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All sourcesNASA NTRSDOE OSTI
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Guiding Integration of Formal Verification in Assurance Cases

Assurance cases are being increasingly acknowledged as away to build trust in complex systems with autonomous capabilities. An assurance case is a comprehensive, defensible, and valid justification that a system will function as intended for a specific mission and operating environment. Formal verification is often reserved for the most critical components of such systems. However, formal verification tools are often complex, and their usage is subject to many constraints and contextual dependencies. This can raise challenges both for performing the verification as well as reflecting the verification results appropriately in the assurance case, especially for non-expert users of the verification tool. To address these challenges, we present a tool-supported methodology for integrating formal verification results in an assurance case by capturing key verification method information in a rigorously constructed assurance case. In particular, we capture the tool specification in terms of its inputs, outputs, and assurance constraints as assumptions over inputs and guarantees provided over its outputs. The tool specification is parametrized over the inputs and outputs to both guide the intended application of the tool, as well as to check that the tool has been applied following the stated assumptions and that the guarantees hold. We define a generic tool assurance argument pattern that enables integration of the verification results in the assurance case by allowing custom refinement and automated instantiation for each tool use. We demonstrate our methodology on two formal verification tools and their applications to the verification of neural network properties for the aircraft domain.

Assurance Cases↗
DOE OSTI2020

A machine learning approach for increased throughput of density functional theory substitutional alloy studies

In this study, a machine learning-based technique is developed to reduce the computational cost required to explore large design spaces of substitutional alloys. The first advancement is based on a neural network (NN) approach to predict the initial position of minority and majority ions prior to DFT relaxation. The second advancement is to allow the NN to predict the total energy for every possibility minority ion position and select the most stable configuration in the absence of relaxing each trial minority configuration. A bismuth oxide materials system, (Bi x La y Yb z ) 2 MoO 6 , was used as the model system to demonstrate the developed methods and quantify the resulting computational speedup. Compared to a brute force method that requires the calculation of every permutation of minority configuration and subsequent DFT relaxation, a 1.3× speedup was realized if the NN predicted the initial configuration of ions prior to relaxation. Implementation of the second advancement allowed the NN to predict the total energy for all possible trial configurations and downselect the most stable configurations prior to relaxation, resulting in a speedup of approximately 37×. Validation was done by comparing position and energy between the NN and DFT predictions. A maximum position vector mean squared error (MSE) of 1.6 × 10 -2 and a maximum energy MSE of 2.3 × 10 -7 was predicted for the worst case configuration. This method demonstrates a significant computational speedup, which has the potential for even greater computational savings for larger compositional design spaces.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A Measure-Theoretic Algorithm for Estimating Bottom Friction in a Coastal Inlet: Case Study of Bay St. Louis during Hurricane Gustav (2008)

The majority of structural damage and loss of life during a hurricane is due to storm surge, thus it is important for communities in hurricane-prone regions to understand their risk due to surge. Storm surge in particular is largely influenced by coastal features such as topography/bathymetry and bottom roughness. Bottom roughness determines how much resistance there is to the flow. Manning’s formula can be used to model the bottom stress with the Manning’s n coefficient, a spatially dependent field. Given a storm surge model and a set of model outputs, an inverse problem may be solved to determine probable Manning’s n fields to use for predictive simulations. The inverse problem is formulated and solved in a measure-theoretic framework using the state-of-the-art Advanced Circulation (ADCIRC) storm surge model. The use of measure theory requires minimal assumptions and involves the direct inversion of the physics-based map from model inputs to output data determined by the ADCIRC model. Thus, key geometric relationships in this map are preserved and exploited. By using a recently available subdomain implementation of ADCIRC that significantly reduces the computational cost of forward model solves, the authors demonstrate the method on a case study using data obtained from an ADCIRC hindcast study of Hurricane Gustav (2008) to quantify uncertainties in Manning’s n within Bay St. Louis. However, the methodology is general and could be applied to any inverse problem that involves a map from model input to output quantities of interest.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2007

Radiative Heating Methodology for the Huygens Probe

The radiative heating environment for the Huygens probe near peak heating conditions for Titan entry is investigated in this paper. The task of calculating the radiation-coupled flowfield, accounting for non-Boltzmann and non-optically thin radiation, is simplified to a rapid yet accurate calculation. This is achieved by using the viscous-shock layer (VSL) technique for the stagnation-line flowfield calculation and a modified smeared rotational band (SRB) model for the radiation calculation. These two methods provide a computationally efficient alternative to a Navier-Stokes flowfield and line-by-line radiation calculation. The results of the VSL technique are shown to provide an excellent comparison with the Navier-Stokes results of previous studies. It is shown that a conventional SRB approach is inadequate for the partially optically-thick conditions present in the Huygens shock-layer around the peak heating trajectory points. A simple modification is proposed to the SRB model that improves its accuracy in these partially optically-thick conditions. This modified approach, labeled herein as SRBC, is compared throughout this study with a detailed line-by-line (LBL) calculation and is shown to compare within 5% in all cases. The SRBC method requires many orders-of-magnitude less computational time than the LBL method, which makes it ideal for coupling to the flowfield. The application of a collisional-radiative (CR) model for determining the population of the CN electronic states, which govern the radiation for Huygens entry, is discussed and applied. The non-local absorption term in the CR model is formulated in terms of an escape factor, which is then curve-fit with temperature. Although the curve-fit is an approximation, it is shown to compare well with the exact escape factor calculation, which requires a computationally intensive iteration procedure.

Johnston, Christopher O.↗
DOE OSTI2018

Transversely Excited Atmospheric CO{sub 2} Laser-Induced Plasma Spectroscopy for the Detection of Heavy Metals in Soil

A rapid detection of heavy metals in soil was presented by the metal-assisted gas plasma method using specific characteristics of a pulsed, transversely excited atmospheric (TEA) CO{sub 2} laser. The soil particles were placed in a hole made of acrylic plate. The sample was covered by a to prevent the soil particles from being blown off. The mesh also functioned to initiate a luminous plasma. When a TEA CO{sub 2} laser (1500 mJ, 200 ns) was focused on the soil sample, passing through the metal mesh, some of the laser energy was used to generate the gas plasma on the mesh surface, and the remaining laser energy was employed to ablate the soil particles. The fine, ablated soil particles moved into the gas plasma region to be dissociated and excited. Using this technique, analysis can be made with reduced sample pretreatment, and therefore a rapid analysis can be performed efficiently. The results proved that the signal to noise ratio (S/N) of the emission spectral lines is much better for the case of the present method (mesh method) compared to the case of standard laser-induced breakdown spectroscopy using the pellet method. Rapid detection of heavy metal elements in soil has been successfully carried out. The detection limits of Cu and Hg in soil were estimated to be 3 and 10 mg/kg, respectively. The present method has good potential for rapid and sensitive detection of heavy metals in soil samples.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Upwind relaxation methods for the Navier-Stokes equations using inner iterations

A supersonic and subsonic test problem is solved using an upwind line relaxation algorithm for the Navier-Stokes equations which employs inner iterations. In the supersonic test case, the inner iteration method was found to require only about 65 percent of the CPU time which was required by the most efficient line relaxation method without inner iterations. In the subsonic test case, poor matrix conditioning resulted in less efficiency than line relaxation methods employing a more conventional CPU-saving strategy.

Taylor, Arthur C., III↗
DOE OSTI2014

Analysis of simulation methodology for calculation of the heat of transport for vacancy thermodiffusion

Computation of the heat of transport Q{sub a}{sup *} in monatomic crystalline solids is investigated using the methodology first developed by Gillan [J. Phys. C: Solid State Phys. 11, 4469 (1978)] and further developed by Grout and coworkers [Philos. Mag. Lett. 74, 217 (1996)], referred to as the Grout-Gillan method. In the case of pair potentials, the hopping of a vacancy results in a heat wave that persists for up to 10 ps, consistent with previous studies. This leads to generally positive values for Q{sub a}{sup *} which can be quite large and are strongly dependent on the specific details of the pair potential. By contrast, when the interactions are described using the embedded atom model, there is no evidence of a heat wave, and Q{sub a}{sup *} is found to be negative. This demonstrates that the dynamics of vacancy hopping depends strongly on the details of the empirical potential. However, the results obtained here are in strong disagreement with experiment. Arguments are presented which demonstrate that there is a fundamental error made in the Grout-Gillan method due to the fact that the ensemble of states only includes successful atom hops and hence does not represent an equilibrium ensemble. This places the interpretation of the quantity computed in the Grout-Gillan method as the heat of transport in doubt. It is demonstrated that trajectories which do not yield hopping events are nevertheless relevant to computation of the heat of transport Q{sub a}{sup *}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Sources of Propane Consumed in California

Project Scope: The objective of this study is to specify the sources of propane consumed in California. It answers the questions, where does the propane used in California come from and how was it produced? The results of this study provide comprehensive, transparent, and verifiable estimates, based on the 2018 market. The information provided in this report is suitable for use to assess the life cycle carbon intensity of propane used as a transportation fuel in California. As the 2009 Low Carbon Fuel Standard (LCFS) aims to reduce California’s greenhouse gas (GHG) emissions and other smog-forming and toxic air pollutants, the appropriate designation of carbon intensity for propane as a transportation fuel is important for evaluating propane’s potential to contribute to GHG goals and understandings in the context of various actions. This study focuses on estimating the shares of total propane consumed in the state of California produced from petroleum refineries, natural gas plants, and bituminous sands sources inside California and elsewhere. Results: An estimated 590 million gallons of propane were consumed in California in 2018, of which, 59.5% originated from refinery production and 40.5% originated from natural gas plants. The majority of this was sourced from refinery production in California, 334 million gallons. Most of the propane imported to California for consumption was sourced from natural gas plants, 113 million gallons, with over half of the imported volume sourced from Canada. The volume sourced from bituminous sand upgrader and fractionator operations was negligible. Details from this analysis are presented in the table below which provides an overview of the propane flows estimated in this study by region and production method. The shares and volumes presented here represent a snapshot for 2018. A significant increase in propane demand, such as could be caused by increased use of propane as a transportation fuel in the state, would affect California’s propane production, imports, and exports. The method and data sources used for the estimates provided in this report also provide the framework which could be used for future updates. Key Method Considerations: The values presented here are based on a two-step approach where the first step was to determine the flows of propane into and out of California from different regions and the second step was to estimate the propane production methods in each region. A volume balance approach is used as the primary method for tracking the volume of propane in and out of California as propane production and import volumes are available by Petroleum Administration of Defense District (PADD) from EIA and neither inter-PADD propane transfers nor state-specific non-prime supplier consumption are available from a public data source. The volume balance performed for this study covered PADD 5 (the West Coast), which includes Arizona, California, Nevada, Oregon, and Washington. The volume balance used all available public datasets to determine propane production, imports, exports, and consumption. Volumes unaccounted for by these datasets were estimated using the resulting volume balance by assuming market equilibrium. Consumption within each state in PADD 5 was estimated based on known import, export, and production volumes and this amount was used to develop the volume balance. EIA only tracks consumption at the state level by prime supplier sales. The volume balance approach provides the basis to correct for additional propane consumed in-states where propane is transferred to California. To determine the California propane sources and trade in 2018. volume of propane consumed in California, the volume balance approach is again used where it was estimated all imported volumes not specifically flagged for re-export were consumed, and the remaining consumption was produced in-state. The California Energy Commission (CEC) provided the total volume of propane imported and exported from California in 2018; this volume data set along with commodity tracking from the Canada Energy Regulator (CER) and the International Trade Commission (ITC) which tracks port of entry and final destination was used to determine where propane originated from and where it was ultimately consumed. For example, the CER tracks propane leaving Canada and entering each state within the U.S. Imported propane from Canada to California – marked for California – is assumed to be consumed in California. When no further data were available, import volumes were assumed to be consumed in California without pass-through (i.e., no propane imported to California was directly sold and exported). In most cases, the production method for each propane source region was applied to the volume of propane transferred to California. In other words, the shares of propane sourced from natural gas and refineries for each production region was assigned to California imports based on their contribution to the total volume flows into California to determine the production method for propane consumed in-state. For volumes imported into California from PADD 4, Washington State, Canada, and the rest of the world (Argentina, Chile, Norway, Peru, South Korea, and Trinidad and Tobago), the volumes sourced from petroleum refineries and natural gas plants reflect the either production ratio for the region or, in cases where the sources specific to the amounts exported to California could be determined, the sources specific to the volumes transferred to California.

03 NATURAL GAS↗
DOE OSTI2019

Modeling and simulation functional needs for molten salt reactor licensing

The modeling and simulation functional needs to license and design molten salt reactor concepts were assessed and an evaluation methodology was developed using a licensing-focused approach considering the modeling and simulation components that contribute to a molten salt reactor safety analysis report. These functional needs were prioritized by identifying the relationships between functional needs and using a quantitative weighting method to identify the most critical components to build a licensing case. This novel weighting method provided a list of functional needs prioritized relative to key advanced reactor licensing outcomes. In addition, functional need inputs were ranked to reveal those that feed the most modeling and simulation components. The findings from this prioritization effort were used to inform the modeling and simulation goals of the US Department of Energy Office of Nuclear Energy (DOE-NE) Molten Salt Reactor campaign.Modeling and simulation needs were grouped into three main categories: (1) source term definition, material accountancy, and radiological consequences, (2) safety analysis, and (3) steady-state neutronics and thermal hydraulics. Here, five near-term goals were identified among these focus areas that add value: (1) deploying a systems and safeguards analysis computational tool, (2) defining source terms for molten salt reactor analysis and interfacing with the US Nuclear Regulatory Commission on accident progression analysis, (3) developing point designs for liquid-fueled thermal-spectrum and fast-spectrum molten salt reactors, (4) building safety analysis specifications and reference solutions for Molten Salt Reactor Experiment transients, and (5) interfacing with the thermophysical and thermodynamic salt chemistry databases.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Simulating nonlinear cosmological structure formation with massive neutrinos

We present a new method for simulating cosmologies that contain massive particles with thermal free streaming motion, such as massive neutrinos or warm/hot dark matter. This method combines particle and fluid descriptions of the thermal species to eliminate the shot noise known to plague conventional N-body simulations. We describe this method in detail, along with results for a number of test cases to validate our method, and check its range of applicability. Using this method, we demonstrate that massive neutrinos can produce a significant scale-dependence in the large-scale biasing of deep voids in the matter field. We show that this scale-dependence may be quantitatively understood using an extremely simple spherical expansion model which reproduces the behavior of the void bias for different neutrino parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1999

A New Stochastic Equivalent Linearization Implementation for Prediction of Geometrically Nonlinear Vibrations

In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

Muravyov, Alexander A.↗
DOE OSTI2013

Fission matrix-based Monte Carlo criticality analysis of fuel storage pools

Standard Monte Carlo transport procedures experience difficulties in solving criticality problems in fuel storage pools. Because of the strong neutron absorption between fuel assemblies, source convergence can be very slow, leading to incorrect estimates of the eigenvalue and the eigenfunction. This study examines an alternative fission matrix-based Monte Carlo transport method that takes advantage of the geometry of a storage pool to overcome this difficulty. The method uses Monte Carlo transport to build (essentially) a fission matrix, which is then used to calculate the criticality and the critical flux. This method was tested using a test code on a simple problem containing 8 assemblies in a square pool. The standard Monte Carlo method gave the expected eigenfunction in 5 cases out of 10, while the fission matrix method gave the expected eigenfunction in all 10 cases. In addition, the fission matrix method provides an estimate of the error in the eigenvalue and the eigenfunction, and it allows the user to control this error by running an adequate number of cycles. Because of these advantages, the fission matrix method yields a higher confidence in the results than standard Monte Carlo. We also discuss potential improvements of the method, including the potential for variance reduction techniques. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

SU-F-T-620: Development of a Convolution/Superposition Dose Engine for CyberKnife System

Purpose: Current CyberKnife treatment planning system (TPS) provided two dose calculation algorithms: Ray-tracing and Monte Carlo. Ray-tracing algorithm is fast, but less accurate, and also can’t handle irregular fields since a multi-leaf collimator system was recently introduced to CyberKnife M6 system. Monte Carlo method has well-known accuracy, but the current version still takes a long time to finish dose calculations. The purpose of this paper is to develop a GPU-based fast C/S dose engine for CyberKnife system to achieve both accuracy and efficiency. Methods: The TERMA distribution from a poly-energetic source was calculated based on beam’s eye view coordinate system, which is GPU friendly and has linear complexity. The dose distribution was then computed by inversely collecting the energy depositions from all TERMA points along 192 collapsed-cone directions. EGSnrc user code was used to pre-calculate energy deposition kernels (EDKs) for a series of mono-energy photons The energy spectrum was reconstructed based on measured tissue maximum ratio (TMR) curve, the TERMA averaged cumulative kernels was then calculated. Beam hardening parameters and intensity profiles were optimized based on measurement data from CyberKnife system. Results: The difference between measured and calculated TMR are less than 1% for all collimators except in the build-up regions. The calculated profiles also showed good agreements with the measured doses within 1% except in the penumbra regions. The developed C/S dose engine was also used to evaluate four clinical CyberKnife treatment plans, the results showed a better dose calculation accuracy than Ray-tracing algorithm compared with Monte Carlo method for heterogeneous cases. For the dose calculation time, it takes about several seconds for one beam depends on collimator size and dose calculation grids. Conclusion: A GPU-based C/S dose engine has been developed for CyberKnife system, which was proven to be efficient and accurate for clinical purpose, and can be easily implemented in TPS.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2011

Role of fourth-order phase-space moments in collective modes of trapped Fermi gases

We study the transition from hydrodynamic to collisionless behavior in collective modes of ultracold trapped Fermi gases. To that end, we solve the Boltzmann equation for the trapped Fermi gas via the moments method. We showed previously that it is necessary to go beyond second-order moments if one wants to reproduce the results of a numerical solution of the Boltzmann equation. Here, we will give the detailed description of the method including fourth-order moments. We apply this method to the case of realistic parameters, and compare the results for the radial quadrupole and scissors modes at unitarity to experimental data obtained by the Innsbruck group. It turns out that the inclusion of fourth-order moments clearly improves the agreement with the experimental data. In particular, the fourth-order moments reduce the effect of collisions and therefore partially compensate the effect of the enhanced in-medium cross section at low temperatures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1998

Case-Based Capture and Reuse of Aerospace Design Rationale

The goal of this project is to apply artificial intelligence techniques to facilitate capture and reuse of aerospace design rationale. The project applies case-based reasoning (CBR) and concept mapping (CMAP) tools to the task of capturing, organizing, and interactively accessing experiences or "cases" encapsulating the methods and rationale underlying expert aerospace design. As stipulated in the award, Indiana University and Ames personnel are collaborating on performance of research and determining the direction of research, to assure that the project focuses on high-value tasks. In the first five months of the project, we have made two visits to Ames Research Center to consult with our NASA collaborators, to learn about the advanced aerospace design tools being developed there, and to identify specific needs for intelligent design support. These meetings identified a number of task areas for applying CBR and concept mapping technology. We jointly selected a first task area to focus on: Acquiring the convergence criteria that experts use to guide the selection of useful data from a set of numerical simulations of high-lift systems. During the first funding period, we developed two software systems. First, we have adapted a CBR system developed at Indiana University into a prototype case-based reasoning shell to capture and retrieve information about design experiences, with the sample task of capturing and reusing experts' intuitive criteria for determining convergence (work conducted at Indiana University). Second, we have also adapted and refined existing concept mapping tools that will be used to clarify and capture the rationale underlying those experiences, to facilitate understanding of the expert's reasoning and guide future reuse of captured information (work conducted at the University of West Florida). The tools we have developed are designed to be the basis for a general framework for facilitating tasks within systems developed by the Advanced Design Technologies Testbed (ADTT) project at ARC. The tenets of our framework are (1) that the systems developed should leverage a designer's knowledge, rather than attempting to replace it; (2) that learning and user feedback must play a central role, so that the system can adapt to how it is used, and (3) that the learning and feedback processes must be as natural and as unobtrusive as possible. In the second funding period we will extend our current work, applying the tools to capturing higher-level design rationale.

Leake, David B.↗
DOE OSTI2016

TU-H-BRC-03: Evaluation of Very High-Energy Electron (VHEE) Beams in Comparison to VMAT and PBS Treatment Plans

Purpose: The aim of this study was to evaluate the performance of very high-energy electron (VHEE) beams in comparison to clinically delivered treatment plans generated with volumetric modulated arc therapy (VMAT) and proton pencil beam scanning (PBS) technology. Methods: Three clinical cases were selected (prostate, lung, and pediatric CNS). The VHEE plans were calculated in the Monte Carlo EGSnrc code and pencil beam doses were calculated using the DOSxyznrc MC code for 100 and 200 MeV beams. Treatment plans with VHEE, VMAT, and PBS were optimized in a research version of RayStation using an in house build script in order to minimize operator bias between the different techniques. Results: For the prostate cancer case, the PBS plan showed lower mean organ at risk (OAR) doses compared to the other modalities. An exception was the femoral heads, due to the lateral beam arrangements. The VMAT plan showed lower mean doses to the rectum and the bladder compared to the 100 MeV VHEE plan. The lung cancer case showed minor differences between the three modalities. However, the PBS plan showed a lower contralateral lung dose. The pediatric CNS case showed a better conformity and lower spinal cord dose for the 100 MeV VHEE plan. For all cases, the 200 MeV VHEE plans were found to be similar to or better than the 100 MeV VHEE plans. Conclusion: The present study showed that VHEE plans are similar or superior to VMAT plans with reduced mean OAR dose and increased target conformity for a variety of clinical cases. With increased VHEE energy, better conformity and even higher reductions in mean OAR doses can be achieved. Funding: DoD, Award#:W81XWH-13-1-0165, Weston Havens Foundation, Bio-X (Stanford University), the Office of the Dean of the Medical School, the Office of the Provost (Stanford University), and the Swedish Childhood Cancer Foundation. BL and PM are founders of TibaRay,Inc. BL and PM have received research grants from Varian and RaySearch Laboratory.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Incorporating single-side sparing in models for predicting parotid dose sparing in head and neck IMRT

Purpose: Sparing of single-side parotid gland is a common practice in head-and-neck (HN) intensity modulated radiation therapy (IMRT) planning. It is a special case of dose sparing tradeoff between different organs-at-risk. The authors describe an improved mathematical model for predicting achievable dose sparing in parotid glands in HN IMRT planning that incorporates single-side sparing considerations based on patient anatomy and learning from prior plan data. Methods: Among 68 HN cases analyzed retrospectively, 35 cases had physician prescribed single-side parotid sparing preferences. The single-side sparing model was trained with cases which had single-side sparing preferences, while the standard model was trained with the remainder of cases. A receiver operating characteristics (ROC) analysis was performed to determine the best criterion that separates the two case groups using the physician's single-side sparing prescription as ground truth. The final predictive model (combined model) takes into account the single-side sparing by switching between the standard and single-side sparing models according to the single-side sparing criterion. The models were tested with 20 additional cases. The significance of the improvement of prediction accuracy by the combined model over the standard model was evaluated using the Wilcoxon rank-sum test. Results: Using the ROC analysis, the best single-side sparing criterion is (1) the predicted median dose of one parotid is higher than 24 Gy; and (2) that of the other is higher than 7 Gy. This criterion gives a true positive rate of 0.82 and a false positive rate of 0.19, respectively. For the bilateral sparing cases, the combined and the standard models performed equally well, with the median of the prediction errors for parotid median dose being 0.34 Gy by both models (p = 0.81). For the single-side sparing cases, the standard model overestimates the median dose by 7.8 Gy on average, while the predictions by the combined model differ from actual values by only 2.2 Gy (p = 0.005). Similarly, the sum of residues between the modeled and the actual plan DVHs is the same for the bilateral sparing cases by both models (p = 0.67), while the standard model predicts significantly higher DVHs than the combined model for the single-side sparing cases (p = 0.01). Conclusions: The combined model for predicting parotid sparing that takes into account single-side sparing improves the prediction accuracy over the previous model.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS1993

Nonlinear rescaling of control values simplifies fuzzy control

Traditional control theory is well-developed mainly for linear control situations. In non-linear cases there is no general method of generating a good control, so we have to rely on the ability of the experts (operators) to control them. If we want to automate their control, we must acquire their knowledge and translate it into a precise control strategy. The experts' knowledge is usually represented in non-numeric terms, namely, in terms of uncertain statements of the type 'if the obstacle is straight ahead, the distance to it is small, and the velocity of the car is medium, press the brakes hard'. Fuzzy control is a methodology that translates such statements into precise formulas for control. The necessary first step of this strategy consists of assigning membership functions to all the terms that the expert uses in his rules (in our sample phrase these words are 'small', 'medium', and 'hard'). The appropriate choice of a membership function can drastically improve the quality of a fuzzy control. In the simplest cases, we can take the functions whose domains have equally spaced endpoints. Because of that, many software packages for fuzzy control are based on this choice of membership functions. This choice is not very efficient in more complicated cases. Therefore, methods have been developed that use neural networks or generic algorithms to 'tune' membership functions. But this tuning takes lots of time (for example, several thousands iterations are typical for neural networks). In some cases there are evident physical reasons why equally space domains do not work: e.g., if the control variable u is always positive (i.e., if we control temperature in a reactor), then negative values (that are generated by equal spacing) simply make no sense. In this case it sounds reasonable to choose another scale u' = f(u) to represent u, so that equal spacing will work fine for u'. In the present paper we formulate the problem of finding the best rescaling function, solve this problem, and show (on a real-life example) that after an optimal rescaling, the un-tuned fuzzy control can be as good as the best state-of-art traditional non-linear controls.

Vanlangingham, H.↗