Gradient generation for parametric control models

This paper presents a numerical method for approximating the solution of complex optimal control problems by a constrained function minimization problem in a finite dimensional space. This end is achieved by approximating only the control functions by a finite set of parameters. The computation of gradients with respect to the parameters modeling the control is explored in depth. A hybrid technique combining the rapid gradient generation capability of the method of gradients with the rapid convergence characteristics of finite-dimensional, variable-metric function minimization algorithms is presented. An algorithm for mapping the impulsive response gradient trajectory generated by the method of gradients into a gradient vector of the performance index with respect to the parameters modeling the control function is presented. The class of local parameterizations is shown to have a distinct computational advantage, from a gradient generation point of view, over the class of continuous polynomial approximations. Detailed results are presented for piecewise linear parametric control models. An algebraic transformation is presented for improving inaccurate gradients generated by a widespread computer implementation of the method of gradients.     

The variability and predictability of the IRI B0, B1 parameters over Grahamstown,South Africa

The International Reference Ionosphere (IRI) parameters B₀ and B₁ provide a representation of the thickness and shape, respectively, of the F2 layer of the bottomside ionosphere. These parameters can be derived from electron density profiles that are determined from vertical incidence ionograms. This paper aims to illustrate the variability of these parameters for a single mid latitude station and demonstrate the ability of the Neural Network (NN) modeling technique for developing a predictive model for these parameters. Grahamstown, South Africa (33.3°S, 26.5°E) was chosen as the mid latitude station used in this study and the B₀ and B₁ parameters for an 11 year period were determined from electron density profiles recorded at that station with a University of Massachusetts Lowell Center for Atmospheric Research (UMLCAR) Digisonde. A preliminary single station NN model was then developed using the Grahamstown data from 1996 to 2005 as a training database, and input parameters known to affect the behaviour of the F2 layer, such as day number, hour, solar and magnetic indices. An analysis of the diurnal, seasonal and solar variations of these parameters was undertaken for the years 2000, 2005 and 2006 using hourly monthly median values. Comparisons between the values derived from measured data and those predicted using the two available IRI-2001 methods (IRI tables and Gulyaeva, T. Progress in ionospheric informatics based on electron density profile analysis of ionograms. Adv. Space Res. 7(6), 39–48, 1987.) and the newly developed NN model are also shown in this paper. The preliminary NN model showed that it is feasible to use the NN technique to develop a prediction tool for the IRI thickness and shape parameters and first results from this model reveal that for the mid latitude location used in this study the NN model provides a more accurate prediction than the current IRI model options.     

Molecular Biosignatures

Life, as we know it, is based on carbon chemistry operating in an aqueous environment. Living organisms process chemicals, make copies of themselves, are autonomous and evolve in concert with the environment. All these characteristics are driven by, and operate through, carbon chemistry. The carbon chemistry of living systems is an exact branch of science and we have detailed knowledge of the basic metabolic and reproductive machinery of living organisms. We can recognise the residual biochemicals long after life has expired and otherwise lost most life-defining features. Carbon chemistry provides a tool for identifying extant and extinct life on Earth and, potentially, throughout the Universe. In recognizing that certain distinctive compounds isolable from living systems had related fossil derivatives, organic geochemists coined the term biological marker compound or biomarker (e.g. Eglinton et al. in Science 145:263–264, 1964) to describe them. In this terminology, biomarkers are metabolites or biochemicals by which we can identify particular kinds of living organisms as well as the molecular fossil derivatives by which we identify defunct counterparts. The terms biomarker and molecular biosignature are synonymous. A defining characteristic of terrestrial life is its metabolic versatility and adaptability and it is reasonable to expect that this is universal. Different physiologies operate for carbon acquisition, the garnering of energy and the storage and processing of information. As well as having a range of metabolisms, organisms build biomass suited to specific physical environments, habitats and their ecological imperatives. This overall ‘metabolic diversity’ manifests itself in an enormous variety of accompanying product molecules (i.e. natural products). The whole field of organic chemistry grew from their study and now provides tools to link metabolism (i.e. physiology) to the occurrence of biomarkers specific to, and diagnostic for, particular kinds of metabolism. Another characteristic of living things, also likely to be pervasive, is that an enormous diversity of large molecules are built from a relatively small subset of universal precursors. These include the four bases of DNA, 20 amino acids of proteins and two kinds of lipid building blocks. Third, life exploits the specificity inherent in the spatial, that is, the three-dimensional qualities of organic chemicals (stereochemistry). These characteristics then lead to some readily identifiable and measurable generic attributes that would be diagnostic as biosignatures. Measurable attributes of molecular biosignatures include:

1. Enantiomeric excess
2. Diastereoisomeric preference
3. Structural isomer preference
4. Repeating constitutional sub-units or atomic ratios
5. Systematic isotopic ordering at molecular and intramolecular levels
6. Uneven distribution patterns or clusters (e.g. C-number, concentration, δ ¹³C) of structurally related compounds.

In this paper we address details of the chemical and biosynthetic basis for these features, which largely arise as a consequence of construction from small, recurring sub-units. We also address how these attributes might become altered during diagenesis and planetary processing. Finally, we discuss the instrumental techniques and further developments needed to detect them.     

Evolution of Ni-based superalloys for single crystal gas turbine blade applications

The chemistry of the Ni-based superalloys designed for single crystal gas turbine blades has significantly evolved since the development of the first generation of alloys derived from columnar grained materials. The overall performance of the second and third generations has been significantly improved by the addition of increasing amounts of rhenium. However, the problems of increased density, grain defects and microstructural stability have also become more and more acute and render necessary to carefully control the level of the various alloying elements in order to effectively benefit from the high potential of the most recently developed third generation alloys.     

Status of the T2L2/Jason2 Experiment

The T2L2 (Time Transfer by Laser Link) project, developed by CNES and OCA will permit the synchronization of remote ultra stable clocks and the determination of their performances over intercontinental distances. The principle of the experiment derives from Satellite Laser Ranging (SLR) technology with dedicated space equipment. T2L2 was accepted in 2005 to be on board the Jason2 altimetry satellite. The payload consists of both event timer and photo detection modules. The system uses the ultra-stable quartz oscillator of DORIS as on-board reference clock on one hand, and the Laser Reflector Array, making T2L2 a real two-way time transfer system on the other hand. The expected time stability of the T2L2 instrument (detection and timing), referenced by the DORIS oscillator and including all internal error sources should be at the level of 10–12 ps at 1 s and <1 ps at 1000 s. The metrological specifications of T2L2 should permit to maintain a precision of 1 to a few ps when measuring the phase of a clock during around 1000 seconds.     

Neural network prediction of the topside electron content over the Euro-African sector derived from Swarm-A measurements

This study presents the first prediction results of a neural network model for the vertical total electron content of the topside ionosphere based on Swarm-A measurements. The model was trained on 5 years of Swarm-A data over the Euro-African sector spanning the period 1 January 2014 to 31 December 2018. The Swarm-A data was combined with solar and geomagnetic indices to train the NN model. The Swarm-A data of 1 January to 30 September 2019 was used to test the performance of the neural network. The data was divided into two main categories: most quiet and most disturbed days of each month. Each category was subdivided into two sub-categories according to the Swarm-A trajectory i.e. whether it was ascending or descending in order to accommodate the change in local time when the satellite traverses the poles. Four pairs of neural network models were implemented, the first of each pair having one hidden layer, and the second of each pair having two hidden layers, for the following cases: 1) quiet day-ascending, 2) quiet day-descending, 3) disturbed day-ascending, and 4) disturbed day-descending. The topside vertical total electron content predicted by the neural network models compared well with the measurements by Swarm-A. The model that performed best was the one hidden layer model in the case of quiet days for descending trajectories, with RMSE = 1.20 TECU, R = 0.76. The worst performance occurred during the disturbed descending trajectories where the one hidden layer model had the worst RMSE = 2.12 TECU, (R = 0.54), and the two hidden layer model had the worst correlation coefficient R = 0.47 (RMSE = 1.57).In all cases, the neural network models performed better than the IRI2016 model in predicting the topside total electron content. The NN models presented here is the first such attempt at comparing NN models for the topside VTEC based on Swarm-A measurements.     

A Numerical Model of the SEIS Leveling System Transfer Matrix and Resonances: Application to SEIS Rotational Seismology and Dynamic Ground Interaction

Both sensors of the SEIS instrument (VBBs and SPs) are mounted on the mechanical leveling system (LVL), which has to ensure a level placement on the Martian ground under currently unknown local conditions, and provide the mechanical coupling of the seismometers to the ground. We developed a simplified analytical model of the LVL structure in order to reproduce its mechanical behavior by predicting its resonances and transfer function. This model is implemented numerically and allows to estimate the effects of the LVL on the data recorded by the VBBs and SPs on Mars. The model is validated through comparison with the horizontal resonances (between 35 and 50 Hz) observed in laboratory measurements. These modes prove to be highly dependent of the ground horizontal stiffness and torque. For this reason, an inversion study is performed and the results are compared with some experimental measurements of the LVL feet’s penetration in a martian regolith analog. This comparison shows that the analytical model can be used to estimate the elastic ground properties of the InSight landing site. Another application consists in modeling the 6 sensors on the LVL at their real positions, also considering their sensitivity axes, to study the performances of the global SEIS instrument in translation and rotation. It is found that the high frequency ground rotation can be measured by SEIS and, when compared to the ground acceleration, can provide ways to estimate the phase velocity of the seismic surface waves at shallow depths. Finally, synthetic data from the active seismic experiment made during the HP³ penetration and SEIS rotation noise are compared and used for an inversion of the Rayleigh phase velocity. This confirms the perspectives for rotational seismology with SEIS which will be developed with the SEIS data acquired during the commissioning phase after landing.     

Analysis of Regolith Properties Using Seismic Signals Generated by InSight’s HP<Superscript>3</Superscript> Penetrator

InSight’s Seismic Experiment for Interior Structure (SEIS) provides a unique and unprecedented opportunity to conduct the first geotechnical survey of the Martian soil by taking advantage of the repeated seismic signals that will be generated by the mole of the Heat Flow and Physical Properties Package (HP³). Knowledge of the elastic properties of the Martian regolith have implications to material strength and can constrain models of water content, and provide context to geological processes and history that have acted on the landing site in western Elysium Planitia. Moreover, it will help to reduce travel-time errors introduced into the analysis of seismic data due to poor knowledge of the shallow subsurface. The challenge faced by the InSight team is to overcome the limited temporal resolution of the sharp hammer signals, which have significantly higher frequency content than the SEIS 100 Hz sampling rate. Fortunately, since the mole propagates at a rate of \(\sim1~\mbox{mm}\) per stroke down to 5 m depth, we anticipate thousands of seismic signals, which will vary very gradually as the mole travels.Using a combination of field measurements and modeling we simulate a seismic data set that mimics the InSight HP3-SEIS scenario, and the resolution of the InSight seismometer data. We demonstrate that the direct signal, and more importantly an anticipated reflected signal from the interface between the bottom of the regolith layer and an underlying lava flow, are likely to be observed both by Insight’s Very Broad Band (VBB) seismometer and Short Period (SP) seismometer. We have outlined several strategies to increase the signal temporal resolution using the multitude of hammer stroke and internal timing information to stack and interpolate multiple signals, and demonstrated that in spite of the low resolution, the key parameters—seismic velocities and regolith depth—can be retrieved with a high degree of confidence.     

Geomagnetic activity indicators for geomagnetically induced current studies in South Africa

Intense geomagnetic activity is known to give rise to large geomagnetically induced currents (GICs) in power transmission grids. Recordings of geomagnetic activity provide an efficient and economical way for power transmission system operators to assess GIC risks in retrospective studies. This study investigates local geomagnetic indicators (i.e., hourly peak value, hourly range indicator and hourly standard deviation) in order to determine their usefulness for understanding the drivers of GICs in the South African power network. Results show that the GICs have a higher correlation with the geomagnetic indicators derived from the East–West component of the horizontal geomagnetic field, than the indicators derived from the North–South component of the horizontal field. This directional dependence corresponds very well with the North–South orientation of the power lines feeding the power transformers at the South African Grassridge electrical substation GIC site. It therefore follows that, the geoelectric field driving the GICs at Grassridge is North–South oriented. Further, it is shown that the hourly range indicator has a higher correlation with the GICs than the hourly standard deviation for this particular network configuration.     

Space solar arrays and concentrators

This paper presents some research activities conducted at the Centre Spatial de Liege (CSL) in the field of space solar arrays and concentration.With the new generation of high efficiency solar cells, solar concentration brings new insights for future high power spacecrafts. A trade-off study is presented in this paper. Two different trough concentrators, and a linear Fresnel lens concentrator are compared to rigid arrays. Thermal and optical behaviors are included in the analysis.Several technical aspects are discussed:

• Off-pointing with concentrators induces collection loss and illumination non uniformity, reducing the PV efficiency.

• Concentrator deployment increases the mission risk.

• Reflective trough concentrators are attractive and already proven. Coating is made of VDA (Aluminum). A comprehensive analysis of PV conversion increase with protected silver is presented.

• Solar concentration increases the heat load on solar cells, while the conversion efficiency is significantly decreasing at warm temperatures.

To conclude, this paper will point out the new trends and the key factors to be addressed for the next generation of solar generators.