and integrated Doppler measurements from satellites of the Global Positioning and baseline determination for geodynamic applications. An analytic method is presented which approximates the statistics of this random process. The procedure starts with a model of the Allan variance for a particular oscillator and develops the statistics of range and integrated Doppler measurements. A series of five first order Markov processes is used to approximate the power spectral density obtained from the Allan variance.

Fell, P. J.↗

Line identification studies using traditional techniques and wavelength coincidence statistics

Traditional line identification techniques result in the assignment of individual lines to an atomic or ionic species. These methods may be supplemented by wavelength coincidence statistics (WCS). The strength and weakness of these methods are discussed using spectra of a number of normal and peculiar B and A stars that have been studied independently by both methods. The present results support the overall findings of some earlier studies. WCS would be most useful in a first survey, before traditional methods have been applied. WCS can quickly make a global search for all species and in this way may enable identifications of an unexpected spectrum that could easily be omitted entirely from a traditional study. This is illustrated by O I. WCS is a subject to well known weakness of any statistical technique, for example, a predictable number of spurious results are to be expected. The danger of small number statistics are illustrated. WCS is at its best relative to traditional methods in finding a line-rich atomic species that is only weakly present in a complicated stellar spectrum.

Cowley, Charles R.↗

Line identification studies using traditional techniques and wavelength coincidence statistics

Traditional line identification techniques result in the assignment of individual lines to an atomic or ionic species. These methods may be supplemented by wavelength coincidence statistics (WCS). The strength and weakness of these methods are discussed using spectra of a number of normal and peculiar B and A stars that have been studied independently by both methods. The present results support the overall findings of some earlier studies. WCS would be most useful in a first survey, before traditional methods have been applied. WCS can quickly make a global search for all species and in this way may enable identifications of an unexpected spectrum that could easily be omitted entirely from a traditional study. This is illustrated by O I. WCS is a subject to well known weakness of any statistical technique, for example, a predictable number of spurious results are to be expected. The danger of small number statistics are illustrated. WCS is at its best relative to traditional methods in finding a line-rich atomic species that is only weakly present in a complicated stellar spectrum.

Cowley, Charles R.↗

Metamodels for Computer-Based Engineering Design: Survey and Recommendations

The use of statistical techniques to build approximations of expensive computer analysis codes pervades much of todays engineering design. These statistical approximations, or metamodels, are used to replace the actual expensive computer analyses, facilitating multidisciplinary, multiobjective optimization and concept exploration. In this paper we review several of these techniques including design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning, and kriging. We survey their existing application in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of statistical approximation techniques in given situations and how common pitfalls can be avoided.

Simpson, Timothy W.↗

Curve fitting and modeling with splines using statistical variable selection techniques

The successful application of statistical variable selection techniques to fit splines is demonstrated. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs, using the B-spline basis, were developed. The program for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.

Smith, P. L.↗

Fatigue failure of materials under narrow band random vibrations. I.

A novel approach for the study of fatigue failure of materials under the multifactor influence of narrow band random vibrations is developed. The approach involves the conduction of an experiment in conjunction with various statistical techniques. Three factors including two statistical properties of the excitation or response are considered and varied simultaneously. A minimum of 6 tests for 3 variables is possible for a fractional f actorial design. The four coefficients of the predicting equation can be independently estimated. A look at 3 predicting equations shows the predominant effect of the root mean square stress of the first order equation.

Huang, T. C.↗