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At least 181 records · Page 10

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DOE OSTI2024

Adaptive Fault Current-Limiting Control of MMC for Protection of Multiterminal HVDC Systems: Preprint

For the development of multi-terminal high voltage DC (MTDC) transmission, it is critical to design the protection system that can selectively isolate the faulty area from the healthy part of the dc grid using DC circuit breakers (DCCBs) while ensuring continuous operation of converter stations in the healthy part. However, because of the lack of fault current blocking capability in half-bridge (HB) modular multilevel converters (MMCs), when a dc fault occurs, the rising fault currents can quickly reach the blocking threshold within a few milliseconds and disrupt the operation of MMCs in the healthy part. Large DC reactors are often considered in series with DCCBs to reduce the rate of rise of fault currents and prevent blocking of MMCs in the healthy part of the grid. However, large DC reactors can prohibitively increase the cost of the system, particularly when they are considered in an offshore environment, for instance in offshore wind projects. Large dc reactors can also introduce stability issues and create post-fault oscillations. This paper presents an adaptive fault current limiting control method for MMCs to avoid their blocking and enable continuous operation of MTDC systems. It contains two parts: The first part is based on circulating current feedforward control that emulates virtual reactors in each arm of an MMC, which is immediately activated when the fault current starts to increase, to reduce the rate of rise of the fault current; the second part is triggered when the fault current exceeds a preset threshold by temporarily bypassing the SMs, serving as a complement to the fault current limiting effect of the first part. Both parts do not require fault detection signal and they are activated automatically during faults. Simulation case studies of a four-terminal bipolar MMC-HVDC system are presented to demonstrate the effectiveness of the proposed control methods.

active fault current limiting↗

NASA NTRS1993

Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

Bramble, James H.↗

DOE OSTI2025

InAs sidewall tunnel diodes enabled by surface states

Negative differential resistance (NDR), where the device current decreases with increasing bias voltage, is a representative phenomenon where quantum mechanics induces counterintuitive physical behavior and offers promising applications such as high-frequency oscillators, amplifiers, and multilevel logic circuits. While the NDR behavior has been extensively studied in various materials and devices, the role of surface properties in NDR, particularly in InAs-based diodes, remains underexplored. In this work, we report the observation of NDR in vertically structured InAs p + n diodes that exhibit a peak-valley current ratio of ∼6, which is suitably high for applications. Circumference-normalized current–voltage characterization revealed that the NDR originates from band-to-band tunneling between the valence band of p + -InAs and the conduction band of an n + -InAs surface, where the n + surface is due to surface states on otherwise n − -InAs. In addition, by comparing devices with various surface passivation methods (without intentional passivation, benzocyclobutene polymer, and silicon nitride), we found that the surface termination significantly affects the NDR characteristics. We present an equivalent circuit model to explain the observed device behavior. These findings offer insights into surface-enabled NDR phenomena and present new knobs for engineering NDR devices.

Circuit theorems↗

NASA NTRS1995

Parallelized modelling and solution scheme for hierarchically scaled simulations

This two-part paper presents the results of a benchmarked analytical-numerical investigation into the operational characteristics of a unified parallel processing strategy for implicit fluid mechanics formulations. This hierarchical poly tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimize memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite element (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications, and computational effort associated with a parallel computing environment, substantial reductions are generated in the sequential mode of application. Such improvements grow with increasing problem size. Along with a theoretical development of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of solving, are presented and discussed. Among these techniques are several interpolative reduction methods. It was found that by combining several of these techniques that a relatively small interpolative reduction resulted in substantial performance gains. Several other unique features/benefits are discussed in this paper. Along with Part 1's theoretical development, Part 2 presents a numerical approach to the HPT along with four prototype CFD applications. These demonstrate the potential of the HPT strategy.

Padovan, Joe↗

DOE OSTI2024

Adaptive Fault Current-Limiting Control of MMC for Protection of Multiterminal HVDC Systems

A crucial requirement of the protection system for multi-terminal high-voltage DC (MTDC) transmission is that it is capable of selectively isolating the faulty area from the healthy part of the network using DC circuit breakers (DCCBs), while ensuring continuous operation of converter stations in the healthy part of the network. But in the half-bridge modular multilevel converters (HB-MMCs) based MTDC system, since HB-MMCs do not have fault current absorption capability, when a DC fault occurs, the rising fault currents can quickly reach the blocking threshold within a few milliseconds and disrupt the operation of the MMCs in the healthy part. To facilitate fault-ride-through capability of MTDC system, large DC reactors are often considered in series with DCCBs to reduce the rate of rise of the fault current and prevent blocking the MMCs in the healthy part of the DC networks; however, large DC reactors prohibitively increase the cost of the system, introduce stability issues and can create post-fault oscillations. This paper presents an adaptive fault current-limiting control method for MMCs to avoid their blocking and enable the continuous operation of the healthy part of MTDC systems. The method contains two parts: The first part is based on circulating current feedforward control, which emulates virtual reactors in each arm of an MMC, and is immediately activated when the fault current starts to increase to reduce the rate of rise of the fault current. The second part temporarily bypasses all the submodules when the fault current exceeds a preset threshold, complementing the fault current-limiting effect of the first part. Neither part requires fault detection signals, and they are automatically activated during faults. Simulation case studies of a four-terminal bipolar MMC-based high-voltage DC system are presented to demonstrate the effectiveness of the proposed control methods.

active fault current limiting↗

NASA NTRS1976

Satellite data for surface-mine inventory

To determine the feasibility of satellite data for surface-mine inventory, particularly as it applies to coal, a case study was conducted in Maryland. A band-ratio method was developed to measure disturbed surface areas, and it proved to be extendible both temporally and geographically. This method was used to measure area changes in the region over three time periods from September 1972 through July 1974 and to map the entire two-county area for 1973. For mines ranging between 31 and 244 acres (12 to 98 hectares) the measurement accuracy of total affected acreage was determined to be 92%. Mines of 120 acres (50 hectares) and larger were measured with greater accuracy, some within one percent of the actual area. The ability to identify, classify, and measure strip-mine surfaces in a two-county area (1,541 square kilometers - 595 square miles) of western Maryland was demonstrated through the use of computer processing. On the basis of these results the use of LANDSAT satellite data and multilevel sampling of aircraft and field verification inspections, multispectral analysis of digital data is shown to be an effective, rapid, and accurate means of monitoring the surface mining cycle.

Anderson, A. T.↗

DOE OSTI2024

Adaptive Narrowband Damping for Improving Harmonic Stability of Modular Multilevel Converter: Preprint

Harmonic instability events between modular multilevel converter (MMC) and ac systems have been widely reported in recent years. To resolve it, this paper proposes an adaptive narrowband damping control that automatically programs, adds and adjusts damping around the oscillation frequency when detect the oscillation. The paper first presents a low-pass filter design for MMC control loops, which pushes all negative damping of MMC impedance down to the medium frequency range (< approximately 1000 Hz). This makes narrowband damping can be more targeted and easier to design because multiple harmonic oscillations are avoided. An adaptive damping control that uses online oscillation detection is then proposed, which can automatically configure the narrowband damper to provide damping to the MMC at the detected oscillation frequency. In contrast to existing narrowband damping methods, the proposed adaptive narrowband damper adjusts the damping gain (e.g., to zero when system resonance disappears) and the width of the damping range automatically based on continuous monitoring of system resonance conditions. Electromagnetic transient (EMT) simulation results validate the efficacy of the proposed method in two typical MMC-based power systems.

active damping↗

DOE OSTI2024

Multi-level Monte Carlo methods in chemical applications with Lennard-Jones potentials and other landscapes with isolated singularities

We describe and compare outcomes of various Multi-Level Monte Carlo (MLMC) method variants, motivated by the potential of improved computational efficiency over rejection based Monte Carlo, which scales poorly with problem dimension. With an eye toward its application to computational chemical physics, we test MLMC's ability to sample trajectories on two problems — a familiar double-well potential, with known stationary distributions, and a Lennard-Jones solid potential (a Galton Board). By sampling Brownian motion trajectories, we are able to compute expectations of observable averages. These multi-basin potential energy problems capture the essence of the challenges with using MLMC, namely, maintaining correspondence of sample paths as time-resolution is varied. Addressing this challenge properly can lead to MLMC significantly outperforming standard Monte Carlo path sampling. We describe the essence of this problem and suggest strategies that circumvent diverging multilevel sample paths for an important class of problems. In the tests we also compare the computational cost of several, “adaptive,” variants of MLMC. Our results demonstrate that MLMC overcomes the collision, time scale limitation of the more familiar Brownian path MC samplers, and our implementation provides tunable error thresholds, making MLMC a promising candidate for application to larger and more complex molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Sub-Doppler Cooling of a Trapped Ion in a Phase-Stable Polarization Gradient

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing tailorable light-matter interactions in the sub-wavelength regime. In this Letter, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of 2⁢𝜋×1.45 MHz we achieve ⟨𝑛⟩=1.56±0.07 in 150 μ⁢s and cooling rates of ∼0.3 quanta/μ⁢s. Here, we examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a multilevel model. Cooling is fast and power efficient, with lower average motional Fock state occupation when compared to simulated operation under the corresponding running wave configuration. Our results demonstrate a well-controlled test bed for studying the dynamics of multilevel atomic systems in a phase-stable polarization gradient.

Atom & ion cooling↗

NASA NTRS2001

Efficiency Improvements to the Displacement Based Multilevel Structural Optimization Algorithm

Multilevel Structural Optimization (MSO) continues to be an area of research interest in engineering optimization. In the present project, the weight optimization of beams and trusses using Displacement based Multilevel Structural Optimization (DMSO), a member of the MSO set of methodologies, is investigated. In the DMSO approach, the optimization task is subdivided into a single system and multiple subsystems level optimizations. The system level optimization minimizes the load unbalance resulting from the use of displacement functions to approximate the structural displacements. The function coefficients are then the design variables. Alternately, the system level optimization can be solved using the displacements themselves as design variables, as was shown in previous research. Both approaches ensure that the calculated loads match the applied loads. In the subsystems level, the weight of the structure is minimized using the element dimensions as design variables. The approach is expected to be very efficient for large structures, since parallel computing can be utilized in the different levels of the problem. In this paper, the method is applied to a one-dimensional beam and a large three-dimensional truss. The beam was tested to study possible simplifications to the system level optimization. In previous research, polynomials were used to approximate the global nodal displacements. The number of coefficients of the polynomials equally matched the number of degrees of freedom of the problem. Here it was desired to see if it is possible to only match a subset of the degrees of freedom in the system level. This would lead to a simplification of the system level, with a resulting increase in overall efficiency. However, the methods tested for this type of system level simplification did not yield positive results. The large truss was utilized to test further improvements in the efficiency of DMSO. In previous work, parallel processing was applied to the subsystems level, where the derivative verification feature of the optimizer NPSOL had been utilized in the optimizations. This resulted in large runtimes. In this paper, the optimizations were repeated without using the derivative verification, and the results are compared to those from the previous work. Also, the optimizations were run on both, a network of SUN workstations using the MPICH implementation of the Message Passing Interface (MPI) and on the faster Beowulf cluster at ICASE, NASA Langley Research Center, using the LAM implementation of UP]. The results on both systems were consistent and showed that it is not necessary to verify the derivatives and that this gives a large increase in efficiency of the DMSO algorithm.

Plunkett, C. L.↗

NASA NTRS1993

Ceramic matrix composites properties/microstresses with complete and partial interphase bond

A multilevel substructuring technique which includes a unique fiber substructuring concept is used for the analysis of continuous fiber reinforced ceramic matrix composites. This technique has four levels of substructuring--from laminate to ply, to supply, and then to fiber. A stand-alone computer code CEMCAN (Ceramic Matrix Composites Analyzer), incorporating this technique and specifically for the simulation of ceramic matrix composites behavior, is currently under development at NASA Lewis Research Center in Cleveland, Ohio. The thermal and mechanical properties, along with the microstresses, for a SiC/RBSN (silicon carbide fiber and reaction bonded silicon nitride matrix) composite at different fiber volume ratios and varying degrees of interfacial bond around the fiber circumference are computed. Values predicted by CEMCAN computer code are shown to bound the experimentally measured values. Results also show that transverse tensile strength test can be a sensitive test method to assess interfacial conditions.

Mital, Subodh K.↗

DOE OSTI2025

Control Oriented Models for Co-Design: Technical Overview of MT HVDC, MVDC, and Solid State Transformer Building Blocks

The electric power system is shifting toward a power electronics–enabled grid, where converter based “building blocks” (e.g., high voltage direct current (HVDC) links, multi terminal HVDC (MT HVDC) networks, medium voltage DC (MVDC) links, and solid state transformers (SSTs)) provide fast, precise control of power flows, voltage, and frequency. This report develops and applies publicly shareable electromagnetic transient (EMT) and phasor models to examine how such building blocks can be composed and coordinated to support offshore wind integration, inter area transfers, feeder support, and resilience. Section 2 documents a modular multilevel converter (MMC)–based MT HVDC modeling framework and two use cases: a compact WSCC/IEEE 9 bus test system and a 240 bus “mini WECC” case with five offshore wind plants (OWFs). Phasor to EMT transfer, initialization, and sanity checks are summarized, and neutral demonstrations of normal and contingency operation are reported. Section 3 frames the problem of wind plant inertial frequency response (IFR): shaping energy release and recovery to improve nadir while avoiding aerodynamic stall; representative simulations illustrate the issues without disclosing proprietary control. Section 4 develops MVDC concepts through an IEEE 16 bus loop and an Olympic Peninsula case study that compares AC vs. MVDC corridors and shows how feeder headroom can be pooled via DC couplers. Section 5 surveys SST architectures and identifies a gap: scalable, communication free coordination of multiple SSTs for islanded feeder networks. Across the report, novel methods and configurations under separate publication and IP review are not disclosed; only topic oriented, replicable setups and non proprietary results are shown. These models and use cases are intended as foundations for future publications and co design studies on architecture, control, and coordination of PE enabled grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-Response Curves

NASA will soon be collecting noise-annoyance community survey data as the X-59 aircraft flies supersonically over several communities in the USA. Sparse measurements of the X-59 sonic thumps will be used together with physics-based simulations to estimate noise doses at survey participant locations. These dose estimates have associated error that affects the accuracy of modeled dose-response curves, which can result in misestimation of annoyance. The precision in dose-response curves is also a consideration in selecting the number of survey participants. To enable pretest studies of dose error and precision, simulated dose-response data were generated based on NASA’s Quiet Supersonic Flights 2018 test. The data included various degrees of dose error and sample size. Frequentist multilevel logistic regression models were fit to the true and perturbed dose-response data. Simple proportional relationships were identified between the model parameters and the perturbation standard deviation. The summary dose-response curves illustrate the impact on accuracy if dose error is not accounted for in the model. The precision in the dose-response curves is also shown as the number of participants and degree of participation is varied. Finally, sampling variability is illustrated by showing the dose-response curves for several replicates with random draws of participants and errors.

X-59↗

NASA NTRS2025

Measuring Unique Contextual Factors: Group Living Skills

BACKGROUND The Human Factors and Behavioral Performance Exploration Measures (HFBP-EM) suite is a set of standardized measures used to assess behavioral health and performance risks related to future exploration-class space missions. During the HFBP-EM suite development, the importance of assessing unique contextual factors to understand the drivers of team dynamics was identified. Group living skills are a unique workplace skill which applies to those coworkers who live and work together. As mission lengths become longer, the line between work and non-work life may blur. Extreme living conditions such as spaceflight can result in increased stress over time, negatively impact mood and well-being, decrease team cohesion and increase conflict, deteriorate task performance, and potentially reduce mission success [1]. With no breaks in their isolated and confined environment possible, living with a messy, inconsiderate crewmember can add to the stress. Alternatively, crews with good group living skills may support one another, mitigating the negative effects of the extreme environment. There was no direct measure of group living skills. This work sought to fill this measurement gap and collect data related to group living in isolated, confined, extreme (ICE) environments. METHODS Group living skills as an astronaut competency area were developed with the input of experts familiar with ICE environments. Distinct aspects of this competency were reviewed and discussed by a NASA-invited group of spaceflight experts in 2015 to identify individual and team behavioral health and performance measures for operational environments. This work resulted in a 5-item measure focused on group living experiences with each crewmember (or the crew as a whole). A 6th item asks whether an individual would go on another mission with a particular crewmember or crew as a measure of future-oriented group living, or team viability. The measure was deployed in 24 teams living and working together in isolated and confined environments (e.g., International Space Station, space mission simulation analogs). RESULTS & DISCUSSION In this presentation, we will summarize results which indicate the Group Living Skills (GLS) Survey is a reliable, valid, and operationally feasible measure. Reliability was evaluated in several ways. Two-way multilevel mixed models revealed strong repeated measures reliability (ICC2 = .902, Omega between = .954). Reliability of change within teams was strong (Rc = .81). Factor analysis showed a consistent two-factor structure when individuals rated either the whole crew, all individuals, just peers, or a focal roommate. The latter used a sociometric approach to rating the GLS of the roommates. The two factors were tidiness and being considerate of others. We assessed the criterion-related validity of GLS, by examining GLS operationalized as the team-level aggregated GLS Survey scores as a predictor of team viability, team cohesion, and team performance. We used generalized mixed models to account for the repeated measures and longitudinal data. The marginal R2 change was used to determine the extent to which GLS were related to the team outcomes while controlling for mission day and campaign. Results suggested GLS was strongly related to team viability (marginal R2 change = .40), team cohesion (marginal R2 change = 0.28), social cohesion (marginal R2 change = 0.25), and moderately related to task cohesion (marginal R2 change = 0.18). GLS scores had a small relationship with team performance (marginal R2 change = .08). Results support GLS as a measure that can be used to capture group living skills of crews who live and work together in ICE. Because the items were written to be broadly applicable, less extreme environments with teams living and working together for some length of time also benefit from this measure (e.g., college roommates, camps). See Landon et al. (2024) for full results [2]. SUMMARY We report reliability and validity evidence for a new measure that assesses the Group Living Skills for teams that live and work in operational environments such as spaceflight.

J C W Miller↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-response Curves

X-59↗

NASA NTRS1995

Equalization and detection for digital communication over nonlinear bandlimited satellite communication channels

This dissertation evaluates receiver-based methods for mitigating the effects due to nonlinear bandlimited signal distortion present in high data rate satellite channels. The effects of the nonlinear bandlimited distortion is illustrated for digitally modulated signals. A lucid development of the low-pass Volterra discrete time model for a nonlinear communication channel is presented. In addition, finite-state machine models are explicitly developed for a nonlinear bandlimited satellite channel. A nonlinear fixed equalizer based on Volterra series has previously been studied for compensation of noiseless signal distortion due to a nonlinear satellite channel. This dissertation studies adaptive Volterra equalizers on a downlink-limited nonlinear bandlimited satellite channel. We employ as figure of merits performance in the mean-square error and probability of error senses. In addition, a receiver consisting of a fractionally-spaced equalizer (FSE) followed by a Volterra equalizer (FSE-Volterra) is found to give improvement beyond that gained by the Volterra equalizer. Significant probability of error performance improvement is found for multilevel modulation schemes. Also, it is found that probability of error improvement is more significant for modulation schemes, constant amplitude and multilevel, which require higher signal to noise ratios (i.e., higher modulation orders) for reliable operation. The maximum likelihood sequence detection (MLSD) receiver for a nonlinear satellite channel, a bank of matched filters followed by a Viterbi detector, serves as a probability of error lower bound for the Volterra and FSE-Volterra equalizers. However, this receiver has not been evaluated for a specific satellite channel. In this work, an MLSD receiver is evaluated for a specific downlink-limited satellite channel. Because of the bank of matched filters, the MLSD receiver may be high in complexity. Consequently, the probability of error performance of a more practical suboptimal MLSD receiver, requiring only a single receive filter, is evaluated.

Gutierrez, Alberto, Jr.↗

NASA NTRS1994

Evaluation of iconic versus F-map microburst displays

Previous studies have shown graphical presentation methods of hazardous wind shear to be superior to textual or audible warnings alone. Positional information and the strength of the hazard were observed to be and were cited by pilots as the most important factors in a display. In this experiment the use of the three different graphical presentations of hazardous wind shear are examined. Airborne predictive detectors of wind shear enable the dissemination of varying levels of information. The effectiveness of iconic and mapping display modes of different complexities are addressed through simulation and analysis. Different positional and time-varying situations are presented in a 'part-task' Boeing 767 simulator using data from actual microburst events. Experienced airline pilots fly approach profiles using both iconic and F-map wind shear alerting displays. Microburst accompanied each event is also shown to the pilot. Mapping display types are expected to be found exceptionally efficient at conveying location comparison information while iconic displays simplify the threat recognition process. Preliminary results from the simulator study are presented. Recommendations concerning the suitability of multilevel iconic and mapping displays are made. Situational problems with current display prototypes are also addressed.

Salzberger, Mark↗

NASA NTRS1995

Displacement based multilevel structural optimization

Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.

Striz, Alfred G.↗