Newton's method and the optimization of nonlinear systems
Newton-Raphson method applied to solution of boundary value problems in trajectory optimization
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Newton-Raphson method applied to solution of boundary value problems in trajectory optimization
Reactor temperature manipulation to increase product yields of chemical reactions is a known technique used in many industrial processes. In the case of exothermic chemical reactions, the well-known Le Chatelier’s principle predicts that a decrease in temperature will displace the chemical reaction toward the formation of products by increasing the value of the equilibrium constant. The reverse is true for endothermic reactions. Reactor temperature manipulation in an industrial system, however, affects the values of many variables, including physical properties, transport parameters, reaction kinetic parameters, etc. In the case of reactive absorption, some variables change with increasing temperatures due to solute absorption, while others change in such a way that the solute absorption rate decreases. For example, temperature drop increases product formation for exothermic reactions but reduces the value of transport parameters, leading to decreasing interfacial concentrations and absorption rates. Therefore, temperature manipulation strategies must be designed carefully to achieve the process goals. In this work, we theoretically study the use of temperature as a tool to increase CO 2 absorption by solvents in a semi-batch reactor. A computer code has been developed and validated using reported experimental data. Calculated results demonstrate an increase in absorbed CO 2 of more than 28% with respect to the highest temperature used. Despite high agitation and high gas flow rate, the system is mass transfer controlled at short times, becoming kinetically controlled as time increases. An operating strategy to decrease cooling energy costs is also proposed. This study reveals that reactor temperature manipulation can be an effective process to improve CO 2 absorption by solvents in two-phase semi-batch reactors.
The present study investigated the effects of remotely piloted unmanned aircraft (UA) voice communication delay on air traffic management operations with different background sector traffic-volume levels. Three one-way UA voice delay lengths of 400, 900, and 2,000 milliseconds (ms) were tested, representing the currently estimated transmission delays for terrestrial, satellite communication (SATCOM), and long SATCOM Command and Control Link System, respectively. All delay values exceeded 390 ms, the FAA’s current requirement for the maximum communication latency in the National Airspace System. Eight retired en route air traffic controllers (ATCs) and eight remote pilots (RPs) participated in a human-inthe-loop simulation study, where a simulated UA flight transitioned through an Oakland en route low-altitude sector to a local non-towered airport. The results showed that, when the 2,000-ms voice delay was present, radio transmission step-ons and detect-and-avoid (DAA) alert level elevations increased. In addition, ATC workload, ATC acceptability for the UA, and RP acceptability for the DAA were negatively affected only when the UA had a 2,000-ms voice delay under the high traffic-volume condition, but not in the other conditions.
The present study investigated the effects of remotely piloted unmanned aircraft (UA) voice communication delay on air traffic management operations with different background sector traffic-volume levels. Three one-way UA voice delay lengths of 400, 900, and 2,000 milliseconds (ms) were tested, representing the currently estimated transmission delays for terrestrial, satellite communication (SATCOM), and long SATCOM Command and Control Link System, respectively. All delay values exceeded 390 ms, the FAA’s current requirement for the maximum communication latency in the National Airspace System. Eight retired en route air traffic controllers (ATCs) and eight remote pilots (RPs) participated in a human-in-the-loop simulation study, where a simulated UA flight transitioned through an Oakland en route low-altitude sector to a local non-towered airport. The results showed that, when the 2,000-ms voice delay was present, radio transmission step-ons and detect-and-avoid (DAA) alert level elevations increased. In addition, ATC workload, ATC acceptability for the UA, and RP acceptability for the DAA were negatively affected only when the UA had a 2,000-ms voice delay under the high traffic-volume condition, but not in the other conditions.
Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.
Background: The phenomenon of fusion hindrance may have important consequences on the nuclear processes occurring in astrophysical scenarios, if it is a general behavior of heavy-ion fusion at extreme subbarrier energies, including reactions involving lighter systems, e.g., reactions in the carbon and oxygen burning stages of heavy stars. The hindrance is generally identified by the observation of a maximum of the S-factor vs energy. Whether there is an S-factor maximum at very low energies for systems with a positive fusion Q value is an experimentally challenging question. Purpose: Our aim has been to search for evidence of fusion hindrance in 12 C+ 24 Mg which is a medium-light m system with positive Q value for fusion, besides the heavier cases where hindrance is recognized to be a general phenomenon. 12 C+ 24 Mg is very close to the 16 O + 16 O and 12 C + 12 C systems that are important for the late evolution of heavy stars. Methods: The experiment has been performed in inverse kinematics using the 24 Mg beam from the XTU Tandem accelerator of LNL in the energy range 26-52 MeV with an intensity of 4-8 pnA. The targets were 12 C evaporations 50 mu g/cm 2 thick, isotopically enriched to 99.9%. The fusion-evaporation residues were detected at small angles by a E-Delta E-ToF detector telescope following an electrostatic beam deflector. Results: Previous measurements of fusion cross section for 12 C+ 24 Mg were limited to above-barrier energies. In the present experiment the excitation function has been extended down to similar or equal to 15 mu b and it appears that the S factor develops a clear maximum vs energy, indicating the presence of hindrance. This is the first convincing evidence of an S factor maximum in a medium-light system with a positive fusion Q value. These results have been fitted following a recently suggested method and a detailed analysis within the coupled-channels model that has been performed using a Woods-Saxon potential and including the ground state rotational band of 24 Mg. The coupled-channels calculations give a good account of the data near and above the barrier but overpredict the cross sections at very low energies. Conclusions: The hindrance phenomenon is clearly observed in 12 C+ 24 Mg, and its energy threshold is in reasonable agreement with the systematics observed for several medium-light systems. The fusion cross sections at the hindrance threshold show that the highest value (sigma(s) = 1.6 mb) is indeed found for this system. Therefore it may even be possible to extend the measurements further down in energy to better establish the position of the S-factor maximum.
Numerous models of physical systems contain parameters whose values are not known exactly. The physical and mathematical complexities arising in the prediction of the statistical behavior of such systems are discussed. Although the discussions are far from providing a satisfactory solution to such problems, they perhaps, by utilization of simple examples, will create a greater awareness of the statistical effect of random parameters.
The planning, observations and adjustment of high-precision gravity survey networks established on the islands of Maui and Oahu as part of the geodetic-geophysical program in support of lunar laser ranging at Haleakala, Maui, Hawaii are described. The gravity survey networks include 43 independently measured gravity differences along the gravity calibration line from Kahului Airport to the summit of Mt. Haleakala, together with some key points close to tidal gauges on Maui, and 40 gravity differences within metropolitan Honolulu. The results of the 1976-1978 survey are compared with surveys made in 1961 and in 1964-1965. All final gravity values are given in the system of the international gravity standardization net 1971 (IGSN 71); values are obtained by subtracting 14.57 mgal from the Potsdam value at the gravity base station at the Hickam Air Force Base, Honolulu.
Knowledge of the isotopic ratios of standards, spikes, and reference materials is fundamental to the accuracy of many geochronological methods. For example, the 238U/235U ratio relevant to U-Pb geochronology was recently re-determined [1] and shown to differ significantly from the previously accepted value employed during age determinations. These underlying values are fundamental to accurate age calculations in many isotopic systems, and uncertainty in these values can represent a significant (and often unrecognized) portion of the uncertainty budget for determined ages. The potassium isotopic composition of mineral standards, or neutron flux monitors, is a critical, but often overlooked component in the calculation of K-Ar and 40Ar/39Ar ages. It is currently assumed that all terrestrial materials have abundances indistinguishable from that of NIST SRM 985 [2]; this is apparently a reasonable assumption at the 0.25per mille level (1σ) [3]. The 40Ar/39Ar method further relies on the assumption that standards and samples (including primary and secondary standards) have indistinguishable 40K/39K values. We will present data establishing the potassium isotopic compositions of NIST isotopic K SRM 985, elemental K SRM 999b, and 40Ar/39Ar biotite mineral standard GA1550 (sample MD-2). Stable isotopic compositions (41K/39K) were measured by the peak shoulder method with high resolution MC-ICP-MS (Thermo Scientific NEPTUNE Plus), using the accepted value of NIST isotopic SRM 985 [2] for fractionation [4] corrections [5]. 40K abundances were measured by TIMS (Thermo Scientific TRITON), using 41K/39K values from ICP-MS measurements (or, for SRM 985, values from [2]) for internal fractionation corrections. Collectively these data represent an important step towards a metrologically traceable calibration of 40K concentrations in primary 40Ar/39Ar mineral standards and improve uncertainties by ca. an order of magnitude in the potassium isotopic compositions of standards.
In the STBO modeler and tactical surface scheduler for ATD-2 project, taxi speed decision trees are used to calculate the unimpeded taxi times of flights taxiing on the airport surface. The initial taxi speed values in these decision trees did not show good prediction accuracy of taxi times. Using the more recent, reliable surveillance data, new taxi speed values in ramp area and movement area were computed. Before integrating these values into the STBO system, we performed test runs using live data from Charlotte airport, with different taxi speed settings: 1) initial taxi speed values and 2) new ones. Taxi time prediction performance was evaluated by comparing various metrics. The results show that the new taxi speed decision trees can calculate the unimpeded taxi-out times more accurately.
The International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook contains thousands of high-quality benchmark measurements that include detailed descriptions of experiment designs and exhaustive accounting of uncertainties. These benchmarks are used extensively by the criticality safety and nuclear data communities. A subcritical benchmark involving bare, highly enriched uranium (HEU) has yet to be accepted to the handbook. The Measurement of Uranium Subcritical and Critical (MUSiC) was proposed to address this gap. MUSiC will be performed at the National Criticality Experiments Research Center (NCERC) and will leverage bare HEU hemisphere shells that can be assembled in a variety of configurations. The measurement has the following key benefits: it will be the first set of fast, subcritical measurements of HEU to be submitted to ICSBEP; ten configurations will be measured spanning from nearly no multiplication to critical (e.g., it is a measurement of similar systems with different re activities); measurements of an all-HEU system will be of value for nuclear data validation, providing results that assist in determining biases in both measurements and simulations. A variety of detector systems will be used including a Neutron Multiplicity Array Detector (NoMAD) system (similar to the MC-15), four small volume 0.635 cm (#8960;) × 7.59 cm 3He detectors (ideal for measuring prompt neutron decay constants due to their fast recovery speed), and an array of eight 5.08 cm (#8960;) × 5.08 cm EJ-309 organic scintillator detectors. The focus of this work is the simulation of the subcritical MUSiC configurations including the EJ-309 detectors and the application of the Rossi-α method. The EJ-309 organic scintillator detector array is a new detection system that will be deployed at NCERC. Organic scintillators are ideal for measurements of fast, subcritical systems due to their short time response on the order of nanoseconds.
Failure analysis of adjoint systems method for determining optimal trajectories
High concentration ratio photovoltaic systems for space applications have generally been considered impractical because of perceived difficulties in controlling solar cell temperatures to reasonably low values. A miniaturized concentrator system is now under development which surmounts this objection by providing acceptable solar cell temperatures using purely passive cell cooling methods. An array of identical miniaturized, rigid Cassegrainian optical systems having a low f-number with resulting short dimensions along their optical axes are rigidly mounted into a frame to form a relatively thin concentrator solar array panel. A number of such panels, approximately 1.5 centimeters thick, are wired as an array and are folded against one another for launch in a stowed configuration. Deployment on orbit is similar to the deployment of conventional planar honeycomb panel arrays or flexible blanket arrays. The miniaturized concept was conceived and studied in the 1978-80 time frame. Progress in the feasibility demonstration to date is reported.
Precipitation of strengthening phases from solid state is a critical process for many materials. For example, the high-temperature creep resistance of Ni-based superalloys is governed by ’ precipitates. However, the interfacial energy which controls the precipitation is expensive to determine experimentally. For simulations, the atomic nature of precipitation events necessitates using Molecular Dynamics (MD) so relying on fitting to a-priori experimental behavior is not required. However, the solid-state precipitation takes orders of magnitude longer time than is accessible for traditional MD simulation. Taking inspiration from Kinetic Monte-Carlo (KMC) methods for simulating diffusion on a rigid lattice, we have developed a hybrid KMC-MD approach to enable simulation of solid-state precipitation (and determination of the interfacial energy). Implementing these methods in LAMMPS, we calculated the interfacial energy for the ’ precipitation out of a super-saturated phase in Ni-based superalloys. The resulting interfacial energy value for the Ni-Al system is well within the accuracy of experimental values, demonstrating the capability of this method. Enabling the calculation of the interfacial energy without a-priori experimental knowledge of the precipitation unlocks a more efficient ICME-based approach for guiding annealing protocols in Ni-based superalloys and other solid-state precipitation systems.
Much of the experimental work on vapor phase lubrication has employed certain organo phosphorous compounds as the vapor phase lubricant. Graham and Klaus, for instance, used tricresyl phosphate (TCP) and tributyl phosphate to vapor phase lubricate a four-ball wear tester using M50 steel balls at 370 C. Makki and Graham were able to vapor phase lubricate a reciprocating pin on plate tribometer using 1018 steel at 280 C with TCP vapor. Although a few organo phosphorous compounds, such as TCP, have been successfully used as vapor phase lubricants in many laboratory experiments, many problems remain unsolved. Two areas of concern relate to the 'durability' of phosphate deposited films and to the ability of the lubricating system to "self-recover" when vapor phase lubricated with an organo phosphorous compound. Durability refers to the ability of the deposited film to provide effective lubrication, for a period of time, after the vapor flow to the lubricating surfaces has been interrupted. Vapor phase lubrication tests, conducted at Cleveland State University with their high temperature tribometer, revealed that when TCP vapor flow to the lubricating surfaces was interrupted the frictional coefficient of the system rapidly increased from a value less than 0.1 to a value of 0.3 which was selected as our failure point. Self-recovery means the ability of the vapor phase lubricant to reduce the frictional coefficient of the lubricating system back down to value less than 0.1 after startup of the interrupted vapor flow. Lubrication tests conducted at Cleveland State University revealed that the high temperature tribometer could not self-recover after startup of the interrupted TCP vapor flow.
A cyber-physical system may have a plurality of monitoring nodes each generating a series of current monitoring node values over time representing current operation of the system. A data-driven features extraction computer platform may receive the series of current monitoring node values and generate current data-driven feature vectors based on the series of current monitoring node values. A residual features extraction computer platform may receive the series of current monitoring node values, execute a system model and utilize a stochastic filter to determine current residual values, and generate current residual-driven feature vectors based on the current residual values. An abnormal detection platform may then receive the current data-driven and residual-driven feature vectors and compare the current data-driven and residual-driven feature vectors with at least one decision boundary associated with an abnormal detection model. An abnormal alert signal may then be transmitted when appropriate based on a result of said comparison.
The generation of condensed compounds in a deep eutectic solvent (DES) pretreatment has become a paramount factor that inhibits the further conversion of pretreated cellulose-rich substrate. Here, this study proposed a novel three-constituent DES system for the value-added utilization of poplar residues by efficiently suppressing hemicellulose derived condensation reactions. The results showed that adding ethanol into the DES system could effectively deconstruct the recalcitrant structure of poplar residues, simultaneously hindering the condensed composition formation. Under optimum ethanol addition (30%), the maximum xylan and lignin removal of 87.94% and 90.99% could be achieved, with more than 90.47% of glucan being preserved. With this, the glucan enzymatic hydrolysis efficiency was remarkably improved to 100% under the pretreatment conditions of 100 °C for 60 min, which was 84.69 times higher than the regular DES-pretreated poplar residues (1.17%). The working mechanism of relieving condensation reactions was characterized by Py-GC–MS, NMR, SEM, FTIR, and others. The results demonstrated that the addition of ethanol could regulate the degradation/conversion pathway of hemicellulose and lignin precipitation, thus inhibit the formation of condensed compounds during the pretreatment.
Abstract With the planned future reliance on variable renewable energy, the ability to store energy for prolonged time periods will be required to reduce the disruption of market fluctuations. This paper presents a method to analyze a hybrid liquid-oxygen (LOx) storage/direct-fired supercritical carbon dioxide (sCO2) power cycle and optimize the economic performance over a diverse range of scenarios. The system utilizes a modified version of the NET Power process to produce energy when energy demand exceeds the supply while displacing much of the cost of the air separation unit (ASU) energy requirements through cryogenic storage of oxygen. The model uses marginal cost of energy data to determine the optimal times to charge and discharge the system over a given scenario. The model then applies ramp rates and other time-dependent factors to generate an economic model for the system without storage considerations. The size of the storage system is then applied to create a realistic model of the plant operation. From the real plant operation model, the amount of energy charged and discharged, the capital expenditures (CAPEX) of each system, energy costs and revenue and other parameters can be calculated. The economic parameters are then combined to calculate the net present value (NPV) of the system for the given scenario. The model was then run through the SMPSO genetic algorithm in Python for a variety of geographic regions and large-scale scenarios (high solar penetration) to maximize the NPV based on multiple parameters for each subsystem. The LOx storage requirements will also be discussed.