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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Evaluation of conformal and body-axis attitude information for spatial awareness

The traditional head-up display (HUD) used in most modern fighter aircraft presents attitude information that is both conformal to the outside world and aligned with the body-axis of the aircraft. The introduction of helmet-mounted display (HMD) technology into simulated and actual flight environments has introduced an interesting issue regarding the presentation of attitude information. This information can be presented conformally or relative to the aircraft's body-axis, but not both (except in the special case where the pilot's line of sight is directly matched with the aircraft's body-axis). The question addressed with this study was whether attitude information displayed in an HMD should be presented with respect to the real world (conformally) or to the aircraft's body-axis. To answer this, both conformal and body-axis attitude symbology were compared under simulated air combat situations. The results of this study indicated that the body-axis concept was a more effective HMD display. A detailed description of the flight task and results of this study will be presented.

Jones, Denise R.↗
NASA NTRS1999

A Framework for Dynamic Constraint Reasoning Using Procedural Constraints

Many complex real-world decision and control problems contain an underlying constraint reasoning problem. This is particularly evident in a recently developed approach to planning, where almost all planning decisions are represented by constrained variables. This translates a significant part of the planning problem into a constraint network whose consistency determines the validity of the plan candidate. Since higher-level choices about control actions can add or remove variables and constraints, the underlying constraint network is invariably highly dynamic. Arbitrary domain-dependent constraints may be added to the constraint network and the constraint reasoning mechanism must be able to handle such constraints effectively. Additionally, real problems often require handling constraints over continuous variables. These requirements present a number of significant challenges for a constraint reasoning mechanism. In this paper, we introduce a general framework for handling dynamic constraint networks with real-valued variables, by using procedures to represent and effectively reason about general constraints. The framework is based on a sound theoretical foundation, and can be proven to be sound and complete under well-defined conditions. Furthermore, the framework provides hybrid reasoning capabilities, as alternative solution methods like mathematical programming can be incorporated into the framework, in the form of procedures.

Jonsson, Ari K.↗
NASA NTRS2011

The Proposed Use of Unmanned Aerial System Surrogate Research Aircraft for National Airspace System Integration Research

Research is needed to determine what procedures, aircraft sensors and other systems will be required to allow Unmanned Aerial Systems (UAS) to safely operate with manned aircraft in the National Airspace System (NAS). This paper explores the use of Unmanned Aerial System (UAS) Surrogate research aircraft to serve as platforms for UAS systems research, development, and flight testing. These aircraft would be manned with safety pilots and researchers that would allow for flight operations almost anywhere in the NAS without the need for a Federal Aviation Administration (FAA) Certificate of Authorization (COA). With pilot override capability, these UAS Surrogate aircraft would be controlled from ground stations like true UAS s. It would be possible to file and fly these UAS Surrogate aircraft in the NAS with normal traffic and they would be better platforms for real world UAS research and development over existing vehicles flying in restricted ranges or other sterilized airspace. These UAS surrogate aircraft could be outfitted with research systems as required such as computers, state sensors, video recording, data acquisition, data link, telemetry, instrumentation, and Automatic Dependent Surveillance-Broadcast (ADS-B). These surrogate aircraft could also be linked to onboard or ground based simulation facilities to further extend UAS research capabilities. Potential areas for UAS Surrogate research include the development, flight test and evaluation of sensors to aide in the process of air traffic "see-and-avoid". These and other sensors could be evaluated in real-time and compared with onboard human evaluation pilots. This paper examines the feasibility of using UAS Surrogate research aircraft as test platforms for a variety of UAS related research.

Howell, Charles T., III↗
NASA NTRS2021

Scheduling the NASA Deep Space Network with Deep Reinforcement Learning

With three complexes spread evenly across the Earth, NASA’s Deep Space Network (DSN) is the primary means of communications as well as a significant scientific instrument for dozens of active missions around the world. A rapidly rising number of spacecraft and increasingly complex scientific instruments with higher bandwidth requirements have resulted in demand that exceeds the network’s capacity across its 12 antennae. The existing DSN scheduling process operates on a rolling weekly basis and is time-consuming; for a given week, generation of the final baseline schedule of spacecraft tracking passes takes roughly 5 months from the initial requirements submission deadline, with several weeks of peer-to-peer negotiations in between. This paper proposes a deep reinforcement learning (RL) approach to generate candidate DSN schedules from mission requests and spacecraft ephemeris data with demonstrated capability to address real-world operational constraints. A deep RL agent is developed that takes mission requests for a given week as input, and interacts with a DSN scheduling environment to allocate tracks such that its reward signal is maximized. A comparison is made between an agent trained using Proximal Policy Optimization and its random, untrained counterpart. The results represent a proof-of-concept that, given a well-shaped reward signal, a deep RL agent can learn the complex heuristics used by experts to schedule the DSN. A trained agent can potentially be used to generate candidate schedules to bootstrap the scheduling process and thus reduce the turnaround cycle for DSN scheduling.

Wilson, Brian↗
NASA NTRS1994

Abstraction Planning in Real Time

When a planning agent works in a complex, real-world domain, it is unable to plan for and store all possible contingencies and problem situations ahead of time. The agent needs to be able to fall back on an ability to construct plans at run time under time constraints. This thesis presents a method for planning at run time that incrementally builds up plans at multiple levels of abstraction. The plans are continually updated by information from the world, allowing the planner to adjust its plan to a changing world during the planning process. All the information is represented over intervals of time, allowing the planner to reason about durations, deadlines, and delays within its plan. In addition to the method, the thesis presents a formal model of the planning process and uses the model to investigate planning strategies. The method has been implemented, and experiments have been run to validate the overall approach and the theoretical model.

ARTIFICIAL INTELLIGENCE↗
NASA NTRS1992

A neuro-fuzzy architecture for real-time applications

Neural networks and fuzzy expert systems perform the same task of functional mapping using entirely different approaches. Each approach has certain unique features. The ability to learn specific input-output mappings from large input/output data possibly corrupted by noise and the ability to adapt or continue learning are some important features of neural networks. Fuzzy expert systems are known for their ability to deal with fuzzy information and incomplete/imprecise data in a structured, logical way. Since both of these techniques implement the same task (that of functional mapping--we regard 'inferencing' as one specific category under this class), a fusion of the two concepts that retains their unique features while overcoming their individual drawbacks will have excellent applications in the real world. In this paper, we arrive at a new architecture by fusing the two concepts. The architecture has the trainability/adaptibility (based on input/output observations) property of the neural networks and the architectural features that are unique to fuzzy expert systems. It also does not require specific information such as fuzzy rules, defuzzification procedure used, etc., though any such information can be integrated into the architecture. We show that this architecture can provide better performance than is possible from a single two or three layer feedforward neural network. Further, we show that this new architecture can be used as an efficient vehicle for hardware implementation of complex fuzzy expert systems for real-time applications. A numerical example is provided to show the potential of this approach.

Ramamoorthy, P. A.↗
NASA NTRS2001

X-traktor: A Rookie Robot, Simple, Yet Complex, Impeccably Designed, a Very Innovative Multidisciplinary Engineering Masterpiece

FIRST is the acronym of For Inspiration and Recognition of Science and Technology. FIRST is a 501.C.3 non-profit organization whose mission is to generate an interest in science and engineering among today's young adults and youth. This mission is accomplished through a robot competition held annually in the spring of each year. NASAs Marshall Space Flight Center, Education Programs Department, awarded a grant to Lee High School, the sole engineering magnet school in Huntsville, Alabama. MSFC awarded the grant in hopes of fulfilling its goal of giving back invaluable resources to its community and engineers, as well as educating tomorrow's work force in the high-tech area of science and technology. Marshall engineers, Lee High School students and teachers, and a host of other volunteers and parents officially initiated this robot design process and competitive strategic game plan. The FIRST Robotics Competition is a national engineering contest, which immerses high school students in the exciting world of science and engineering. Teaming with engineers from government agencies, businesses, and universities enables the students to learn about the engineering profession. The students and engineers have six weeks to work together to brainstorm, design, procure, construct, and test their robot. The team then competes in a spirited, 'no-holds barred' tournament, complete with referees, other FIRST-designed robots, cheerleaders, and time clocks. The partnerships developed between schools, government agencies, businesses, and universities provide an exchange of resources and talent that build cooperation and expose students to new and rewarding career options. The result is a fun, exciting, and stimulating environment in which all participants discover the important connections between classroom experiences and real-world applications. This paper will highlight the story, engineering development, and evolutionary design of Xtraktor, the rookie robot, a manufacturing marvel and engineering achievement.

Henderson, A. J., Jr.↗
NASA NTRS1988

Range data description based on multiple characteristics

An algorithm for describing range images based on Mean curvature (H) and Gaussian curvature (K) is presented. Range images are unique in that they directly approximate the physical surfaces of a real world 3-D scene. The curvature parameters are derived from the fundamental theorems of differential geometry and provides visible invariant pixel labels that can be used to characterize the scene. The sign of H and K can be used to classify each pixel into one of eight possible surface types. Due to the sensitivity of these parameters to noise the resulting HK-sing map does not directly identify surfaces in the range images and must be further processed. A region growing algorithm based on modeling the scene points with a Markov Random Field (MRF) of variable neighborhood size and edge models is suggested. This approach allows the integration of information from multiple characteristics in an efficient way. The performance of the proposed algorithm on a number of synthetic and real range images is discussed.

Al-Hujazi, Ezzet↗
NASA NTRS2016

NASA WorldWind: Open Source Visualization Technology for Earth Observation

NASA WorldWind: Open Source Visualization Technology for Earth Observation WorldWind, open source virtual globe technology for Java, iOS, Android and Web, is provided by NASA and is architected as API-centric modular componentry. This enable it to be continually optimized and feature-enriched in ways that allow applications based on this SDK (Software Development Kit) to benefit Earth Observation, especially Open Science, with minimal or no adjustment for the decade ahead. The next-generation National Airspace System (NAS) aviation management system for the U.S. Federal Aviation Administration, FAA, uses WorldWind, as do applications currently being developed by the European Space Agency, along with several other US and European government agencies and industry partners. This presentation will demonstrate several NASA open source use cases for WorldWind technology that include advances being made to optimize access to NetCDF and HDF data via WebWorldWind.NASA WorldWind: Multidimensional Geospatial Web Platform The ability to see spatial data in its native context is essential for that data to be appreciated whether by the scientific community, policy and decision-makers or the general public. Recently, the accessibility of spatial data has dramatically improved. Without the need to install an application, spatial data can now be experienced via any web browser, mobile devices included. For developers, by simply updating the app on your server, the latest version of your application is now immediately available to your entire usercommunity. Unlike other virtual globes such as Google Earth, NASA World Wind offers something very special, full control to customize the interface with any features or functionalities you might need. You decide how the data is accessed and experienced. This allows you to provide maximum value of the information to your user community. The web version of NASA WorldWind (WebWorldWind) has made it possible for a whole new suite of applications for managing and sharing spatial data. Apps built with this web version are ideal for immediate social media type activity and also facilitate delivery of sophisticated data exchange scenarios such as weather and climate research, disaster response, personal navigation, and industrial-strength tracking for transportation, supply chain, aviation and satellites. WebWorldWind is an application component, not an app in itself. It is written in JavaScript and provides the real world geographic context for spatial data and information visualization, using a rich set of shapes and graphic primitives. WebWorldWind also provides platform independence, while accommodating any number of data types. Web WorldWind runs on any platform via a browser, i.e., Internet Explorer, Firefox, Chrome and Safari. Features include, 3D virtual globe, 2D map with multiple projection choices (Mercator, Polar, UPS, Equirectangular), imagery and elevation import, extensible, data retrieval (via REST, WMS, WCS, WFS, Bing, User-Defined), decluttering, measurement, accurate line-ofsight, subsurface visualization, and more.

Open Source Mapping↗
NASA NTRS2011

Fused Reality for Enhanced Flight Test Capabilities

The feasibility of using Fused Reality-based simulation technology to enhance flight test capabilities has been investigated. In terms of relevancy to piloted evaluation, there remains no substitute for actual flight tests, even when considering the fidelity and effectiveness of modern ground-based simulators. In addition to real-world cueing (vestibular, visual, aural, environmental, etc.), flight tests provide subtle but key intangibles that cannot be duplicated in a ground-based simulator. There is, however, a cost to be paid for the benefits of flight in terms of budget, mission complexity, and safety, including the need for ground and control-room personnel, additional aircraft, etc. A Fused Reality(tm) (FR) Flight system was developed that allows a virtual environment to be integrated with the test aircraft so that tasks such as aerial refueling, formation flying, or approach and landing can be accomplished without additional aircraft resources or the risk of operating in close proximity to the ground or other aircraft. Furthermore, the dynamic motions of the simulated objects can be directly correlated with the responses of the test aircraft. The FR Flight system will allow real-time observation of, and manual interaction with, the cockpit environment that serves as a frame for the virtual out-the-window scene.

Bachelder, Ed↗
NASA NTRS2019

Concept Evaluation: NASA Reference Model 2-Side by Side

Urban Air Mobility (UAM) is an up and coming topic in the world of aerosciences. A variety of companies, most notably Uber, has begun working towards making air taxis a regular part of day to day life. However, the implementation of this system into society will require a significant amount of work: making helicopters that can handle these flights and operate safely in urban environments, having landing zones, and working out new technologies to lower costs. NASA has also taken interest in this new idea and has formed a focus group of interns to tackle some of these problems. They have started by designing a few concept models for what these air taxis could look like, focusing on low noise, multiple passenger configurations, and the potential for electric or hybrid helicopters. One particular model is known as NR2, or the "Side by Side," which features two rotors spinning in opposite directions. Though these models are purely conceptual at this point, understanding the real-world aerodynamics and performance of this model is crucial to its future development. Using a program known as Rotorcraft Computational Fluid Dynamics (RotCFD), the performance characteristics of the rotors and aircraft, such as the lift, drag, thrust and power can be determined. These simulations can be run in a variety of flight configurations, with hover, forward flight, and climb being focused on in this study. The rotor collective angle can also be changed and used to get results about the lift and drag for the blades and the model body. These simulations can provide information for future model construction and wind tunnel testing.

Reference Model↗
NASA NTRS2015

Applied Operations Research: Augmented Reality in an Industrial Environment

Augmented reality is the application of computer generated data or graphics onto a real world view. Its use provides the operator additional information or a heightened situational awareness. While advancements have been made in automation and diagnostics of high value critical equipment to improve readiness, reliability and maintenance, the need for assisting and support to Operations and Maintenance staff persists. AR can improve the human machine interface where computer capabilities maximize the human experience and analysis capabilities. NASA operates multiple facilities with complex ground based HVCE in support of national aerodynamics and space exploration, and the need exists to improve operational support and close a gap related to capability sustainment where key and experienced staff consistently rotate work assignments and reach their expiration of term of service. The initiation of an AR capability to augment and improve human abilities and training experience in the industrial environment requires planning and establishment of a goal and objectives for the systems and specific applications. This paper explored use of AR in support of Operation staff in real time operation of HVCE and its maintenance. The results identified include identification of specific goal and objectives, challenges related to availability and computer system infrastructure.

Cole, Stuart K.↗
NASA NTRS2016

Initial Demonstration of the Real-Time Safety Monitoring Framework for the National Airspace System Using Flight Data

As new operational paradigms and additional aircraft are being introduced into the National Airspace System (NAS), maintaining safety in such a rapidly growing environment becomes more challenging. It is therefore desirable to have an automated framework to provide an overview of the current safety of the airspace at different levels of granularity, as well an understanding of how the state of the safety will evolve into the future given the anticipated flight plans, weather forecast, predicted health of assets in the airspace, and so on. Towards this end, as part of our earlier work, we formulated the Real-Time Safety Monitoring (RTSM) framework for monitoring and predicting the state of safety and to predict unsafe events. In our previous work, the RTSM framework was demonstrated in simulation on three different constructed scenarios. In this paper, we further develop the framework and demonstrate it on real flight data from multiple data sources. Specifically, the flight data is obtained through the Shadow Mode Assessment using Realistic Technologies for the National Airspace System (SMART-NAS) Testbed that serves as a central point of collection, integration, and access of information from these different data sources. By testing and evaluating using real-world scenarios, we may accelerate the acceptance of the RTSM framework towards deployment. In this paper we demonstrate the framework's capability to not only estimate the state of safety in the NAS, but predict the time and location of unsafe events such as a loss of separation between two aircraft, or an aircraft encountering convective weather. The experimental results highlight the capability of the approach, and the kind of information that can be provided to operators to improve their situational awareness in the context of safety.

Real-time Safety Monitoring↗
NASA NTRS1998

Current Limitations on VLBI Accuracy

The contribution of VLBI to geophysics and geodesy arises from its ability to measure distances between stations in a network and to determine the orientation of stations in the network as well as the orientation of the network with respect to the external reference frame of extragalactic radio objects. Integrating nearly two decades of observations provides useful information about station positions and velocities and the orientation of the Earth, but the complications of the real world and the limitations of observing, modeling and analysis prevent recovery of all effects. Of the factors that limit the accuracy of seemingly straightforward geodetic parameters, the neutral propagation medium has been subject to the greatest scrutiny, but the treatment of the mapping function, the wet component and spatial/temporal inhomogeneities is still improving. These affect both the terrestrial scale and consistency over time. The modeling of non-secular site motions (tides and loading) has increased in sophistication, but there are some differences between the models and the observations. VLBI antennas are massive objects, so their behavior is quite unlike GPS monuments, but antenna deformations add some (generally) unmodeled signal. Radio sources used in geodetic VLBI observations are selected for strength and (relative) absence of structure, but apparent changes in position can leak into geodetic parameters. A linear rate of change of baseline or site parameters is the simplest model and its error improves with time span. However, in most cases the VLBI data distribution is insufficient to look for real non-linear behavior that might affect the average rate. A few sites have multiple VLBI antennas, and some show small differences in rate. VLBI intrinsically measures relative positions and velocities, but individual site positions and velocities are generally more useful. The creation of the VLBI terrestrial reference frame, which transforms relative information into individual results, is an empirical process that has intrinsic errors. While UT1 is uniquely measured by VLBI, the geographical distribution and availability of VLBI stations, especially in the southern hemisphere, and the consistency of the VLBI terrestrial reference frame may limit the accuracy of Earth orientation measurements. The effects of particular error sources on geodetic and geophysical parameters derived from VLBI data will be illustrated.

Ma, Chopo↗
NASA NTRS1999

Interoperability Trends in Extravehicular Activity (EVA) Space Operations for the 21st Century

No other space operations in the 21 st century more comprehensively embody the challenges and dependencies of interoperability than EVA. This discipline is already functioning at an W1paralleled level of interagency, inter-organizational and international cooperation. This trend will only increase as space programs endeavor to expand in the face of shrinking budgets. Among the topics examined in this paper are hardware-oriented issues. Differences in design standards among various space participants dictate differences in the EVA tools that must be manufactured, flown and maintained on-orbit. Presently only two types of functional space suits exist in the world. However, three versions of functional airlocks are in operation. Of the three airlocks, only the International Space Station (ISS) Joint Airlock can accommodate both types of suits. Due to functional differences in the suits, completely different operating protocols are required for each. Should additional space suit or airlock designs become available, the complexity will increase. The lessons learned as a result of designing and operating within such a system are explored. This paper also examines the non-hardware challenges presented by interoperability for a discipline that is as uniquely dependent upon the individual as EVA. Operation of space suits (essentially single-person spacecrafts) by persons whose native language is not that of the suits' designers is explored. The intricacies of shared mission planning, shared control and shared execution of joint EVA's are explained. For example, once ISS is fully functional, the potential exists for two crewmembers of different nationality to be wearing suits manufactured and controlled by a third nation, while operating within an airlock manufactured and controlled by a fourth nation, in an effort to perform tasks upon hardware belonging to a fifth nation. Everything from training issues, to procedures development and writing, to real-time operations is addressed. Finally, this paper looks to the management challenges presented by interoperability in general. With budgets being reduced among all space-faring nations, the need to expand cooperation in the highly expensive field of human space operations is only going to intensify. The question facing management is not if the trend toward interoperation will continue, but how to best facilitate its doing so. Real-world EVA interoperability experience throughout the ShuttlelMir and ISS Programs is discussed to illustrate the challenges and

Miller, Gerald E.↗
NASA NTRS1995

Helmet-Mounted Display Research Capabilities of the NASA/Army Rotorcraft Aircrew Systems Concepts Airborne Laboratory (RASCAL)

The Rotorcraft Aircrew Systems Concepts Airborne Laboratory (RASCAL) is a UH-60A Black Hawk helicopter that is being modified by the US Army and NASA for flight systems research. The principal systems that are being installed in the aircraft are a Helmet Mounted Display (HMD) and imaging system, and a programmable full authority Research Flight Control System (RFCS). In addition, comprehensive instrumentation of both the rigid body of the helicopter and the rotor system is provided. The paper will describe the capabilities of these systems and their current state of development. A brief description of initial research applications is included. The wide (40 X 60 degree) field-of-view HMD system has been provided by Kaiser Electronics. It can be configured as a monochromatic system for use in bright daylight conditions, a two color system for darker ambients, or a full color system for use in night viewing conditions. Color imagery is achieved using field sequential video and a mechanical color wheel. In addition to the color symbology, high resolution computer-gene rated imagery from an onboard Silicon Graphics Reality Engine Onyx processor is available for research in virtual reality applications. This synthetic imagery can also be merged with real world video from a variety of imaging systems that can be installed easily on the front of the helicopter. These sensors include infrared or tv cameras, or potentially small millimeter wave radars. The Research Flight Control System is being developed for the aircraft by a team of contractors led by Boeing Helicopters. It consists of a full authority high bandwidth fly-by-wire actuators that drive the main rotor swashplate actuators and the tail rotor actuator in parallel. This arrangement allows the basic mechanical flight control system of the Black Hawk to be retained so that the safety pilot can monitor the operation of the system through the action of his own controls. The evaluation pilot will signal the fly-by-wire actuators through the flight computer from electrical sidearm controllers located in the right hand cockpit. The system will have very substantial input/output capacity and impressive computational power. These systems are installed in the aircraft using predominantly a MIL-STD 1553B data bus architecture. Sensor data from the RFCS, the basic aircraft and rotor system instrumentation including navigation information, and the HMD system are easily exchanged among user systems, or are available at the systems operator station located in the cabin for real time monitoring or data recording.

Jacobsen, R. A.↗
NASA NTRS2010

The NASA Langley Research Center's Unmanned Aerial System Surrogate Research Aircraft

Research is needed to determine what procedures, aircraft sensors and other systems will be required to allow Unmanned Aerial Systems (UAS) to safely operate with manned aircraft in the National Airspace System (NAS). The NASA Langley Research Center has transformed a Cirrus Design SR22 general aviation (GA) aircraft into a UAS Surrogate research aircraft to serve as a platform for UAS systems research, development, flight testing and evaluation. The aircraft is manned with a Safety Pilot and systems operator that allows for flight operations almost anywhere in the NAS without the need for a Federal Aviation Administration (FAA) Certificate of Authorization (COA). The UAS Surrogate can be controlled from a modular, transportable ground station like a true UAS. The UAS Surrogate is able to file and fly in the NAS with normal traffic and is a better platform for real world UAS research and development than existing vehicles flying in restricted ranges or other sterilized airspace. The Cirrus Design SR22 aircraft is a small, singleengine, four-place, composite-construction aircraft that NASA Langley acquired to support NASA flight-research programs like the Small Aircraft Transportation System (SATS) Project. Systems were installed to support flight test research and data gathering. These systems include: separate research power; multi-function flat-panel displays; research computers; research air data and inertial state sensors; video recording; data acquisition; data-link; S-band video and data telemetry; Common Airborne Instrumentation System (CAIS); Automatic Dependent Surveillance-Broadcast (ADS-B); instrumented surfaces and controls; and a systems operator work station. The transformation of the SR22 to a UAS Surrogate was accomplished in phases. The first phase was to modify the existing autopilot to accept external commands from a research computer that was connected by redundant data-link radios to a ground control station. An electro-mechanical auto-throttle was added in the next phase to provide ground station control of airspeed. Additional phases are in progress to add waypoint navigation and long range satellite voice and data communications. Potential areas for UAS Surrogate research include the development, flight test and evaluation of sensors to aid in the process of air traffic detect-sense-and-avoid. These sensors could be evaluated in real-time and compared with onboard human evaluation pilots. This paper describes the systems and design considerations that were incorporated in the development of the UAS Surrogate along with details of development problems encountered and the corresponding solutions.

Howell, Charles T., III↗
NASA NTRS1992

Machine Learning Techniques in Optimal Design

Many important applications can be formalized as constrained optimization tasks. For example, we are studying the engineering domain of two-dimensional (2-D) structural design. In this task, the goal is to design a structure of minimum weight that bears a set of loads. A solution to a design problem in which there is a single load (L) and two stationary support points (S1 and S2) consists of four members, E1, E2, E3, and E4 that connect the load to the support points is discussed. In principle, optimal solutions to problems of this kind can be found by numerical optimization techniques. However, in practice [Vanderplaats, 1984] these methods are slow and they can produce different local solutions whose quality (ratio to the global optimum) varies with the choice of starting points. Hence, their applicability to real-world problems is severely restricted. To overcome these limitations, we propose to augment numerical optimization by first performing a symbolic compilation stage to produce: (a) objective functions that are faster to evaluate and that depend less on the choice of the starting point and (b) selection rules that associate problem instances to a set of recommended solutions. These goals are accomplished by successive specializations of the problem class and of the associated objective functions. In the end, this process reduces the problem to a collection of independent functions that are fast to evaluate, that can be differentiated symbolically, and that represent smaller regions of the overall search space. However, the specialization process can produce a large number of sub-problems. This is overcome by deriving inductively selection rules which associate problems to small sets of specialized independent sub-problems. Each set of candidate solutions is chosen to minimize a cost function which expresses the tradeoff between the quality of the solution that can be obtained from the sub-problem and the time it takes to produce it. The overall solution to the problem, is then obtained by solving in parallel each of the sub-problems in the set and computing the one with the minimum cost. In addition to speeding up the optimization process, our use of learning methods also relieves the expert from the burden of identifying rules that exactly pinpoint optimal candidate sub-problems. In real engineering tasks it is usually too costly to the engineers to derive such rules. Therefore, this paper also contributes to a further step towards the solution of the knowledge acquisition bottleneck [Feigenbaum, 1977] which has somewhat impaired the construction of rulebased expert systems.

Cerbone, Giuseppe↗