Some problems and some recent results in stochastic control.
Stochastic optimal control applications in dynamic programming for linear and nonlinear systems
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Stochastic optimal control applications in dynamic programming for linear and nonlinear systems
The objective is to show whether or not pulsed excimer laser annealing (PELA) of ion-implanted junctions is a cost effective replacement for diffused junctions in fabricating crystalline silicon solar cells. The preliminary economic analysis completed shows that the use of PELA to fabricate both the front junction and back surface field (BSF) would cost approximately 35 cents per peak watt (Wp), compared to a cost of 15 cents/Wp for diffusion, aluminum BSF and an extra cleaning step in the baseline process. The cost advantage of the PELA process depends on improving the average cell efficiency from 14% to 16%, which would lower the overall cost of the module by about 15 cents/Wp. An optimized PELA process compatible with commercial production is to be developed, and increased cell efficiency with sufficient product for adequate statistical analysis demonstrated. An excimer laser annealing station was set-up and made operational. The first experiment used 248 nm radiation to anneal phosphorus implants in polished and texture-etched silicon.
Although designed to remove organic contaminants from a variety of waste water streams, the planned U.S.- and present Russian-provided water processing systems onboard the International Space Station (ISS) have capacity limits for some of the more common volatile cleaning solvents used for housekeeping purposes. Using large quantities of volatile cleaning solvents during the ground processing and in-flight operational phases of a crewed spacecraft such as the ISS can lead to significant challenges to the water processing systems. To understand the challenges facing the management of water processing capacity, the relationship between cabin atmospheric quality and humidity condensate loading is presented. This relationship is developed as a tool to determine the cabin atmospheric loading that may compromise water processing system performance. A comparison of cabin atmospheric loading with volatile cleaning solvents from ISS, Mir, and Shuttle are presented to predict acceptable limits to maintain optimal water processing system performance.
Parallel processing of real-time dynamic systems simulation on a multiprocessor system named OSCAR is presented. In the simulation of dynamic systems, generally, the same calculation are repeated every time step. However, we cannot apply to Do-all or the Do-across techniques for parallel processing of the simulation since there exist data dependencies from the end of an iteration to the beginning of the next iteration and furthermore data-input and data-output are required every sampling time period. Therefore, parallelism inside the calculation required for a single time step, or a large basic block which consists of arithmetic assignment statements, must be used. In the proposed method, near fine grain tasks, each of which consists of one or more floating point operations, are generated to extract the parallelism from the calculation and assigned to processors by using optimal static scheduling at compile time in order to reduce large run time overhead caused by the use of near fine grain tasks. The practicality of the scheme is demonstrated on OSCAR (Optimally SCheduled Advanced multiprocessoR) which has been developed to extract advantageous features of static scheduling algorithms to the maximum extent.
Autonomous assembly of large structures is one of the fundamental challenges on the way towards NASA’s objectives of deep space exploration. In this work, we propose an algorithmic framework to optimize the assembly process of a prescribed target structure by constraining the assembly effort as well as maintaining structural soundness throughout the process. This framework uses structural topology optimization with assembly effort metrics to generate checkpoints for robotic traversal algorithms. Assembly effort is quantified by the Wasserstein metric between consecutive structural configurations during the assembly process. The robotic assembly task is split into two subtasks, where we first optimize for a set of key frames, then perform reconfiguration between consecutive frames. Key frames are optimized by adopting topology optimization techniques to reduce assembly effort and maintain structural integrity during the assembly process, while reconfiguration between key frames is performed using a path planning algorithm with a minimum weight maximum matching approach on a bipartite graph. We employ a Crystalline robot model in which each structural element is capable of locomotion through the structure and locking into place with neighboring elements after reaching its destination. An example assembly of a two-dimensional cantilever beam under volume constraints and structural compliance considerations is presented to demonstrate the approach. Finally, we conclude by discussing possible future extensions to this work, including adoption of better metrics, extension to three-dimensional large-scale problems, and exacting finer control of structural integrity during the path-planning phase.
The purpose of this program is to demonstrate the technical readiness of a cost effective process sequence that has the potential for the production of flat plate photovoltaic modules which met the price goal in 1986 of $.70 or less per watt peak. Program efforts included: preliminary design review, preliminary cell fabrication using the proposed process sequence, verification of sandblasting back cleanup, study of resist parameters, evaluation of pull strength of the proposed metallization, measurement of contact resistance of Electroless Ni contacts, optimization of process parameter, design of the MEPSDU module, identification and testing of insulator tapes, development of a lamination process sequence, identification, discussions, demonstrations and visits with candidate equipment vendors, evaluation of proposals for tabbing and stringing machine.
A method is set forth for assessing strain-rate profiles that can be used to develop a scale-up theory for blown-film extrusion. Strain rates are evaluated by placing four ink dots on the stalk of an extruded bubble to follow the displacements of the dots as a function of time. The instantaneous Hencky strain is obtained with the displacement data and plotted for analysis. Specific attention is given to potential sources of error in the distance measurements and corrections for these complex bubble geometries. The method is shown to be effective for deriving strain-rate data related to different processing parameters for the production of balloon film. The strain rates can be compared to frostline height, blow-up ratio, and take-up ratio to optimize these processing variables.
This study sought to compare four aircraft wing configurations at a conceptual level using a multi-disciplinary optimization (MDO) process. The MDO framework used was created by Georgia Institute of Technology and Virginia Polytechnic Institute and State University. They created a multi-disciplinary design and optimization environment that could capture the unique features of the truss-braced wing (TBW) configuration. The four wing configurations selected for the study were a low wing cantilever installation, a high wing cantilever, a strut-braced wing, and a single jury TBW. The mission that was used for this study was a 160 passenger transport aircraft with a design range of 2,875 nautical miles at the design payload, flown at a cruise Mach number of 0.78. This paper includes discussion and optimization results for multiple design objectives. Five design objectives were chosen to illustrate the impact of selected objective on the optimization result: minimum takeoff gross weight (TOGW), minimum operating empty weight, minimum block fuel weight, maximum start of cruise lift-to-drag ratio, and minimum start of cruise drag coefficient. The results show that the design objective selected will impact the characteristics of the optimized aircraft. Although minimum life cycle cost was not one of the objectives, TOGW is often used as a proxy for life cycle cost. The low wing cantilever had the lowest TOGW followed by the strut-braced wing.
In this project, the team developed tough and degradable biocomposite thermoplastic polyurethanes (TPUs) by incorporating bacterial spores into TPUs as a biofunctional living filler. The team screened various bacteria and selected the Bacillus subtilis ATCC 6633 strain as the final candidate, primarily due to its genomic availability, sporulation ability and TPU assimilation activity. The heat-shock tolerance of ATCC 6633 spores was further improved through evolutionary engineering via Adaptive Laboratory Evolution (ALE), demonstrating a 17.7-fold enhanced germination efficiency post heat-shock treatment compared to the wild-type strain (WT). The team fabricated biocomposite TPUs by incorporating lyophilized powder of heat-shock tolerized (HST) spores during the hot melt extrusion (HME) of TPU at 135 °C. The baseline TPU used in this project is a commercially available soft-grade TPU (BCF45) manufactured by BASF. Colony forming unit (CFU) assays quantified that WT and HST spores in the TPU matrix retained approximately 20% and 100% survivability, respectively, after HME. Tensile testing demonstrated that the spores behaved as a polymer-reinforcing filler, positively affecting the overall tensile properties of the biocomposite TPU. For example, biocomposite TPU with WT and HST spores (BC TPU WT and BC TPU HST , respectively) exhibited up to 25% and 37% improved toughness, respectively, compared to TPU without spores. BC TPU HST showed remarkably improved disintegration in autoclaved compost (92% mass loss in 5 months), which simulated a microbially poor environment for TPU degradation. When compared to TPU without spores (44% mass loss in 5 months) the acceleration of degradation is marked. Respirometry confirmed that 72% of BC TPU HST was biomineralized into CO2 within 6 months, indicating that spores in the biocomposite TPU were germinated by utilizing nutrients in the autoclaved compost, facilitating TPU degradation at the end of the material's life. The team demonstrated the scale-up of biocomposite TPU fabrication using continuous extrusion and injection molding techniques. Processing conditions optimized in a lab-scale microcompounder were successfully transferred to a continuous extruder with a 30-fold increased throughput. Biocomposite TPUs prepared using these industry-relevant processes showed comparable toughness improvements to samples prepared in the lab-scale extruder. Excitingly, following compounding in the pilot-extruder the composite material could be injection molded, while retaining high spore viability and similar toughness improvements. The team also found that spores in biocomposite TPU served as antioxidants, preventing toughness decay during the recycled extrusion of BC TPU HST . Long-term storage tests over one year showed that the addition of spores had no negative effect on the longevity of the TPU. Furthermore, the team demonstrated the fabrication of spore-bearing biocomposite polymers with other polyesters such as PBAT, PLA, and PCL. We obtained promising preliminary data that showed overall toughness improvements for all polymers with spore addition. Finally, life cycle assessment (LCA) and techno-economic analysis (TEA) were carried out, which indicated minimal additional cost of fabrication. Overall, a tough and degradable biocomposite thermoplastic was successfully developed through this project, with all tasks completed successfully, achieving >100% of the objectives.
Theoretical calculations have shown that highest efficiency III-V multi-junction solar cells require alloy structures that cannot be grown on a lattice-matched substrate. Ever since the first demonstration of high efficiency metamorphic single junction 1.1 eV and 1.2 eV InGaAs solar cells by Essential Research Incorporated (ERI), interest has grown in the development of multi-junction cells of this type using graded buffer layer technology. ERI is currently developing a dual-junction 1.6 eV InGaP/1.1 eV InGaAs tandem cell (projected practical air-mass zero (AM0), one-sun efficiency of 28%, and 100-sun efficiency of 37.5%) under a Ballistic Missile Defense Command (BMDO) SBIR Phase II program. A second ongoing research effort at ERI involves the development of a 2.1 eV AlGaInP/1.6 eV InGaAsP/1.2 eV InGaAs triple-junction concentrator tandem cell (projected practical AM0 efficiency of 36.5% under 100 suns) under a SBIR Phase II program funded by the Air Force. We are in the process of optimizing the dual-junction cell performance. In case of the triple-junction cell, we have developed the bottom and the middle cell, and are in the process of developing the layer structures needed for the top cell. A progress report is presented in this paper.
A fundamental characteristic of fluid is viscosity; that is, the fluid resists forces that cause it to flow. This characteristic, or parameter, is used by manufacturers and end-users to describe the physical properties of a specific material so that they know what to expect when a material, such as a polymer, is processed through an extruder, a film blower, or a fiber-spinning apparatus. Normally, researchers will report a shear viscosity that depends on the rate of an imposed shearing flow. Although this type of characterization is sufficient for some processes, simple shearing experiments do not provide a complete picture of what a processor may expect for all materials. Extensional stretching flows are common in many polymer-processing operations such as extrusion, blow molding, and fiber spinning. Therefore, knowledge of the complete rheological (ability to flow and be deformed) properties of the polymeric fluid being processed is required to accurately predict and account for the flow behavior. In addition, if numerical simulations are ever able to serve as a priori design tools for optimizing polymer processing operations such as those described above, an accurate knowledge of the extensional viscosity of a polymer system and its variation with temperature, concentration, molecular weight, and strain rate is critical.
A report describes the Entry Descent Landing Data Analysis (EDA), which is a system of signal-processing software and computer hardware for acquiring status data conveyed by multiple-frequency-shift-keying tone signals transmitted by a spacecraft during descent to the surface of a remote planet. The design of the EDA meets the challenge of processing weak, fluctuating signals that are Doppler-shifted by amounts that are only partly predictable. The software supports both real-time and post processing. The software performs fast-Fourier-transform integration, parallel frequency tracking with prediction, and mapping of detected tones to specific events. The use of backtrack and refinement parallel-processing threads helps to minimize data gaps. The design affords flexibility to enable division of a descent track into segments, within each of which the EDA is configured optimally for processing in the face of signal conditions and uncertainties. A dynamic-lock-state feature enables the detection of signals using minimum required computing power less when signals are steadily detected, more when signals fluctuate. At present, the hardware comprises eight dual-processor personal-computer modules and a server. The hardware is modular, making it possible to increase computing power by adding computers.
Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.
Computer program implements thermochemical model of processing of carbon-fiber/phenolic-matrix composite materials into molded parts of various sizes and shapes. Directed toward improving fabrication of rocket-engine-nozzle parts, also used to optimize fabrication of other structural components, and material-property parameters changed to apply to other materials. Reduces costs by reducing amount of laboratory trial and error needed to optimize curing processes and to predict properties of cured parts.
Abstract The treatment of Hanford tank waste is one of the most challenging environmental cleanup activities to date. To expedite the processing of liquid waste stored in underground tanks in Washington State it is necessary to remove the significant dose contributor, 137 Cs. Crystalline silicotitanate ion exchanger is currently used to remove 137 Cs from the aqueous phase of Hanford tank wastes in preparation for vitrification at the Waste Treatment and Immobilization Plant (WTP). Improving the understanding of potassium impacts on ion exchange behavior of Cs will help in the operation of a critical component of one of the most complex treatment processes in the world today. Optimization of this process can result in significant cost savings and less waste production. Toward this effort, a series of batch contact tests varied in potassium concentration were conducted to look at the impact of potassium concentration on Cs distribution. Experimental distribution ratios ( K d ) were compared to the distribution ratios predicted using the ZAM model. A significant underprediction of Cs capacity in the presence of potassium was seen with the existing model. A revision of the equilibrium constants was determined and provided a statistically better fit for determining the Cs K d values in tank waste matrices.
Solidified CO2 pellets are an effective blast media for the cleaning of a variety of materials. CO2 is obtained from the waste gas streams generated from other manufacturing processes and therefore does not contribute to the greenhouse effect, depletion of the ozone layer, or the environmental burden of hazardous waste disposal. The system is capable of removing as much as 90 percent of the contamination from a surface in one pass or to a high cleanliness level after multiple passes. Although the system is packaged and designed for manual hand held cleaning processes, the nozzle can easily be attached to the end effector of a robot for automated cleaning of predefined and known geometries. Specific tailoring of cleaning parameters are required to optimize the process for each individual geometry. Using optimum cleaning parameters the CO2 systems were shown to be capable of cleaning to molecular levels below 0.7 mg/sq ft. The systems were effective for removing a variety of contaminants such as lubricating oils, cutting oils, grease, alcohol residue, biological films, and silicone. The system was effective on steel, aluminum, and carbon phenolic substrates.
Signal- and image-processing methods are commonly needed to extract information from the waves, improve resolution of, and highlight defects in an image. Since some similarity exists for all waveform-based nondestructive evaluation (NDE) methods, it would seem that a common software platform containing multiple signal- and image-processing techniques to process the waveforms and images makes sense where multiple techniques, scientists, engineers, and organizations are involved. NDE Wave & Image Processor Version 2.0 software provides a single, integrated signal- and image-processing and analysis environment for total NDE data processing and analysis. It brings some of the most useful algorithms developed for NDE over the past 20 years into a commercial-grade product. The software can import signal/spectroscopic data, image data, and image series data. This software offers the user hundreds of basic and advanced signal- and image-processing capabilities including esoteric 1D and 2D wavelet-based de-noising, de-trending, and filtering. Batch processing is included for signal- and image-processing capability so that an optimized sequence of processing operations can be applied to entire folders of signals, spectra, and images. Additionally, an extensive interactive model-based curve-fitting facility has been included to allow fitting of spectroscopy data such as from Raman spectroscopy. An extensive joint-time frequency module is included for analysis of non-stationary or transient data such as that from acoustic emission, vibration, or earthquake data.
The aircraft engine design process seeks to optimize the overall system-level performance, weight, and cost for a given concept. Steady-state simulations and data are used to identify trade-offs that should be balanced to optimize the system in a process known as systems analysis. These systems analysis simulations and data may not adequately capture the true performance trade-offs that exist during transient operation. Dynamic systems analysis provides the capability for assessing the dynamic tradeoffs at an earlier stage of the engine design process. The dynamic systems analysis concept, developed tools, and potential benefit are presented in this paper. To provide this capability, the Tool for Turbine Engine Closed-loop Transient Analysis (TTECTrA) was developed to provide the user with an estimate of the closed-loop performance (response time) and operability (high pressure compressor surge margin) for a given engine design and set of control design requirements. TTECTrA along with engine deterioration information, can be used to develop a more generic relationship between performance and operability that can impact the engine design constraints and potentially lead to a more efficient engine.