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NASA NTRS1997

Technical Report Series on Global Modeling and Data Assimilation: Comparison of Satellite Global Rainfall Algorithms - Volume 12

Seventeen months of rainfall data (August 1987-December 1988) from nine satellite rainfall algorithms (Adler, Chang, Kummerow, Prabhakara, Huffman, Spencer, Susskind, and Wu) were analyzed to examine the uncertainty of satellite-derived rainfall estimates. The variability among algorithms, measured as the standard deviation computed from the ensemble of algorithms, shows regions of high algorithm variability tend to coincide with regions of high rain rates. Histograms of pattern correlation (PC) between algorithms suggest a bimodal distribution, with separation at a PC-value of about 0.85. Applying this threshold as a criteria for similarity, our analyses show that algorithms using the same sensor or satellite input tend to be similar, suggesting the dominance of sampling errors in these satellite estimates.

Suarez, Max J.↗
NASA NTRS1997

An Impact-Location Estimation Algorithm for Subsonic Uninhabited Aircraft

An impact-location estimation algorithm is being used at the NASA Dryden Flight Research Center to support range safety for uninhabited aerial vehicle flight tests. The algorithm computes an impact location based on the descent rate, mass, and altitude of the vehicle and current wind information. The predicted impact location is continuously displayed on the range safety officer's moving map display so that the flightpath of the vehicle can be routed to avoid ground assets if the flight must be terminated. The algorithm easily adapts to different vehicle termination techniques and has been shown to be accurate to the extent required to support range safety for subsonic uninhabited aerial vehicles. This paper describes how the algorithm functions, how the algorithm is used at NASA Dryden, and how various termination techniques are handled by the algorithm. Other approaches to predicting the impact location and the reasons why they were not selected for real-time implementation are also discussed.

Bauer, Jeffrey E.↗
NASA NTRS1996

Soft-Output Decoding Algorithms in Iterative Decoding of Turbo Codes

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.

Benedetto, S.↗
NASA NTRS1997

Algorithms for Multiple Fault Diagnosis With Unreliable Tests

In this paper, we consider the problem of constructing optimal and near-optimal multiple fault diagnosis (MFD) in bipartite systems with unreliable (imperfect) tests. It is known that exact computation of conditional probabilities for multiple fault diagnosis is NP-hard. The novel feature of our diagnostic algorithms is the use of Lagrangian relaxation and subgradient optimization methods to provide: (1) near optimal solutions for the MFD problem, and (2) upper bounds for an optimal branch-and-bound algorithm. The proposed method is illustrated using several examples. Computational results indicate that: (1) our algorithm has superior computational performance to the existing algorithms (approximately three orders of magnitude improvement), (2) the near optimal algorithm generates the most likely candidates with a very high accuracy, and (3) our algorithm can find the most likely candidates in systems with as many as 1000 faults.

Shakeri, Mojdeh↗
NASA NTRS1999

Backup Attitude Control Algorithms for the MAP Spacecraft

The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The MAP spacecraft will perform its mission, studying the early origins of the universe, in a Lissajous orbit around the Earth-Sun L(sub 2) Lagrange point. Due to limited mass, power, and financial resources, a traditional reliability concept involving fully redundant components was not feasible. This paper will discuss the redundancy philosophy used on MAP, describe the hardware redundancy selected (and why), and present backup modes and algorithms that were designed in lieu of additional attitude control hardware redundancy to improve the odds of mission success. Three of these modes have been implemented in the spacecraft flight software. The first onboard mode allows the MAP Kalman filter to be used with digital sun sensor (DSS) derived rates, in case of the failure of one of MAP's two two-axis inertial reference units. Similarly, the second onboard mode allows a star tracker only mode, using attitude and derived rate from one or both of MAP's star trackers for onboard attitude determination and control. The last backup mode onboard allows a sun-line angle offset to be commanded that will allow solar radiation pressure to be used for momentum management and orbit stationkeeping. In addition to the backup modes implemented on the spacecraft, two backup algorithms have been developed in the event of less likely contingencies. One of these is an algorithm for implementing an alternative scan pattern to MAP's nominal dual-spin science mode using only one or two reaction wheels and thrusters. Finally, an algorithm has been developed that uses thruster one shots while in science mode for momentum management. This algorithm has been developed in case system momentum builds up faster than anticipated, to allow adequate momentum management while minimizing interruptions to science. In this paper, each mode and algorithm will be discussed, and simulation results presented.

ODonnell, James R., Jr.↗
NASA NTRS1999

Novel, Miniature Multi-Hole Probes and High-Accuracy Calibration Algorithms for their use in Compressible Flowfields

Two new calibration algorithms were developed for the calibration of non-nulling multi-hole probes in compressible, subsonic flowfields. The reduction algorithms are robust and able to reduce data from any multi-hole probe inserted into any subsonic flowfield to generate very accurate predictions of the velocity vector, flow direction, total pressure and static pressure. One of the algorithms PROBENET is based on the theory of neural networks, while the other is of a more conventional nature (polynomial approximation technique) and introduces a novel idea of local least-squares fits. Both algorithms have been developed to complete, user-friendly software packages. New technology was developed for the fabrication of miniature multi-hole probes, with probe tip diameters all the way down to 0.035". Several miniature 5- and 7-hole probes, with different probe tip geometries (hemispherical, conical, faceted) and different overall shapes (straight, cobra, elbow probes) were fabricated, calibrated and tested. Emphasis was placed on the development of four stainless-steel conical 7-hole probes, 1/16" in diameter calibrated at NASA Langley for the entire subsonic regime. The developed calibration algorithms were extensively tested with these probes demonstrating excellent prediction capabilities. The probes were used in the "trap wing" wind tunnel tests in the 14'x22' wind tunnel at NASA Langley, providing valuable information on the flowfield over the wing. This report is organized in the following fashion. It consists of a "Technical Achievements" section that summarizes the major achievements, followed by an assembly of journal articles that were produced from this project and ends with two manuals for the two probe calibration algorithms developed.

Rediniotis, Othon K.↗
NASA NTRS1999

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗
NASA NTRS1999

Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm

The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.

Mavriplis, Dimitri J.↗
NASA NTRS2002

Navigation Algorithms for the SeaWiFS Mission

The navigation algorithms for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) were designed to meet the requirement of 1-pixel accuracy-a standard deviation (sigma) of 2. The objective has been to extract the best possible accuracy from the spacecraft telemetry and avoid the need for costly manual renavigation or geometric rectification. The requirement is addressed by postprocessing of both the Global Positioning System (GPS) receiver and Attitude Control System (ACS) data in the spacecraft telemetry stream. The navigation algorithms described are separated into four areas: orbit processing, attitude sensor processing, attitude determination, and final navigation processing. There has been substantial modification during the mission of the attitude determination and attitude sensor processing algorithms. For the former, the basic approach was completely changed during the first year of the mission, from a single-frame deterministic method to a Kalman smoother. This was done for several reasons: a) to improve the overall accuracy of the attitude determination, particularly near the sub-solar point; b) to reduce discontinuities; c) to support the single-ACS-string spacecraft operation that was started after the first mission year, which causes gaps in attitude sensor coverage; and d) to handle data quality problems (which became evident after launch) in the direct-broadcast data. The changes to the attitude sensor processing algorithms primarily involved the development of a model for the Earth horizon height, also needed for single-string operation; the incorporation of improved sensor calibration data; and improved data quality checking and smoothing to handle the data quality issues. The attitude sensor alignments have also been revised multiple times, generally in conjunction with the other changes. The orbit and final navigation processing algorithms have remained largely unchanged during the mission, aside from refinements to data quality checking. Although further improvements are certainly possible, future evolution of the algorithms is expected to be limited to refinements of the methods presented here, and no substantial changes are anticipated.

Hooker, Stanford B.↗
NASA NTRS2002

A Lightning Channel Retrieval Algorithm for the North Alabama Lightning Mapping Array (LMA)

A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The network will support on-going ground validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.

Koshak, William↗
NASA NTRS2002

Evaluation of Improvements to the TRMM Microwave Rain Algorithm

Improvements made to the Version 5 TRMM passive microwave rain retrieval algorithm (2A-12) are evaluated using independent data. Surface rain rate estimates from the Version 5 TRMM TMI (2A-12), PR (2A-25) and TMI/PR Combined (2B-31) algorithms and ground-based radar estimates for selected coincident subset datasets in 1998 over Melbourne and Kwajalein show varying degrees of agreement. The surface rain rates are then classified into convective and stratiform rain types over ocean, land, and coastal areas for more detailed comparisons to the ground radar measurements. These comparisons lead to a better understanding of the relative performances of the current TRMM rain algorithms. For example, at Melbourne more than 80% of the radar-derived rainfall is classified as convective rain. Convective rain from the TRMM rain algorithms is less than that from ground radar measurements, while TRMM stratiform rain is much greater. Rain area coverage from 2A-12 is also in reasonable agreement with ground radar measurements, with about 25% more over ocean and 25% less over land and coastal areas. Retrieved rain rates from the improved (Version 6) 2A-12 algorithm will be compared to 2A-25, 2B-31, and ground-based radar measurements to evaluate the impact of improvements to 2A-12 in Version 6. An important improvement to the Version 6 2A-12 algorithm is the retrieval of Q1/Q2 (latent heating/drying) profiles in addition to the surface rain rate and hydrometeor profiles. In order to ascertain the credibility of the new products, retrieved Q1/Q2 profiles are compared to independent ground-based estimates. Analyses of dual-Doppler radar data in conjunction with coincident rawinsonde data yield estimates of the vertical distributions of diabatic heating/drying at high horizontal resolution for selected cases over the Kwajalein and LBA field sites. The estimated vertical heating/drying structures appear to be reasonable. Comparisons of Q1/Q2 profiles from Version 6 2A-12 and the ground-based estimates are in progress. Retrieved Q1/Q2 structures will also be compared to MM5 hurricane simulations for selected cases. The results of these intercomparisons will be presented at the conference.

Yang, Song↗
NASA NTRS2003

Algorithm Updates for the Fourth SeaWiFS Data Reprocessing

The efforts to improve the data quality for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) data products have continued, following the third reprocessing of the global data set in May 2000. Analyses have been ongoing to address all aspects of the processing algorithms, particularly the calibration methodologies, atmospheric correction, and data flagging and masking. All proposed changes were subjected to rigorous testing, evaluation and validation. The results of these activities culminated in the fourth reprocessing, which was completed in July 2002. The algorithm changes, which were implemented for this reprocessing, are described in the chapters of this volume. Chapter 1 presents an overview of the activities leading up to the fourth reprocessing, and summarizes the effects of the changes. Chapter 2 describes the modifications to the on-orbit calibration, specifically the focal plane temperature correction and the temporal dependence. Chapter 3 describes the changes to the vicarious calibration, including the stray light correction to the Marine Optical Buoy (MOBY) data and improved data screening procedures. Chapter 4 describes improvements to the near-infrared (NIR) band correction algorithm. Chapter 5 describes changes to the atmospheric correction and the oceanic property retrieval algorithms, including out-of-band corrections, NIR noise reduction, and handling of unusual conditions. Chapter 6 describes various changes to the flags and masks, to increase the number of valid retrievals, improve the detection of the flag conditions, and add new flags. Chapter 7 describes modifications to the level-la and level-3 algorithms, to improve the navigation accuracy, correct certain types of spacecraft time anomalies, and correct a binning logic error. Chapter 8 describes the algorithm used to generate the SeaWiFS photosynthetically available radiation (PAR) product. Chapter 9 describes a coupled ocean-atmosphere model, which is used in one of the changes described in Chapter 4. Finally, Chapter 10 describes a comparison of results from the third and fourth reprocessings along the US. Northeast coast.

Hooker, Stanford, B.↗
NASA NTRS2003

Quantum Adiabatic Algorithms and Large Spin Tunnelling

We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.

Boulatov, A.↗
NASA NTRS2003

GOME Total Ozone and Calibration Error Derived Usign Version 8 TOMS Algorithm

The Global Ozone Monitoring Experiment (GOME) is a hyper-spectral satellite instrument measuring the ultraviolet backscatter at relatively high spectral resolution. GOME radiances have been slit averaged to emulate measurements of the Total Ozone Mapping Spectrometer (TOMS) made at discrete wavelengths and processed using the new TOMS Version 8 Ozone Algorithm. Compared to Differential Optical Absorption Spectroscopy (DOAS) techniques based on local structure in the Huggins Bands, the TOMS uses differential absorption between a pair of wavelengths including the local stiucture as well as the background continuum. This makes the TOMS Algorithm more sensitive to ozone, but it also makes the algorithm more sensitive to instrument calibration errors. While calibration adjustments are not needed for the fitting techniques like the DOAS employed in GOME algorithms, some adjustment is necessary when applying the TOMS Algorithm to GOME. Using spectral discrimination at near ultraviolet wavelength channels unabsorbed by ozone, the GOME wavelength dependent calibration drift is estimated and then checked using pair justification. In addition, the day one calibration offset is estimated based on the residuals of the Version 8 TOMS Algorithm. The estimated drift in the 2b detector of GOME is small through the first four years and then increases rapidly to +5% in normalized radiance at 331 nm relative to 385 nm by mid 2000. The lb detector appears to be quite well behaved throughout this time period.

Gleason, J.↗
NASA NTRS2003

Ocean Primary Production Estimates from Terra MODIS and Their Dependency on Satellite Chlorophyll Alpha Algorithms

Simplistic models relating global satellite ocean color, temperature, and light to ocean net primary production (ONPP) are sensitive to the accuracy and limitations of the satellite estimate of chlorophyll and other input fields, as well as the primary productivity model. The standard MODIS ONPP product uses the new semi-analytic chlorophyll algorithm as its input for two ONPP indexes. The three primary MODIS chlorophyll Q estimates from MODIS, as well as the SeaWiFS 4 chlorophyll product, were used to assess global and regional performance in estimating ONPP for the full mission, but concentrating on 2001. The two standard ONPP algorithms were examined with 8-day and 39 kilometer resolution to quantify chlorophyll algorithm dependency of ONPP. Ancillary data (MLD from FNMOC, MODIS SSTD1, and PAR from the GSFC DAO) were identical. The standard MODIS ONPP estimates for annual production in 2001 was 59 and 58 GT C for the two ONPP algorithms. Differences in ONPP using alternate chlorophylls were on the order of 10% for global annual ONPP, but ranged to 100% regionally. On all scales the differences in ONPP were smaller between MODIS and SeaWiFS than between ONPP models, or among chlorophyll algorithms within MODIS. Largest regional ONPP differences were found in the Southern Ocean (SO). In the SO, application of the semi-analytic chlorophyll resulted in not only a magnitude difference in ONPP (2x), but also a temporal shift in the time of maximum production compared to empirical algorithms when summed over standard oceanic areas. The resulting increase in global ONPP (6-7 GT) is supported by better performance of the semi-analytic chlorophyll in the SO and other high chlorophyll regions. The differences are significant in terms of understanding regional differences and dynamics of ocean carbon transformations.

Essias, Wayne E.↗
NASA NTRS1997

Developments in Human Centered Cueing Algorithms for Control of Flight Simulator Motion Systems

The authors conducted further research with cueing algorithms for control of flight simulator motion systems. A variation of the so-called optimal algorithm was formulated using simulated aircraft angular velocity input as a basis. Models of the human vestibular sensation system, i.e. the semicircular canals and otoliths, are incorporated within the algorithm. Comparisons of angular velocity cueing responses showed a significant improvement over a formulation using angular acceleration input. Results also compared favorably with the coordinated adaptive washout algorithm, yielding similar results for angular velocity cues while eliminating false cues and reducing the tilt rate for longitudinal cues. These results were confirmed in piloted tests on the current motion system at NASA-Langley, the Visual Motion Simulator (VMS). Proposed future developments by the authors in cueing algorithms are revealed. The new motion system, the Cockpit Motion Facility (CMF), where the final evaluation of the cueing algorithms will be conducted, is also described.

Houck, Jacob A.↗
NASA NTRS2005

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

Venter, Gerhard↗
NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗