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NASA NTRS2008

Anticipating Cycle 24 Minimum and its Consequences: An Update

This Technical Publication updates estimates for cycle 24 minimum and discusses consequences associated with cycle 23 being a longer than average period cycle and cycle 24 having parametric minimum values smaller (or larger for the case of spotless days) than long term medians. Through December 2007, cycle 23 has persisted 140 mo from its 12-mo moving average (12-mma) minimum monthly mean sunspot number occurrence date (May 1996). Longer than average period cycles of the modern era (since cycle 12) have minimum-to-minimum periods of about 139.0+/-6.3 mo (the 90-percent prediction interval), inferring that cycle 24 s minimum monthly mean sunspot number should be expected before July 2008. The major consequence of this is that, unless cycle 24 is a statistical outlier (like cycle 21), its maximum amplitude (RM) likely will be smaller than previously forecast. If, however, in the course of its rise cycle 24 s 12-mma of the weighted mean latitude (L) of spot groups exceeds 24 deg, then one expects RM >131, and if its 12-mma of highest latitude (H) spot groups exceeds 38 deg, then one expects RM >127. High-latitude new cycle spot groups, while first reported in January 2008, have not, as yet, become the dominant form of spot groups. Minimum values in L and H were observed in mid 2007 and values are now slowly increasing, a precondition for the imminent onset of the new sunspot cycle.

Wilson, Robert M.↗

NASA NTRS2009

LDPC Codes with Minimum Distance Proportional to Block Size

Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding thresholds and reasonably low error floors. However, the minimum Hamming distances of those codes do not grow linearly with code-block sizes. Codes that have this minimum-distance property exhibit very low error floors. Examples of such codes include regular LDPC codes with variable degrees of at least 3. Unfortunately, the decoding thresholds of regular LDPC codes are high. Hence, there is a need for LDPC codes characterized by both low decoding thresholds and, in order to obtain acceptably low error floors, minimum Hamming distances that are proportional to code-block sizes. The present codes were developed to satisfy this need. The minimum Hamming distances of the present codes have been shown, through consideration of ensemble-average weight enumerators, to be proportional to code block sizes. As in the cases of irregular ensembles, the properties of these codes are sensitive to the proportion of degree-2 variable nodes. A code having too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code having too many such nodes tends not to exhibit a minimum distance that is proportional to block size. Results of computational simulations have shown that the decoding thresholds of codes of the present type are lower than those of regular LDPC codes. Included in the simulations were a few examples from a family of codes characterized by rates ranging from low to high and by thresholds that adhere closely to their respective channel capacity thresholds; the simulation results from these examples showed that the codes in question have low error floors as well as low decoding thresholds. As an example, the illustration shows the protograph (which represents the blueprint for overall construction) of one proposed code family for code rates greater than or equal to 1.2. Any size LDPC code can be obtained by copying the protograph structure N times, then permuting the edges. The illustration also provides Field Programmable Gate Array (FPGA) hardware performance simulations for this code family. In addition, the illustration provides minimum signal-to-noise ratios (Eb/No) in decibels (decoding thresholds) to achieve zero error rates as the code block size goes to infinity for various code rates. In comparison with the codes mentioned in the preceding article, these codes have slightly higher decoding thresholds.

Divsalar, Dariush↗

DOE OSTI2019

Oxide Solubility Minimum in Liquid Fe-M-O Alloy

The origin of the solubility minimum of oxide (M{sub x}O{sub y}) in liquid Fe-M-O alloy was investigated, and the minimum was predicted based on thermodynamic calculations. Due to the characteristic property of activities of M and O in the liquid, a maximum exists in the product between the two activities if the affinity of M to O is significantly high, as most deoxidizing elements are. A critical activity product is defined, which is an indicator of the solubility minimum of the M{sub x}O{sub y} in the liquid Fe-M-O alloy according to the following relationship: max(a{sub M}{sup x}×a{sub O{sub -}{sup y}})=K{sub M{sub xO{sub y}}}×a{sub M{sub xO{sub y}}}, where the a{sub M{sub xO{sub y}}} is unity if the alloy is in equilibrium with the pure M{sub x}O{sub y}. The origin of the solubility minimum was explained using the change of the activity product by composition. Available CALPHAD assessments for several binary Fe-M liquid alloys and Wagner’s solvation shell model were combined to calculate the activity product in the Fe-M-O alloy, which can be used to predict the solubility minimum of M{sub x}O{sub y}. A favorable agreement was obtained when M=Al, B, Cr, Mn, Nb, Si, Ta, Ti, V, and Zr. The Gibbs energy of dissolution of O in pure liquid M (Δg{sub O{sub -(M)}{sup ∘}}) and the Gibbs energy of the formation of M{sub x}O{sub y} per mole of atoms (Δg{sub M{sub xO{sub y}{sup ∘}}}/(x+y)) play important roles in determining the solubility minimum, as long as an interaction between Fe and M is less significant than the interaction between metal (Fe and M) and O. Predictions of the solubility minima of CaO and MgO were not satisfactory, requiring further improvement of the present analysis.

36 MATERIALS SCIENCE↗

NASA NTRS1983

The remarkable spectrum of the RV Tauri star R Scuti at deep minimum

In September 1981 R Sct H-alpha declined in brightness to V about 8.5, an exceptionally faint minimum. A 15 A/mm spectrogram of the H-alpha region of R Sct two days past minimum brightness, when the visual magnitude was about 8.3, was obtained. This is apparently the first spectral observation of R Sct close to such a deep minimum. Contrary to spectroscopic observations during 'ordinary' minima of V about 6-7, at this deep minimum the expected G-K Ia absorption spectrum is not seen. Instead, a fantastic array of dozens of strong, narrow emission features and strong TiO absorption bands are present. The emission lines are due to neutral metals, and closely resemble a reversed photospheric spectrum. The deep minimum spectrum is apparently purely chromospheric, and is not produced in a stellar wind or extended atmosphere. The spectroscopic behavior of R Sct at deep minimum, as well as a number of other kinematic and photometric properties, is surprisingly similar to that of the R Coronae Borealis variables.

Howell, S. B.↗

NASA NTRS1986

Minimum-fuel control of high-order systems

The minimum-fuel control problem is of special interest in various space systems. To date, solutions of minimum-fuel control problems have been carried out for relatively low-order systems. Space structures, however, are generally characterized by a large number of degrees of freedom, so that minimum-fuel control of such systems requires a new approach. In the independent modal-space control (IMSC) method, the control laws are designed in the modal space for each mode independently. The minimum-fuel problem reduces to that of a set of independent second-order systems, so that minimum-fuel control is possible. This paper shows how the IMSC method can be used to control a space structure with a minimum amount of fuel. A numerical example is presented.

Shenhar, J.↗

NASA NTRS1994

A combined algorithm for minimum time slewing of flexible spacecraft

The use of Pontryagin's Maximum Principle for the large-angle slewing of large flexible structures usually results in the so-called two-point boundary-value problem (TPBVP), in which many requirements (e.g., minimum time, small flexible amplitude, and limited control powers, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical computational algorithm. There are many candidate algorithms available for his problem (e.g., quasilinearization, gradient, and shooting, etc.). In this paper, a proposed algorithm, which combines the quasilinearization method with a time shortening technique and a shooting method, is applied to the minimum-time, three-dimensional, and large-angle maneuver of flexible spacecraft, particularly the orbiting Spacecraft Control Laboratory Experiment (SCOLE) configuration. Theoretically, the nonlinear TPBVP can be solved only through the shooting method to find the 'exact' switching times for the bang-bang controls. However, computationally, a suitable guess for the missing initial costates is crucial because the convergence range of the unknown initial costates is usually narrow, especially for systems with high dimensions and when a multi-bang-bang control strategy is needed. On the other hand, the problems of near minimum time attitude maneuver of general rigid spacecraft and fast slewing of flexible spacecraft have been examined by the authors through a numerical approach based on the quasilinearization algorithm with a time shortening technique. Computational results have demonstrated its broad convergence range and insensitivity to initial costate choices. Consequently, a combined approach is naturally suggested here to solve the minimum time slewing problem. That is, in the computational process, the quasilinearization method is used first to obtain a near minimum time solution. Then, the acquired converged initial costates from the quasilinearization approach are transformed (tailored) to and used as the initial costate guess for starting the shooting method. Finally, the shooting method takes over the remaining calculations until the minimum-time solution converges. The nonlinear equations of motion of the SCOLE are formulated by using Lagrange's equations, with the mast modeled as a continuous beam subject to three-dimensional deformations. The numerical results will be presented and some related computational issues will also be discussed.

Bainum, P. M.↗

NASA NTRS1996

On the Importance of Cycle Minimum in Sunspot Cycle Prediction

The characteristics of the minima between sunspot cycles are found to provide important information for predicting the amplitude and timing of the following cycle. For example, the time of the occurrence of sunspot minimum sets the length of the previous cycle, which is correlated by the amplitude-period effect to the amplitude of the next cycle, with cycles of shorter (longer) than average length usually being followed by cycles of larger (smaller) than average size (true for 16 of 21 sunspot cycles). Likewise, the size of the minimum at cycle onset is correlated with the size of the cycle's maximum amplitude, with cycles of larger (smaller) than average size minima usually being associated with larger (smaller) than average size maxima (true for 16 of 22 sunspot cycles). Also, it was found that the size of the previous cycle's minimum and maximum relates to the size of the following cycle's minimum and maximum with an even-odd cycle number dependency. The latter effect suggests that cycle 23 will have a minimum and maximum amplitude probably larger than average in size (in particular, minimum smoothed sunspot number Rm = 12.3 +/- 7.5 and maximum smoothed sunspot number RM = 198.8 +/- 36.5, at the 95-percent level of confidence), further suggesting (by the Waldmeier effect) that it will have a faster than average rise to maximum (fast-rising cycles have ascent durations of about 41 +/- 7 months). Thus, if, as expected, onset for cycle 23 will be December 1996 +/- 3 months, based on smoothed sunspot number, then the length of cycle 22 will be about 123 +/- 3 months, inferring that it is a short-period cycle and that cycle 23 maximum amplitude probably will be larger than average in size (from the amplitude-period effect), having an RM of about 133 +/- 39 (based on the usual +/- 30 percent spread that has been seen between observed and predicted values), with maximum amplitude occurrence likely sometime between July 1999 and October 2000.

Wilson, Robert M.↗

NASA NTRS2007

Anticipating Cycle 24 Minimum and Its Consequences

On the basis of the 12-mo moving average of monthly mean sunspot number (R) through November 2006, cycle 23 has persisted for 126 mo, having had a minimum of 8.0 in May 1996, a peak of 120.8 in April 2000, and an ascent duration of 47 mo. In November 2006, the 12-mo moving average of monthly mean sunspot number was 12.7, a value just outside the upper observed envelope of sunspot minimum values for the most recent cycles 16-23 (range 3.4-12.3), but within the 90-percent prediction interval (7.8 +/- 6.7). The first spotless day during the decline of cycle 23 occurred in January 2004, and the first occurrence of 10 or more and 20 or more spotless days was February 2006 and April 2007, respectively, inferring that sunspot minimum for cycle 24 is imminent. Through May 2007, 121 spotless days have accumulated. In terms of the weighted mean latitude (weighed by spot area) (LAT) and the highest observed latitude spot (HLS) in November 2006, 12-mo moving averages of these parameters measured 7.9 and 14.6 deg, respectively, these values being the lowest values yet observed during the decline of cycle 23 and being below corresponding mean values found for cycles 16-23. As yet, no high-latitude new-cycle spots have been seen nor has there been an upturn in LAT and HLS, these conditions having always preceded new cycle minimum by several months for past cycles. Together, these findings suggest that cycle 24 s minimum amplitude still lies well beyond November 2006. This implies that cycle 23 s period either will lie in the period "gap" (127-134 mo), a first for a sunspot cycle, or it will be longer than 134 mo, thus making cycle 23 a long-period cycle (like cycle 20) and indicating that cycle 24 s minimum will occur after July 2007. Should cycle 23 prove to be a cycle of longer period, a consequence might be that the maximum amplitude for cycle 24 may be smaller than previously predicted.

Wilson, Robert M.↗

NASA NTRS2004

Computationally-Efficient Minimum-Time Aircraft Routes in the Presence of Winds

A computationally efficient algorithm for minimizing the flight time of an aircraft in a variable wind field has been invented. The algorithm, referred to as Neighboring Optimal Wind Routing (NOWR), is based upon neighboring-optimal-control (NOC) concepts and achieves minimum-time paths by adjusting aircraft heading according to wind conditions at an arbitrary number of wind measurement points along the flight route. The NOWR algorithm may either be used in a fast-time mode to compute minimum- time routes prior to flight, or may be used in a feedback mode to adjust aircraft heading in real-time. By traveling minimum-time routes instead of direct great-circle (direct) routes, flights across the United States can save an average of about 7 minutes, and as much as one hour of flight time during periods of strong jet-stream winds. The neighboring optimal routes computed via the NOWR technique have been shown to be within 1.5 percent of the absolute minimum-time routes for flights across the continental United States. On a typical 450-MHz Sun Ultra workstation, the NOWR algorithm produces complete minimum-time routes in less than 40 milliseconds. This corresponds to a rate of 25 optimal routes per second. The closest comparable optimization technique runs approximately 10 times slower. Airlines currently use various trial-and-error search techniques to determine which of a set of commonly traveled routes will minimize flight time. These algorithms are too computationally expensive for use in real-time systems, or in systems where many optimal routes need to be computed in a short amount of time. Instead of operating in real-time, airlines will typically plan a trajectory several hours in advance using wind forecasts. If winds change significantly from forecasts, the resulting flights will no longer be minimum-time. The need for a computationally efficient wind-optimal routing algorithm is even greater in the case of new air-traffic-control automation concepts. For air-traffic-control automation, thousands of wind-optimal routes may need to be computed and checked for conflicts in just a few minutes. These factors motivated the need for a more efficient wind-optimal routing algorithm.

Jardin, Matthew R.↗

NASA NTRS2013

Elemental GCR Observations during the 2009-2010 Solar Minimum Period

Using observations from the Cosmic Ray Isotope Spectrometer (CRIS) onboard the Advanced Composition Explorer (ACE), we present new measurements of the galactic cosmic ray (GCR) elemental composition and energy spectra for the species B through Ni in the energy range approx. 50-550 MeV/nucleon during the record setting 2009-2010 solar minimum period. These data are compared with our observations from the 1997-1998 solar minimum period, when solar modulation in the heliosphere was somewhat higher. For these species, we find that the intensities during the 2009-2010 solar minimum were approx. 20% higher than those in the previous solar minimum, and in fact were the highest GCR intensities recorded during the space age. Relative abundances for these species during the two solar minimum periods differed by small but statistically significant amounts, which are attributed to the combination of spectral shape differences between primary and secondary GCRs in the interstellar medium and differences between the levels of solar modulation in the two solar minima. We also present the secondary-to-primary ratios B/C and (Sc+Ti+V)/Fe for both solar minimum periods, and demonstrate that these ratios are reasonably well fit by a simple "leaky-box" galactic transport model that is combined with a spherically symmetric solar modulation model.

Solar Modulation↗

NASA NTRS2017

The 2014 X-Ray Minimum of Eta Carinae as Seen by Swift

We report on Swift X-ray Telescope observations of Eta Carinae ( Car), an extremely massive, long-period, highly eccentric binary obtained during the 2014.6 X-ray minimumperiastron passage. These observations show that Car may have been particularly bright in X-rays going into the X-ray minimum state, while the duration of the 2014 X-ray minimum was intermediate between the extended minima seen in 1998.0 and 2003.5 by Rossi X-Ray Timing Explorer (RXTE), and the shorter minimum in 2009.0. The hardness ratios derived from the Swift observations showed a relatively smooth increase to a peak value occurring 40.5 days after the start of the X-ray minimum, though these observations cannot reliably measure the X-ray hardness during the deepest part of the X-ray minimum when contamination by the central constant emission component is significant. By comparing the timings of the RXTE and Swift observations near the X-ray minima, we derive an updated X-ray period of P X equals 2023.7 +/- 0.7 days, in good agreement with periods derived from observations at other wavelengths, and we compare the X-ray changes with variations in the He ii lambda 4686 emission. The middle of the Deep Minimum interval, as defined by the Swift column density variations, is in good agreement with the time of periastron passage derived from the He ii 4686 line variations.

binaries: general↗

NASA NTRS2018

Output Feedback Adaptive Control of Non-Minimum Phase Systems Using Optimal Control Modification

This paper describes output feedback adaptive control approaches for non-minimum phase SISO systems with relative degree 1 and non-strictly positive real (SPR) MIMO systems with uniform relative degree 1 using the optimal control modification method. It is well-known that the standard model-reference adaptive control (MRAC) cannot be used to control non-SPR plants to track an ideal SPR reference model. Due to the ideal property of asymptotic tracking, MRAC attempts an unstable pole-zero cancellation which results in unbounded signals for non-minimum phase SISO systems. The optimal control modification can be used to prevent the unstable pole-zero cancellation which results in a stable adaptation of non-minimum phase SISO systems. However, the tracking performance using this approach could suffer if the unstable zero is located far away from the imaginary axis. The tracking performance can be recovered by using an observer-based output feedback adaptive control approach which uses a Luenberger observer design to estimate the state information of the plant. Instead of explicitly specifying an ideal SPR reference model, the reference model is established from the linear quadratic optimal control to account for the non-minimum phase behavior of the plant. With this non-minimum phase reference model, the observer-based output feedback adaptive control can maintain stability as well as tracking performance. However, in the presence of the mismatch between the SPR reference model and the non-minimum phase plant, the standard MRAC results in unbounded signals, whereas a stable adaptation can be achieved with the optimal control modification. An application of output feedback adaptive control for a flexible wing aircraft illustrates the approaches.

Adaptive Contro↗

NASA NTRS2024

High Reliability at Minimum Cost

This paper investigates the minimum cost of improving the reliability of complex technical systems. The two major methods to improve reliability are redesigning the system for higher reliability or providing redundant components to replace failed elements. The costs of redesign for reliability or adding redundancy are estimated. The most cost-effective combination for high reliability can be identified. The cost of increasing the intrinsic reliability of a system can be modeled as cost proportional to 1/(system failure rate) a , where the exponent “a” measures the difficulty of increasing reliability. The “a” exponent can vary from 0.25 to about 2.5. Operational reliability can also be increased by using redundant systems. The failure rate for N parallel redundant units is (system failure rate) N . The cost of redundancy is N times the system cost. The total redundant system cost is proportional to N/(system failure rate) a . The cost of redundancy increases as N gets larger, but larger N allows a higher system failure rate, which reduces the system design cost. There is a certain N, a certain level of redundancy, that has the minimum cost to achieve the required overall redundant system failure rate. The minimum cost for the redundant system is achieved at the optimum level of redundancy. The N for minimum cost is equal to -a ln (redundant system failure rate). The minimum cost of the N redundant systems is proportional to N * (original system failure rate) a . The optimum redesigned individual system failure rate is proportional to exp (-1/a), so the greater the difficulty, the higher the optimum individual system failure rate. Increasing the intrinsic reliability of a system encounters diminishing returns and at some point it becomes more cost-effective to add redundancy. The difficulty of increasing intrinsic system reliability determines the optimum design for high reliability at minimum cost.

reliability↗

NASA NTRSDate not supplied

High Reliability at Minimum Cost

reliability↗

NASA NTRS2005

The Minimum Impulse Thruster

The Minimum Impulse Thruster (MIT) was developed to improve the state-of-the-art minimum impulse capability of hydrazine monopropellant thrusters. Specifically, a new fast response solenoid valve was developed, capable of responding to a much shorter electrical pulse width, thereby reducing the propellant flow time and the minimum impulse bit. The new valve was combined with the Aerojet MR-103, 0.2 lbf (0.9 N) thruster and put through an extensive Delta-qualification test program, resulting in a factor of 5 reduction in the minimum impulse bit, from roughly 1.1 milli-lbf-seconds (5 milliNewton seconds) to - 0.22 milli-lbf-seconds (1 mN-s). To maintain it's extensive heritage, the thruster itself was left unchanged. The Minimum Impulse Thruster provides mission and spacecraft designers new design options for precision pointing and precision translation of spacecraft.

thruster↗

DOE OSTI2022

Data-driven Minimum Entropy Control for Stochastic Nonlinear Systems using the Cumulant-Generating Function

Here, we present a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.

42 ENGINEERING↗

NASA NTRS1972

Minimum distance classification in remote sensing

The utilization of minimum distance classification methods in remote sensing problems, such as crop species identification, is considered. Literature concerning both minimum distance classification problems and distance measures is reviewed. Experimental results are presented for several examples. The objective of these examples is to: (a) compare the sample classification accuracy of a minimum distance classifier, with the vector classification accuracy of a maximum likelihood classifier, and (b) compare the accuracy of a parametric minimum distance classifier with that of a nonparametric one. Results show the minimum distance classifier performance is 5% to 10% better than that of the maximum likelihood classifier. The nonparametric classifier is only slightly better than the parametric version.

Wacker, A. G.↗

NASA NTRS1974

The minimum free-stream wind speed for initiating motion of surface material on Mars

Estimates of the minimum free-stream wind speed that is required for initiating the motion of surficial material on Mars have ranged from 30 to about 200 meters per second. Thus the best value for this quantity is not well established. Graphical comparison of much of the pertinent data taken in the laboratory and in the field on Earth provides a minimum value for the Bagnold coefficient of 0.08 and this in turn provides a minimum value for the threshold friction velocity of 1.3 meters per second for initiating motion of particulate matter on Mars at low elevations where the pressure is 7 millibars. The most appropriate value of the ratio of friction velocity to free-stream velocity for putative unstable condition appears to be 0.026. Thus the minimum free-stream wind speed for initiating motion is obtained as 50 meters per second. If the surface material on Mars, however, is less cohesive than that on earth, the minimum value may be smaller.

Wood, G. P.↗