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Development of Electronics for Low Temperature Space Missions

The operation of electronic systems at cryogenic temperatures is anticipated for many future NASA space missions such as deep space probes and planetary surface exploration. For example, an unheated interplanetary probe launched to explore the rings of Saturn would reach an average temperature near Saturn of about -183 C. In addition to surviving the deep space harsh environment, electronics capable of low temperature operation would contribute to improving circuit performance, increasing system efficiency, and reducing payload development and launch costs. Terrestrial applications where components and systems must operate in low temperature environments include cryogenic instrumentation, superconducting magnetic energy storage, magnetic levitation transportation system, and arctic exploration. An on-going research and development program on low temperature electronics at the NASA Glenn Research Center focuses on the development of efficient power systems capable of surviving and exploiting the advantages of low temperature environments. Inhouse efforts include the design, fabrication, and characterization of low temperature power systems and the development of supporting technologies for low temperature operations, such as dielectric and insulating materials, semiconductor devices, passive power components, opto-electronic devices, as well as packaging and integration of the developed components into prototype flight hardware.

Patterson, Richard L.↗

Development of High Conductivity Lithium-Ion Electrolytes for Low Temperature Cell Applications

NASA has continued interest in developing power sources which are capable of operating at low temperatures (-20 C and below) to enable future missions, such as the Mars Rover and Lander. Thus, under a program sponsored by the Mars Exploration Program, we have been involved in developing Li-ion batteries with improved low temperature performance. To accomplish this task, the focus of the research has been upon the development of advanced electrolyte systems with improved low temperature properties. This had led to the identification of a carbonate-based electrolyte, consisting of 1.0 M LiPF6 in EC + DEC + DMC (33:33:34), which has been shown to have excellent performance at -20 C in Li-ion AA-size prototype cells. Other groups are also actively engaged in developing electrolytes which can result in improved low temperature performance of Li-ion cells, including Polystor, Yardney, and Covalent. In addition to developing cells capable of operation at -20 C, there is continued interest in systems which can successfully operate at even lower temperatures (less than -30 C) and at high discharge rates (greater than C/2). Thus, we are currently focusing upon developing advanced electrolytes which are highly conductive at low temperatures and will result in cells capable of operation at -40 C. One approach to improve the low temperature conductivity of ethylene carbonate-based electrolytes involves adding co-solvents which will decrease the viscosity and extend the liquid range. Candidate solvent additives include formates, acetates, cyclic and aliphatic ethers, lactones, as well as other carbonates. Using this approach, we have prepared a number of electrolytes which contain methyl formate (MF), methyl acetate (MA), ethyl acetate (EA), ethyl proprionate (EP), and 1,2-dimethoxyethane (DME), some of which have been characterized and reported. Other groups have also reported electrolytes based on mixtures of carbonates and acetates. In the present study, electrolytes which have been identified to have good low temperature conductivity and stability were incorporated into lithium-graphite cells for evaluation. Using various electrochemical methods, including ac impedence and DC micropolarization techniques, the film formation characteristics of graphite electrodes in contact with various lectrolyte formulations was investigated.

Smart, M. C.↗

The Combined Influence of Molecular Weight and Temperature on the Aging and Viscoelastic Response of a Glassy Thermoplastic Polyimide

The effect of molecular weight on the viscoelastic performance of an advanced polymer (LaRC-SI) was investigated through the use of creep compliance tests. Testing consisted of short-term isothermal creep and recovery with the creep segments performed under constant load. The tests were conducted at three temperatures below the glass transition temperature of five materials of different molecular weight. Through the use of time-aging-time superposition procedures, the material constants, material master curves and aging-related parameters were evaluated at each temperature for a given molecular weight. The time-temperature superposition technique helped to describe the effect of temperature on the timescale of the viscoelastic response of each molecular weight. It was shown that the low molecular weight materials have higher creep compliance and creep rate, and are more sensitive to temperature than the high molecular weight materials. Furthermore, a critical molecular weight transition was observed to occur at a weight-average molecular weight of M (bar) (sub w) 25000 g/mol below which, the temperature sensitivity of the time-temperature superposition shift factor increases rapidly. The short-term creep compliance data were used in association with Struik's effective time theory to predict the long-term creep compliance behavior for the different molecular weights. At long timescales, physical aging serves to significantly decrease the creep compliance and creep rate of all the materials tested.

Nicholson, Lee M.↗

Regularization for Atmospheric Temperature Retrieval Problems

Passive remote sensing of the atmosphere is used to determine the atmospheric state. A radiometer measures microwave emissions from earth's atmosphere and surface. The radiance measured by the radiometer is proportional to the brightness temperature. This brightness temperature can be used to estimate atmospheric parameters such as temperature and water vapor content. These quantities are of primary importance for different applications in meteorology, oceanography, and geophysical sciences. Depending on the range in the electromagnetic spectrum being measured by the radiometer and the atmospheric quantities to be estimated, the retrieval or inverse problem of determining atmospheric parameters from brightness temperature might be linear or nonlinear. In most applications, the retrieval problem requires the inversion of a Fredholm integral equation of the first kind making this an ill-posed problem. The numerical solution of the retrieval problem requires the transformation of the continuous problem into a discrete problem. The ill-posedness of the continuous problem translates into ill-conditioning or ill-posedness of the discrete problem. Regularization methods are used to convert the ill-posed problem into a well-posed one. In this paper, we present some results of our work in applying different regularization techniques to atmospheric temperature retrievals using brightness temperatures measured with the SSM/T-1 sensor. Simulation results are presented which show the potential of these techniques to improve temperature retrievals. In particular, no statistical assumptions are needed and the algorithms were capable of correctly estimating the temperature profile corner at the tropopause independent of the initial guess.

Velez-Reyes, Miguel↗

Low Temperature Growth of Nanostructured Diamond Films on Metals

The field of nanocrystalline diamond and tetrahedral amorphous carbon films has been the focus of intense experimental activity in the last few years for applications in field emission display devices, optical windows, and tribological coatings, The choice of substrate used in most studies has typically been silicon. For metals, however, the thermal expansion mismatch between the diamond film and substrate gives rise to thermal stress that often results in delamination of the film. To avoid this problem in conventional CVD deposition low substrate temperatures (less than 700 C) have been used, often with the incorporation of oxygen or carbon monoxide to the feedgas mixture. Conventionally grown CVD diamond films are also rough and would require post-deposition polishing for most applications. Therefore, there is an obvious need to develop techniques for deposition of well-adhered, smooth nano-structured diamond films on metals for various tribological applications. In our work, nanostructured diamond films are grown on a titanium alloy substrate using a two-step deposition process. The first step is performed at elevated temperature (820 C) for 30 minutes using a H2/CH4/N2 gas mixture in order to grow a thin (approx. 600 nm) nanostructured diamond layer and improve film adhesion. The remainder of the deposition involves growth at low temperature (less than 600 C) in a H2/CH4/O2 gas mixture. Laser reflectance Interferometry (LRI) pattern during growth of a nanostructured diamond film on Ti-6Al-4V alloy. The first 30 minutes are at a high temperature of 820 C and the rest of the film is grown at a low temperature of 580 T. The fringe pattern is observed till the very end due to extremely low surface roughness of 40 nm. The continuation of the smooth nanostructured diamond film growth during low temperature deposition is confirmed by in-situ laser reflectance interferometry and by post-deposition micro-Raman spectroscopy and surface profilometry. Similar experiments performed without the starting nanostructured diamond layer resulted in poorly adhered films with a more crystalline appearance and a higher surface roughness. This low temperature deposition of nanostructured diamond films on metals offers advantages in cases where high residual thermal stress leads to delamination at high temperatures.

Baker, Paul A.↗

An Analysis of Simulated and Observed Global Mean Near-Surface Air Temperature Anomalies from 1979 to 1999: Trends and Attribution of Causes

The 1979 - 1999 response of the climate system to variations in solar spectral irradiance is estimated by comparing the global averaged surface temperature anomalies simulated by a 2D (two dimensional) energy balance climate model to observed temperature anomalies. We perform a multiple regression of southern oscillation index and the individual model responses to solar irradiance variations, stratospheric and tropospheric aerosol loading, stratospheric ozone trends, and greenhouse gases onto each of five near-surface temperature anomaly data sets. We estimate the observed difference in global mean near surface air temperature attributable to the solar irradiance difference between solar maximum and solar minimum to be between 0.06 and 0.11 K, and that 1.1 - 3.8% of the total variance in monthly mean near-surface air temperature data is attributable to nations in solar spectral irradiance. For the five temperature data sets used in our analysis, the trends in raw monthly mean temperature anomaly data have a large range, spanning a factor of 3 from 0.06 to 0.17 K/decade. However. our analysis suggests that trends in monthly temperature anomalies attributable to the combination of greenhouse gas, stratospheric ozone, and tropospheric sulfate aerosol variations are much more consistent among data sets, ranging from 0.16 to 0.24 K/decade. Our model results suggest that roughly half of the warming from greenhouse gases is cancelled by the cooling from changes in stratospheric ozone. Tropospheric sulfate aerosol loading in the present day atmospheric contributes significantly to the net radiative forcing of the present day climate system. However, because the change in magnitude and latitudinal distribution of tropospheric sulfate aerosol has been small over the past 20 years, the change in the direct radiative forcing attributable to changes in aerosol loading over this time is also small.

MacKay, R. M.↗

Estimating Expressed Temperature and Fractional Area of Hot Lava at the Kilauea Vent with AVIRIS Spectral Measurements

Imaging spectroscopy offers a framework based in physics and chemistry for scientific investigation of a wide range of phenomena of interest in the Earth environment. In the scientific discipline of volcanology knowledge of lava temperature and distribution at the surface provides insight into the volcano status and subsurface processes. A remote sensing strategy to measure surface lava temperatures and distribution would support volcanology research. Hot targets such as molten lava emit spectral radiance as a function of temperature. A figure shows a series of Planck functions calculated radiance spectra for hot targets at different temperatures. A maximum Lambertian solar reflected radiance spectrum is shown as well. While similar in form, each hot target spectrum has a unique spectral shape and is distinct from the solar reflected radiance spectrum. Based on this temperature-dependent signature, imaging spectroscopy provides an innovative approach for the remote-sensing-based measurement of lava temperature. A natural site for investigation of the measurement of lava temperature is the Big Island of Hawaii where molten lava from the Kilauea vent is present at the surface. In the past, Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data sets have been used for the analysis of hot volcanic targets and hot burning fires. The research presented here builds upon and extends this earlier work. The year 2000 Hawaii AVIRIS data set has been analyzed to derive lava temperatures taking into account factors of fractional fill, solar reflected radiance, and atmospheric attenuation of the surface emitted radiance. The measurements, analyses, and current results for this research are presented here.

Green, Robert O.↗

Low Temperature Reflectance Spectra of Titan Tholins

Compositional interpretation of remotely obtained reflectance spectra of outer solar system surfaces is achieved by a variety of methods. These include matching spectral curves, matching spectral features, quantitative spectral interpretation, and theoretical modeling of spectra. All of these approaches rely upon laboratory measurements of one kind or another. The bulk of these laboratory measurements are obtained with the sample of interest at ambient temperatures and pressures. However, surface temperatures of planets, satellites, and asteroids in the outer solar system are significantly cooler than ambient laboratory conditions on Earth. The infrared spectra of many materials change as a function of temperature. As has been recently demonstrated it is important to assess what effects colder temperatures have on spectral properties and hence, compositional interpretations. Titan tholin is a solid residue created by energetic processing of H-, C-, and N-bearing gases. Such residues can also be created by energetic processing if the gases are condensed into ices. Titan tholin has been suggested as a coloring agent for several surfaces in the outer solar system. Here we report laboratory measurements of Titan tholin at a temperature of 100 K and compare these to measurements of the same sample near room temperature. At low temperature the absorption features beyond 1 micrometer narrow slightly. At wavelengths greater than approx. 0.8 micrometer the overall reflectance of the sample decreases slightly making the sample less red at low temperatures. We will discuss the implications of the laboratory measurements for interpretation of cold outer solar system surfaces.

Roush, T. L.↗

High-Temperature Electronics: A Role for Wide Bandgap Semiconductors?

It is increasingly recognized that semiconductor based electronics that can function at ambient temperatures higher than 150 C without external cooling could greatly benefit a variety of important applications, especially-in the automotive, aerospace, and energy production industries. The fact that wide bandgap semiconductors are capable of electronic functionality at much higher temperatures than silicon has partially fueled their development, particularly in the case of SiC. It appears unlikely that wide bandgap semiconductor devices will find much use in low-power transistor applications until the ambient temperature exceeds approximately 300 C, as commercially available silicon and silicon-on-insulator technologies are already satisfying requirements for digital and analog very large scale integrated circuits in this temperature range. However, practical operation of silicon power devices at ambient temperatures above 200 C appears problematic, as self-heating at higher power levels results in high internal junction temperatures and leakages. Thus, most electronic subsystems that simultaneously require high-temperature and high-power operation will necessarily be realized using wide bandgap devices, once the technology for realizing these devices become sufficiently developed that they become widely available. Technological challenges impeding the realization of beneficial wide bandgap high ambient temperature electronics, including material growth, contacts, and packaging, are briefly discussed.

Neudeck, Philip G.↗

Simultaneous Temperature and Strain Sensing for Cryogenic Applications Using Dual-Wavelength Fiber Bragg Gratings

A new technique has been developed for sensing both temperature and strain simultaneously by using dual-wavelength fiber-optic Bragg gratings. Two Bragg gratings with different wavelengths were inscribed at the same location in an optical fiber to form a sensor. By measuring the wavelength shifts that resulted from the fiber being subjected to different temperatures and strains, the wavelength-dependent thermo-optic coefficients and photoelastic coefficients of the fiber were determined. This enables the simultaneous measurement of temperature and strain. In this study, measurements were made over the temperature range from room temperature down to about 10 K, addressing much of the low temperature range of cryogenic tanks. A structure transition of the optical fiber during the temperature change was found. This transition caused splitting of the waveforms characterizing the Bragg gratings, and the determination of wavelength shifts was consequently complicated. The effectiveness and sensitivities of these measurements in different temperature ranges are also discussed.

Wu, Meng-Chou↗

Potential High-Temperature Shape-Memory Alloys Identified in the Ti(Ni,Pt) System

"Shape memory" is a unique property of certain alloys that, when deformed (within certain strain limits) at low temperatures, will remember and recover to their original predeformed shape upon heating. It occurs when an alloy is deformed in the low-temperature martensitic phase and is then heated above its transformation temperature back to an austenitic state. As the material passes through this solid-state phase transformation on heating, it also recovers its original shape. This behavior is widely exploited, near room temperature, in commercially available NiTi alloys for connectors, couplings, valves, actuators, stents, and other medical and dental devices. In addition, there are limitless applications in the aerospace, automotive, chemical processing, and many other industries for materials that exhibit this type of shape-memory behavior at higher temperatures. But for high temperatures, there are currently no commercial shape-memory alloys. Although there are significant challenges to the development of high-temperature shape-memory alloys, at the NASA Glenn Research Center we have identified a series of alloy compositions in the Ti-Ni-Pt system that show great promise as potential high-temperature shape-memory materials.

Noebe, Ronald D.↗

Packaging Technology Developed for High-Temperature SiC Sensors and Electronics

A ceramic- and thick-film-materials-based prototype electronic package designed for silicon carbide (SiC) high-temperature sensors and electronics has been successfully tested at 500 C in an oxygen-containing air environment for 500 hours. This package was designed, fabricated, assembled, and electronically evaluated at the NASA Glenn Research Center at Lewis Field with an in-house-fabricated SiC semiconductor test chip. High-temperature electronics and sensors are necessary for harsh-environment space and aeronautical applications, such as space missions to the inner solar system or the emission control electronics and sensors in aeronautical engines. Single-crystal SiC has such excellent physical and chemical material properties that SiC-based semiconductor electronics can operate at temperatures over 600 C, which is significantly higher than the limit for Si-based semiconductor devices. SiC semiconductor chips were recently demonstrated to be operable at temperatures as high as 600 C, but only in the probe station environment because suitable packaging technology for sensors and electronics at temperatures of 500 C and beyond did not exist. Thus, packaging technology for SiC-based sensors and electronics is immediately needed for both application and commercialization of high-temperature SiC sensors and electronics. In response to this need, researchers at Glenn designed, fabricated, and assembled a prototype electronic package for high-temperature electronics, sensors, and microelectromechanical systems (MEMS) using aluminum nitride (AlN) substrate and gold (Au) thick-film materials. This prototype package successfully survived a soak test at 500 C in air for 500 hours. Packaging components tested included thick-film high-temperature metallization, internal wire bonds, external lead bonds, and a SiC diode chip die-attachment. Each test loop, which was composed of thick-film printed wire, wire bond, and lead bond was subjected to a 50-mA direct current for 250 hours at 500 C.

Chen, Liang-Yu↗

Damage Assessment of Stress-Thermal Cycled high temperature

We report on the characterization of bismaleimide and polyimide carbon fiber composite, microcrack development under stress thermal cycling loading. Such cycles range from cryogenic temperatures associated with cryogenic fuel (LN, LOX) containment to high temperatures of 300 degrees Celsius associated with future hypervelocity aeropropulsion systems. Microcrack development thresholds as a function of temperature range of the thermal cycle; the number of cycles; the applied stress level imposed on the composite are reported. We have conducted stress-thermal cycles on thin bismaleimide-woven carbon fiber foils for three temperature range cycles: 1. Ambient temperature - -196 degrees celsius. 2. Ambient temperature - 150 degrees Celsius; 200 degrees Celsius; 250 degrees Celsius. 3. -196 degrees Celsius - 250 degrees Celsius. The Principle findings are that the full cycles from -196 degrees Celsius to to 250 degrees Celsius cause the most significant microcrack of development. These observations indicate that the high temperature portion of the cycle under load causes fiber-matrix interface failure and subsequent exposure to higher stresses at the cryogenic, low temperature region results in composite matrix microcracking as a result of the additional stresses associate with the fiber-matrix thermal expansion mismatch. Our initial studies for 12 ply PMR-II-50 polyimide/M60JB carbon fabric [0f,90f,90f,0f,0f,90f]ls composites will be presented. The stress-thermal cycle test procedure for these will be described. Moisture absorption characteristics between cycles will be used to monitor interconnected microcrack development. The applied stress level will be 75% of the composite cryogenic (-196 degrees Celsius) ultimate strength.

Ju, Jae-Hyung↗

Development of Low Conductivity and Ultra High Temperature Ceramic Coatings Using A High-Heat-Flux Testing Approach

The development of low conductivity, robust thermal and environmental barrier coatings requires advanced testing techniques that can accurately and effectively evaluate coating thermal conductivity and cyclic resistance at very high surface temperatures (up to 17OOOC) under large thermal gradients. In this study, a laser high-heat-flux test approach is established for evaluating advanced low conductivity, ultra-high temperature ceramic thermal and environmental barrier coatings under the NASA Ultra Efficient Engine Technology (UEET) program. The test approach emphasizes the real-time monitoring and assessment of the coating thermal conductivity: the initial conductivity rise under a steady-state high temperature thermal gradient test due to coating sintering, and the later coating conductivity reduction under a subsequent cyclic thermal gradient test due to coating cracking/delamination. The coating system is then evaluated based on the damage accumulations and failure after the combined steady-state and cyclic thermal gradient tests. The lattice and radiation thermal conductivity of advanced ceramic coatings can also be evaluated using laser heat-flux techniques. The coating external radiation resistance is assessed based on the measured specimen temperature response under a laser heated intense radiation flux source. The coating internal radiation contribution is investigated based on the measured apparent coating conductivity increases with the coating surface test temperature under large thermal gradient test conditions. Since an increased radiation contribution is observed at these very high surface test temperatures, by varying the laser heat-flux and coating average test temperature, the complex relation between the lattice and radiation conductivity as a function of surface and interface test temperature is derived.

Zhu, Dongming↗

Properties of a Ni(sub 19.5)Pd(sub 30)Ti(sub 50.5) high-temperature shape memory alloy in tension and compression

Potential applications involving high-temperature shape memory alloys have been growing in recent years. Even in those cases where promising new alloys have been identified, the knowledge base for such materials contains gaps crucial to their maturation and implementation in actuator and other applications. We begin to address this issue by characterizing the mechanical behavior of a Ni19.5Pd30Ti50.5 high-temperature shape memory alloy in both uniaxial tension and compression at various temperatures. Differences in the isothermal uniaxial deformation behavior were most notable at test temperatures below the martensite finish temperature. The elastic modulus of the material was very dependent on strain level; therefore, dynamic Young#s Modulus was determined as a function of temperature by an impulse excitation technique. More importantly, the performance of a thermally activated actuator material is dependent on the work output of the alloy. Consequently, the strain-temperature response of the Ni19.5Pd30Ti50.5 alloy under various loads was determined in both tension and compression and the specific work output calculated and compared in both loading conditions. It was found that the transformation strain and thus, the specific work output were similar regardless of the loading condition. Also, in both tension and compression, the strain-temperature loops determined under constant load conditions did not close due to the fact that the transformation strain during cooling was always larger than the transformation strain during heating. This was apparently the result of permanent plastic deformation of the martensite phase with each cycle. Consequently, before this alloy can be used under cyclic actuation conditions, modification of the microstructure or composition would be required to increase the resistance of the alloy to plastic deformation by slip.

Noebe, Ronald↗

Should We Believe Atmospheric Temperatures Measured by Entry Accelerometers Traveling at "Slow" Near-Sonic Speeds?

Mars Pathfinder's Accelerometer instrument measured an unexpected and large temperature inversion between 10 and 20 kilometer altitude. Other instruments have failed to detect similar temperature inversions. I test whether this inversion is real or not by examining what changes have to be made to the assumptions in the accelerometer data processing to obtain a more "expected" temperature profile. Changes in derived temperature of up to 30K, or 15%, are necessary, which correspond to changes in derived density of up to 25% and changes in derived pressure of up to 10%. If the drag coefficient is changed to satisfy this, then instead of decreasing from 1.6 to 1.4 from 20 kilometers to 10 kilometers, the drag coefficient must increase from 1.6 to 1.8 instead. If winds are invoked, then speeds of 60 meters per second are necessary, four times greater than those predicted. Refinements to the equation of hydrostatic equilibrium modify the temperature profile by an order of magnitude less than the desired amount. Unrealistically large instrument drifts of 0.5-1.0 meters per square second are needed to adjust the temperature profile as desired. However, rotational contributions to the accelerations may have the necessary magnitude and direction to make this correction. Determining whether this hypothesis is true will require further study of the rigid body equations of motion, with detailed knowledge of the positions of all six accelerometers. The paradox concerning this inversion is not yet resolved. It is important to resolve it because the paradox has some startling implications. At one extreme, are temperature profiles derived from accelerometers inherently inaccurate by 20K or more? At the other extreme, are RS temperature profiles inaccurate by this same amount?

Withers, Paul↗

Cryogenic Temperature-dependent Refractive Index Measurements of N-BK7, BaLKN3, and SF15 for NOTES PDI

In order to enable high quality lens designs using N-BK7, BaLKN3, and SF15 at cryogenic temperatures, we have measured the absolute refractive index of prisms of these three materials using the Cryogenic, High-Accuracy Refraction Measuring System (CHARMS) at NASA's Goddard Space Flight Center, as a function of both wavelength and temperature. For N-BK7, we report absolute refractive index and thermo-optic coefficient (dn/dT) at temperatures ranging from 50 to 300 K at wavelengths from 0.45 to 2.7 micrometers; for BaLKN3 we cover temperatures ranging from 40 to 300 K and wavelengths from 0.4 to 2.6 micrometers; for SF15 we cover temperatures ranging from 50 to 300 K and wavelengths from 0.45 to 2.6 micrometers. We compare our measurements with others in the literature and provide temperature-dependent Sellmeier coefficients based on our data to allow accurate interpolation of index to other wavelengths and temperatures. While we generally find good agreement (plus or minus 2 x 10(exp -4) for N-BK7, less than 1 x 10(exp -4) for the other materials) at room temperature between our measured values and those provided by the vendor, there is some variation between the datasheets provided with the prisms we measured and the catalog values published by the vendor. This underlines the importance of measuring the absolute refractive index of the material when precise knowledge of the refractive index is required.

Frey, Bradley J.↗

Electronic clinical predictive thermometer using logarithm for temperature prediction

A thermometer that rapidly predicts body temperature based on the temperature signals received from a temperature sensing probe when it comes into contact with the body. The logarithms of the differences between the temperature signals in a selected time frame are determined. A line is fit through the logarithms and the slope of the line is used as a system time constant in predicting the final temperature of the body. The time constant in conjunction with predetermined additional constants are used to compute the predicted temperature. Data quality in the time frame is monitored and if unacceptable, a different time frame of temperature signals is selected for use in prediction. The processor switches to a monitor mode if data quality over a limited number of time frames is unacceptable. Determining the start time on which the measurement time frame for prediction is based is performed by summing the second derivatives of temperature signals over time frames. When the sum of second derivatives in a particular time frame exceeds a threshold, the start time is established.

Cambridge, Vivien J.↗