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Nonlinear Dynamic Models in Advanced Life Support

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Jones, Harry

Accelerated Testing Methodology in Constant Stress-Rate Testing for Advanced Structural Ceramics: A Preloading Technique

Preloading technique was used as a means of an accelerated testing methodology in constant stress-rate ('dynamic fatigue') testing for two different brittle materials. The theory developed previously for fatigue strength as a function of preload was further verified through extensive constant stress-rate testing for glass-ceramic and CRT glass in room temperature distilled water. The preloading technique was also used in this study to identify the prevailing failure mechanisms at elevated temperatures, particularly at lower test rate in which a series of mechanisms would be associated simultaneously with material failure, resulting in significant strength increase or decrease. Two different advanced ceramics including SiC whisker-reinforced composite silicon nitride and 96 wt% alumina were used at elevated temperatures. It was found that the preloading technique can be used as an additional tool to pinpoint the dominant failure mechanism that is associated with such a phenomenon of considerable strength increase or decrease.

Choi, Sung R.

Accelerated Testing Methodology in Constant Stress-Rate Testing for Advanced Structural Ceramics: A Preloading Technique

Preloading technique was used as a means of an accelerated testing methodology in constant stress-rate (dynamic fatigue) testing for two different brittle materials. The theory developed previously for fatigue strength as a function of preload was further verified through extensive constant stress-rate testing for glass-ceramic and CRT glass in room temperature distilled water. The preloading technique was also used in this study to identify the prevailing failure mechanisms at elevated temperatures, particularly at lower test rates in which a series of mechanisms would be associated simultaneously with material failure, resulting in significant strength increase or decrease. Two different advanced ceramics including SiC whisker-reinforced composite silicon nitride and 96 wt% alumina were used at elevated temperatures. It was found that the preloading technique can be used as an additional tool to pinpoint the dominant failure mechanism that is associated with such a phenomenon of considerable strength increase or decrease.

Choi, Sung R.

High dynamic range infrared radiometry and imaging

The use is described of cryogenically cooled, extrinsic silicon infrared detectors in an unconventional mode of operation which offers an unusually large dynamic range. The system performs intensity-to-frequency conversion at the focal plane via simple circuits with very low power consumption. The incident IR intensity controls the repetition rate of short duration output pulses over a pulse rate dynamic range of about 10(6). Theory indicates the possibility of monotonic and approx. linear response over the full dynamic range. A comparison between the theoretical and the experimental results shows that the model provides a reasonably good description of experimental data. Some measurements of survivability with a very intense IR source were made on these devices and found to be very encouraging. Evidence continues to indicate that some variations in interpulse time intervals are deterministic rather than probabilistic.

Coon, Darryl D.

Accelerated Testing Methodology for the Determination of Slow Crack Growth of Advanced Ceramics

Constant stress-rate (dynamic fatigue) testing has been used for several decades to characterize slow crack growth behavior of glass and ceramics at both ambient and elevated temperatures. The advantage of constant stress-rate testing over other methods lies in its simplicity: Strengths are measured in a routine manner at four or more stress rates by applying a constant crosshead speed or constant loading rate. The slow crack growth parameters (n and A) required for design can be estimated from a relationship between strength and stress rate. With the proper use of preloading in constant stress-rate testing, an appreciable saving of test time can be achieved. If a preload corresponding to 50 % of the strength is applied to the specimen prior to testing, 50 % of the test time can be saved as long as the strength remains unchanged regardless of the applied preload. In fact, it has been a common, empirical practice in strength testing of ceramics or optical fibers to apply some preloading (less then 40%). The purpose of this work is to study the effect of preloading on the strength to lay a theoretical foundation on such an empirical practice. For this purpose, analytical and numerical solutions of strength as a function of preloading were developed. To verify the solution, constant stress-rate testing using glass and alumina at room temperature and alumina silicon nitride, and silicon carbide at elevated temperatures was conducted in a range of preloadings from O to 90 %.

Choi, Sung R.

Statistical physics and physiology: monofractal and multifractal approaches

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

NASA Discipline Cardiopulmonary

Accelerated Testing Methodology Developed for Determining the Slow Crack Growth of Advanced Ceramics

Constant stress-rate ("dynamic fatigue") testing has been used for several decades to characterize the slow crack growth behavior of glass and structural ceramics at both ambient and elevated temperatures. The advantage of such testing over other methods lies in its simplicity: strengths are measured in a routine manner at four or more stress rates by applying a constant displacement or loading rate. The slow crack growth parameters required for component design can be estimated from a relationship between strength and stress rate. With the proper use of preloading in constant stress-rate testing, test time can be reduced appreciably. If a preload corresponding to 50 percent of the strength is applied to the specimen prior to testing, 50 percent of the test time can be saved as long as the applied preload does not change the strength. In fact, it has been a common, empirical practice in the strength testing of ceramics or optical fibers to apply some preloading (<40 percent). The purpose of this work at the NASA Lewis Research Center is to study the effect of preloading on measured strength in order to add a theoretical foundation to the empirical practice.

Choi, Sung R.

High-Temperature Slow Crack Growth of Silicon Carbide Determined by Constant-Stress-Rate and Constant-Stress Testing

High-temperature slow-crack-growth behaviour of hot-pressed silicon carbide was determined using both constant-stress-rate ("dynamic fatigue") and constant-stress ("static fatigue") testing in flexure at 1300 C in air. Slow crack growth was found to be a governing mechanism associated with failure of the material. Four estimation methods such as the individual data, the Weibull median, the arithmetic mean and the median deviation methods were used to determine the slow crack growth parameters. The four estimation methods were in good agreement for the constant-stress-rate testing with a small variation in the slow-crack-growth parameter, n, ranging from 28 to 36. By contrast, the variation in n between the four estimation methods was significant in the constant-stress testing with a somewhat wide range of n= 16 to 32.

Choi, Sung H.

Slow Crack Growth Analysis of Brittle Materials with Finite Thickness Subjected to Constant Stress-Rate Flexural Loading

A two-dimensional, numerical analysis of slow crack growth (SCG) was performed for brittle materials with finite thickness subjected to constant stress-rate ("dynamic fatigue") loading in flexure. The numerical solution showed that the conventional, simple, one-dimensional analytical solution can be used with a maximum error of about 5% in determining the SCG parameters of a brittle material with the conditions of a normalized thickness (a ratio of specimen thickness to initial crack size) T > 3.3 and of a SCG parameter n > 10. The change in crack shape from semicircular to elliptical configurations was significant particularly at both low stress rate and low T, attributed to predominant difference in stress intensity factor along the crack front. The numerical solution of SCG parameters was supported within the experimental range by the data obtained from constant stress-rate flexural testing for soda-lime glass microslides at ambient temperature.

Chio, S. R.

Catalytic resonance theory for parametric uncertainty of programmable catalysis

Microkinetic models are useful tools for screening catalytic materials; however, errors in their input parameters can lead to significant uncertainty in model predictions of catalyst performance. Here, in this work, we investigate the impact of linear scaling and Brønsted-Evans-Polanyi relation parametric uncertainty on microkinetic predictions of programmable-catalyst performance. Two case studies are considered: a generic A-to-B prototype reaction and the oxygen evolution reaction (OER). The results show that error-unaware models can accurately predict trends and, for the prototype reaction, values of optimal waveform parameters. The specific model parameters driving output uncertainty are identified via variance-based global sensitivity analysis. However, predictions of dynamic rate enhancement can decrease when uncertainty is propagated into the models. In both cases, we identify operating conditions where the programmable catalyst achieves a rate enhancement of at least one order of magnitude despite parametric uncertainty in the model, supporting programmable catalysis as a viable strategy for exceeding the Sabatier limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Progressing Analysis of Variable Electric Rates (PAVER) Study

The Progressing Analysis of Variable Electric Rates (PAVER) study analyzed the impact of a range of time-varying electric rates on the performance of a regional electric grid and the resulting costs for participating and non-participating customers. This analysis leveraged and extended the work of PNNL’s Distribution System Operator with Transactive (DSO+T) study. Five different rate designs were included: a flat volumetric energy charge, a typical Time of Use (TOU) rate, a dynamic energy (DE) rate (based on wholesale locational marginal prices), a dynamic energy and capacity (DE+C) rate, and, finally, a Block and Swing (B&S) rate that billed customers based on their average load profile at constant pricing, but used the DE+C dynamic price for load deviations from their average profile. These rates were analyzed in a large-scale co-simulation of an entire regional grid with a customer population representative of the current state. A large fraction (80%) of residential and commercial customers were assumed to participate in these time-varying rates with automatically controlled HVAC, water heaters, electric vehicles, and batteries. This study assumed no industrial sector participation. The DE and DE+C rates saw system peak loads reduced by 6-7%, while the large participation in the TOU rate case saw a significant rebound effect and a resulting peak load increase of >5%. The impacts to the annual and peak system demand impacted system wholesale prices and the overall grid operating costs. This cost structure determined the revenue needed to be collected from customers by each rate design. Participating customers on the DE and DE+C rates (located in one of the modeled DSOs) saw reductions in average annual electricity bills of 11-17% with average increases in monthly bill variation of no more than 13%. At such high participation levels, TOU customers saw 10% higher average annual bills (due to system-wide rebound effects) and average increased monthly bill variation of 16%. Residential owners of large flexible loads (such as electric vehicles) saw larger bill savings (17-20%) when on a fully dynamic rate. The presence of on-site generation (such as rooftop solar) did not appear to appreciably change customer outcomes. Customers on the Block and Swing rate did see 6% lower monthly bill variation (as intended) than the flat rate case, but at the expense of appreciable bill savings, which were only 3%, comparable to the savings seen by non-participants. Given this finding we recommend that additional research be conducted into how best various bill protection mechanisms can balance minimizing customer bill variation with providing financial incentives commensurate with the flexibility customers provide. We also recommend that customer outcomes be explored across a range of regions using current actual customer and system cost data.

29 ENERGY PLANNING, POLICY, AND ECONOMY

Titanium alloy response sensitivity to variations in spectral reconstructions of National Ignition Facility xenon line-emission x-ray sources

Thermomechanical shock experiments on the National Ignition Facility (NIF) aim to study high strain rate dynamic material response. In such experiments, the NIF laser is used to generate high fluence x-ray emission sources, which irradiate material samples of interest. Under sufficiently high x-ray energy deposition, thermomechanical impulses are generated in the materials. While it is known that the characteristics of x-ray generated impulses vary as a function of incident x-ray spectra, it remains unclear how spectral assumptions and uncertainties in NIF spectral reconstructions affect our interpretation of impulsive loading. Here, in this paper, we simulate the response of a standard titanium alloy baseline sample to synthetic analytically derived and measured NIF xenon line-emission x-ray sources with a radiation hydrodynamics code. We vary the source spectral characteristics based on different source reconstruction techniques to understand the resulting variation in baseline sample response and compare the simulated response with experimental results. We find that the response is highly sensitive to assumptions made about the spectral contents and that knowledge of spectral uncertainties bounds our understanding of the resulting material response. The results of this effort help to extend our ability to use baseline material samples to extract quantitative properties from x-ray experiments on the NIF.

Alloys

GEOS-3 Doppler difference tracking

The Doppler difference method as applied to track the GEOS 3 spacecraft is discussed. In this method a pair of 2 GHz ground tracking stations simultaneously track a spacecraft beacon to generate an observable signal in which bias and instability of the carrier frequency cancel. The baselines are formed by the tracking sites at Bermuda, Rosman, and Merritt Island. Measurements were made to evaluate the effectiveness of the Doppler differencing procedure in tracking a beacon target with the high dynamic rate of the GEOS 3 orbit. Results indicate the precision of the differenced data to be at a level comparable to the conventional precise two way Doppler tracking.

Rosenbaum, B.

Identification of aerodynamic indicial functions using flight data

It is pointed out that the use of indicial function representation provides a model superior to the aerodynamic derivative model. Specific derivatives can be approximated from the indicial models. The model can also be used to compute equivalent stability and control parameters not usually available from flight data. It is shown that derivatives regarding the angle-of-attack and the side slip angle can be derived directly from the indicial functions without any identifiability problem. Attention is given to the pitch moment coefficient, linear indicial function representation, the identification problem for the pitch moment equation, the identifiability of linear systems, parametric representations of the indicial functions, an identification technique, angle-of-attack and pitch rate dynamics in the pitch plane, multivariate linear models, nonlinear aerodynamic indicial functions, measurement system accuracy, and poststall and spin-entry data from a scaled research vehicle.

Gupta, N. K.

Electron radiation effects on the thermal expansion of graphite/resin composites

The effects of 1 MeV electron radiation on the thermal expansion characteristics of two graphite reinforced resin matrix composite systems were studied. Specimens of both graphite/epoxy (T300/5208) and graphite/polyimide (C6000/PMR15) were irradiated to a total dose of 6 x 10 to the 9th rads at two different rates. Dynamic mechanical analyses (DMA) were performed to study changes in resin chemistry. Thermal expansion results indicate that radiation did produce permanent residual strains of up to -70 x 10 to the -6th for the graphite/epoxy when exposed to temperatures up to +280 F. However, no permaanent changes in the coefficient of thermal expansion (CTE) were observed. No permanent residual strains or changes in the CTE attributable to radiation were observed for the graphite/polyimide specimens. DMA results indicate that electron radiation caused chemical changes in the epoxy matrix. These changes resulted in a lower glass transition temperature and broader 'rubbery region' which extended into the temperature range of the thermal expansion tests.

Bowles, D. E.

Rotor-state feedback in the design of flight control laws for a hovering helicopter

The use of rigid-body and rotor-state feedback gains in the design of helicopter flight control laws was investigated analytically on a blade element, articulated rotor, helicopter model. The study was conducted while designing a control law to meet an existing military rotorcraft handling qualities design specification (ADS-33C) in low-speed flight. A systematic approach to meet this specification was developed along with an assessment of the function of these gains in the feedback loops. Using the results of this assessment, the pitch and roll crossover behavior was easily modified by adjusting the body attitude and rotor-flap feedback gains. Critical to understanding the feedback gains is that the roll and pitch rate dynamics each have second-order behavior, not the classic first-order behavior, which arises from a quasi-static rotor, six degree-of-freedom model.

Takahashi, Marc D.

Estimation of Slow Crack Growth Parameters for Constant Stress-Rate Test Data of Advanced Ceramics and Glass by the Individual Data and Arithmetic Mean Methods

The two estimation methods, individual data and arithmetic mean methods, were used to determine the slow crack growth (SCG) parameters (n and D) of advanced ceramics and glass from a large number of room- and elevated-temperature constant stress-rate ('dynamic fatigue') test data. For ceramic materials with Weibull modulus greater than 10, the difference in the SCG parameters between the two estimation methods was negligible; whereas, for glass specimens exhibiting Weibull modulus of about 3, the difference was amplified, resulting in a maximum difference of 16 and 13 %, respectively, in n and D. Of the two SCG parameters, the parameter n was more sensitive to the estimation method than the other. The coefficient of variation in n was found to be somewhat greater in the individual data method than in the arithmetic mean method.

Choi, Sung R.

Detailed Comparison of Observed Dose-Time Profile of October 19-20, 1989 SPE on Mir with Model Calculations

The dose rate dynamics of the October 19-20,1989 solar energetic particle (SPE) event as observed by the Liulin instrument onboard the Mir orbital station was analyzed in light of new calculations of the geomagnetic cutoff and improved estimates of the less than 100 MeV energy spectra from the GOES satellite instrument. The new calculations were performed using the as-flown Mir orbital trajectory and includes time variations of the cutoff rigidity due to changes in the kappa (sub p) index. Although the agreement of total event integrated calculated dose to the measured dose is good, it results from some measured dose-time profile been higher and some lower than model calculations. They point to the need to include the diurnal variation of the geomagnetic cutoff and modifications of the cutoffs to variations in kappa (sub p) in model calculations. Understanding of such events in light of the upcoming construction of the International Space Station during the period of maximum solar activity needs to be vigorously pursued.

Badhwar, Gautam D.